Chapter 20 Quality Control

8/9/2019 Chapter 20 Quality Control

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Chapter 20 Six Sigma

Management


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j Six Sigma (a registered trademark of the Motorola

Corp.) is the relentless and rigorous pursuit of thereduction of variation in all critical processes toachieve continuous and breakthrough improvementsthat impact the bottom line of the organization andincrease customer satisfaction.

j It is an organizational initiative designed to createmanufacturing, service and administrative processesthat produce approximately 3.4 defects per million.Opportunities (DPMO).


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Relationship between the Voice of theCustomer and the Voice of the Process

j Six Sigma management promotes the idea that thedistribution of output for a process (the Voice of theProcess) should take up no more than half of the

tolerance allowed by the specification limits (theVoice of the Customer)

j This assumes that the measurement data is from astable and normal distribution of output whose meancan shift by as much as 1.5 standard deviations over

time.


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j The following figure shows the Voice of the Customeras spoken in the language of a nominal value, m, and

the lower and upper specification limits, LSL andUSL, for a quality characteristic.

j This assumes Distribution of process output is measurement data

The process is stable

The distribution is normal

The process average is on nominal

The distance between nominal and either specification limitis 3 times the process standard deviation

j If these five conditions are met we all the process a3-sigma process.

j A 3-sigma process will produce 2,700 defects permillion opportunities.


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LSL USL3-sigma Process


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An Example of a 3-sigma Process

j The number of days to complete a month accountingreport is stable and normally distributed with anaverage of 7 days and a standard deviation of 1 day.

j The lower specification limit is 4 days and the upper

specification limits is 10 days.


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j Next we see a quality characteristic represented bymeasurement data that: Is stable

Is normally distributed

Has a process output that can shift by as much as 1.5standard deviations on either side of nominal

Has a distance between nominal and either specificationlimit of 3 standard deviations of process output.

j This is a 3-sigma process with a 1.5 sigma shift in themean.

j This process will generate 66,811 defects per million

opportunities or 93.33189% of its output between thespecification limits.


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Accounting process with process average shifts of 1.5

standard deviations.


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j Next we see a scenario where the voice of the

process takes up only half the distance between thespecification limits. The process mean remains thesame, but the process standard deviation has beenreduced to one half-day


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Output for the monthly accounting process with the

standard deviation reduced to one-half day through process

improvement activities.


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j Next we will see the voice of the customer and the

voice of the process for a quality characteristic that: Is represented by measurement data

Is stable

Is normally distributed

Has a process average that can shift by as much as 1.5

standard deviations on either side of nominal Has the distance between nominal and either specification

limit is 6 standard deviations of the process output.

j This is a process that will generate 3.4 defects permillion opportunities, or 99.99966% of its outputwithin specification limits in the near future.


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Six sigma accounting process with a 1.5 sigma shift in

the mean


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The DMAIC Model

j The model that is used to improve a process in SixSigma management is called the DMAIC model. Thisstands for: Define

Measure

Analyze

Improve

Control


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Define Phase

j The define phase involves: Preparing a business charter (rationale for the project)

SIPOC Understanding the relationships between

Suppliers

Inputs

Process

Outputs

Customers

Gathering and analyzing voice of the customer data toidentify the critical-to-quality (CTQ) characteristicsimportant to customers

Developing a project charter (statement of the project)


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Measure Phase

j The measure phase involves Developing operational definitions for each CTQ

characteristic

Performing studies to determine the validity (repeatabilityand reproducibility) of the measurement procedure for each

CTQ

Collecting baseline capabilities for each CTQ

Determining the process capability for each CTQ


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Analyze Phase

j The analyze phase involves Identifying upstream variables (xs) for each CTQ

Operationally defining each x

Collecting baseline data for each x

Performing studies to determine the validity (repeatabilityand reproducibility) of the measurement process for each x

Establishing baseline capabilities for each x

Understanding the effect of each x on each CTQ


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Improve Phase

j The improve phase involves Designing experiments to understand the relationships

between the CTQs and the xs

Determining the optimal levels of critical xs that optimize the

spread, shape and center of the CTQs

Developing action plans to implement the optimal level of thexs into the process under study

Conducting a pilot test of the revised process


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Control Phase

j The control phase involves Avoiding potential problems with the revised settings of the

xs through risk abatement planning and mistake-proofing

Standardizing successful process revisions in training

manuals

Controlling the revised settings of the critical xs

Turning the revised process over to the process owner forcontinuous improvement using the PDSA cycle


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Benefits and Costs of Six SigmaManagement

j A successful six sigma program will yield thefollowing benefits to the management of theorganization Improved process flows

Improved communication through six sigma terminology (forexample, DPMO and process sigma)

Reduced cycle times

Enhanced knowledge and enhanced ability to manage thatknowledge

Higher levels of customer satisfaction

Higher levels of employee satisfaction

Increased Productivity


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Reduced total defects

Decreased work-in-progress (WIP)

Decreased inventory Improved capacity and output

Increased quality and reliability

Decreased unit costs

Increased price flexibility

Decreased time to market

Faster delivery time

Increased liquid capital


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j Resources required by Six Sigma management

Training time costs Material costs

Training manual development costs

Administrative and operating costs for DMAIC projects

Infrastructure costs such as the sots of constructing and

using organizational metric tracking systems Monitoring DMAIC project costs

Anecdotal evidence strongly indicates that he benefitsof a Six Sigma process far outweigh the costs.


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Six Sigma Roles and Responsibilities

j The Senior Executive provides the impetus,direction and alignment necessary for the ultimatesuccess of Six Sigma management.

j Roles and responsibilities of a senior executive Leads the Executive Committee (EC) Participates in high-level policy management and cross-

functional project teams.

Monitors and balances all Six Sigma activities to avoid localoptimization and organizational suboptimization.

Maintains a long-term view of the organization and acts as aliaison to stakeholders

Conducts Presidential reviews of Six Sigma dailymanagement and cross functional management projects.


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j Top management must be totally committed to theprocess.

j The CEO must allocate substantial resources to SixSigma management.

j Leadership must be willing to engage all levels of theorganization through organizational metric tracking

systems and daily management and cross-functionalSix Sigma and DMAIC projects.

j The CEO must have a burning desire to createrevolutionary change in the enterprise.


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j Members of the Executive Committee (EC) mustoperate with the same level of commitment as the

senior executive.j The EC must

Create an organizational metric tracking systemthat cascades, or deploys, key objectives and keyindicators throughout the organization via policymanagement

Empower the Policy Deployment Committee(PDC) to deploy key objective throughout theorganization through policy management.

Manage the organizational Six Sigma projectportfolio toward optimization of the entireorganizations bottom line


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Use catchball to establish a reasonable andequitable project portfolio for each

division/department within the organization.

Improve the Six Sigma process through constantiteration of the PDSA cycle.

Provide the resources necessary for Six Sigma

management.


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j The role and responsibilities of a black belt are: Full time change agent

Master of the change process rather than a master of theprocess under study

Supervise green belts working on a Six Sigma project

Prepare a draft project charter for the Six Sigma projectsunder his/her supervision.

Work closely with a project team to keep it functioning andprogressing toward a conclusion to its Six Sigma project.

Communicate with the individual responsible for the financialand political well-being of the team

Serve as the team leader for Six Sigma projects

Help team members analyze data and design experiments


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Provide training in Six Sigma theory, tools and methods

Help team members prepare for management and

presidential reviews Recommend Six Sigma teams for six Sigma projects

Lead and coach green belts leading simpler Six Sigmaprojects

j A black belt must pass a certification examinationand lead at least two successful Six Sigma projects.


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j Most green belts serve as team members on SixSigma projects.

j If a green belt acts as a team leader for simplerprojects he/she: Prepares a draft charter for the Six Sigma project

Selects the project team members

Communicates with the champion, black belt and processowner concerning the status of the project

Facilitates the project members

Provides training in the basic Six Sigma tools and methods.

j A green belt must pass a certification examination

and participate in at least one successful Six Sigmaproject.


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j A master black belts responsibilities are: To be a proven team leader and technical expert

To be a teacher and mentor of black belts and green belts Simultaneously supervise several black belts and green

belts

To be an ambassador (in conjunction with the seniorexecutive, members of the executive committee, and

champions) of Six Sigma management To work continuously to improve and innovate the Six Sigma

management process.

j A master black belt must complete a certificationexamination and successfully supervise at least twoblack belts in their completion of two successful SixSigma projects each.


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j A champion is a member of the EC, or at least anindividual who is trusted to report directly to a

member of the EC.j A champion takes a very active leadership and

sponsorship role in implementing Six Sigmamanagement, and works closely with the EC, blackbelts and master black belts to:

Translate key objectives and key indicators from his sectionof the organizational metric tracking system into Six Sigmaprojects as a part of policy management

Prepares an initial draft of a project charter for each SixSigma project under his auspices

Assigns green belts and black belts to the Six Sigmaprojects under his auspices

Removes obstacles to the effective functioning of the SixSigma project teams under his auspices


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Provides a direct line of communication between a Six sigmaproject team and the EC

Obtains and manages the resources necessary for a SixSigma project team to meet its project charter

Conducts management review of each Six Sigma projectteam under his auspices focused by providing direction andguidance on the attainment of its project charter

A champion must pass a certification examination.


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j A process owneris the individual who has theultimate authority to change a process.

j The process owner should be identified for everyproject or task that is entered onto an organizationalmetric tracking system.

j The process owner:

Monitors the performance of his/her process through keyindicators

Empowers the people who work in the process

Works with all Six Sigma project teams in the area to enablethem to successfully complete their projects

Manages the process after completion to the Six Sigmaproject to sustain the gains made.


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Continues to improve and/or innovate the process throughthe application of the PDCA cycle.

j A process owner should pass the championcertification examination.


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Six Sigma Terminology

jj UnitUnit A unit is the item (e.g. product or component,service or service step, or time period) to be studiedwith a Six Sigma project.

jj

DefectiveDefective A nonconforming unit is a defective.jj DefectDefect A defect is a nonconformance on one of

many possible quality characteristics of a unit thatcauses customer dissatisfaction.

jj Defect OpportunityDefect Opportunity a defect opportunity is themost fundamental area for a defect. There may beseveral opportunities for defects within a defined unit.


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jj Defects perUnit (DPU)Defects perUnit (DPU) - Defects per unit refers tothe average of all defects for a given number of units,

that is, the total number of defects for n units dividedby n.

jj Defects per Opportunity (DPO)Defects per Opportunity (DPO) Defects peropportunity refers to the number of defects divided by

the number of opportunities.jj Defects per Million Opportunities (DPMO)Defects per Million Opportunities (DPMO) DPMO

equals DPO multiplied by 1,000,000.

jj Observed YieldObserved Yield Observed yield is the proportion of

units within specification divided by the total numberof units.


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jj Rolled Throughput Yield (RTY)Rolled Throughput Yield (RTY) RTY is theproduct of the observed yield s from each step in a

process. It is the probability of a unit passing throughall steps of a process and incurring no defects.

jj Process SigmaProcess Sigma Process sigma is a measure of theprocess performance determined by using DPMO

and a normal distribution table. Process sigma is ametric that allows for process performancecomparisons across processes, departments,divisions, companies, and countries. In Six Sigmaterminology, the sigma value of a process is a metric

used to indicate the number of defects per millionopportunities, or how well the process is performingwith respect to customer needs and wants.


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A Six Sigma Case StudyBackground

j Paper Organizers International (POI) offers a fullrange of filling, organizing, and paper shufflingservices.

j POI purchases Metallic Securing Devices (MSDs),

staplers, hole punchers, folders, three-ring binders,and a full range of related products to serve itscustomers in paper handling needs.

j The employees, or internal customers, of PaperOrganizers use MSDs to organize piles of paperpending placement into folders or binders.


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j The purchasing department has noticed anincrease in complaints from employees in thePaper Shuffling Department (PSD) about MSDsbreaking and failing to keep papers together.

j This creates opportunities for client papers to bemixed together.

j The Purchasing Department would like to improvethe purchasing process for purchasing MSDs toeliminate complaints from employees in the PaperShuffling Department.


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Origin of the MSD Six Sigma Project

Mission Statement:

j

Put theR

ightInformation in the right Place.

j RIP it!


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POIs Business Objectives and Indicators with Potential Six Sigma Projects

President Director of Paper Shuffling Department

BusinessObjectives

BusinessIndicators

Area Objectives Area Indicators Potential SixSigma Projects

Increase thenumber of orders

# orders /month(c-chart)

Increase thenumber of ordersin PSD

# orders inPSD/month(c-chart)

New CustomerPromotionsProject

Increase thenumber of POIservices (filing,organizing, etc)utilized by eachcustomer

1. Average # ofservices utilizedper customer /quarter2. Standarddeviation ofnumber ofservices utilizedpercustomer/quarter(x-bar and s chart)

Increase thenumber ofservices utilizedby each customerin PSD

1. Average # ofservices utilizedper PSDcustomer/quarter2. Standarddeviation ofnumber ofservices utilizedper PSDcustomer/quarter(x-bar and s chart)

Existing CustomerPromotionsProject

Minimizeproduction costs

Productioncosts/month(I and MR chart)

Minimizeproduction costsin PSD

Production costsin PSD/month(I&MR chart)

MSDQualityProject

Eliminateemployeecomplaints

# of employeecomplaints/month(c-chart)

Eliminateemployeecomplaints fromPSD

# of employeecomplaints fromPSD/month(c-chart)

Employee MoraleProject


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Individual and Moving Range Chart of Monthly

Production Costs in the Paper Shuffling Department

Su

group

Individual

alue

Mean=

C

=

C

=

MovingRange

R=

C

=

C

=

I and MR Chart for Production C

Production costs are sta le (no special causes such as pointseyond a control limit or too many runs up and down, etc.) in

the PSD with an average monthly cost of $ , , and astandard deviation of

$116,672.128$111,672/1d/R 2 !!


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Distribution of Monthly Production Costs in the PSD

Production costs are approximately normally distributed.Team members discovered that PSD management considersmonthly production costs to be very high given the volume ofwork being processed by the department.

! "

#

"

Production Costs in PSD

re

uency

istogram of Production Costs in PSD


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Prioritization of Six Sigma Projects

j Top management generated four potential SixSigma Projects.

j The following table is used to estimate theimportance of each potential Six Sigma project on

POIs business objectives.


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Business Objectives

Potential Six Sigma Projects

NewCustomerPromotionsProject

ExistingCustomerPromotionsProject

MSDQualityProject

EmployeeMoraleProject

Increasethe numberof orders

WEIGHT

S

.35 3 3 0 0

Increase

the numberof POIservicesutilized byeachcustomer

.10 1 3 0 0

Minimizeproductioncosts

.40 0 0 9 3

Eliminateemployeecomplaints

.15 0 0 9 9

Weighted Average of Potential SixSigma Projects

1.15 1.35 4.95 2.55


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j The cell values are assigned by top managementand are defined as follows: 0 no relationship, 1

weak relationship, 3 moderate relationship, and9 strong relationship.

j The Finance Department developed theimportance weights for each business objective tomaximize the impact of Six Sigma projects on the

bottom-line of the organization.j Consequently, the most critical project in respect to

the business objectives is the MSD quality project,see 4.95 in the last row of the table.

j The Champion and Process Owner of the MSD

process prepared an initial project charter. Itpresented the business case for the MSD qualityproject to the members of the MSD quality projectteam.


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j The define phase has three components:

prepare a business case with a project charter do a SIPOC analysis

conduct a Voice of the Customer analysis.

Prepare a Business Case with a Project Charter

j Preparing a business case with project charterrequires team members to answer the followingpartially redundant questions. The redundancy in

the questions helps team members distill thecritical elements of the business case.

Define Phase


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1. What is the name of the process?

MSD Purchasing Process. The first step in the supply chain for the MSD processis the process for purchasing MSDs.

Hence, the first operation to be investigated by MSDquality project team members is the process for

purchasing MSDs. Team members may study other factors that affect thequality of MSDs such as method of use or shelf life at alater time.


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2. What is the aim of the process?j The aim of the purchasing process as it relates to this project

is to purchase MSDs that improve the productivity andmorale of the employees in the Paper Shuffling Department(PSD).

3. What is the business case (economic rationale) for theproject?

j Question 3 is answered by addressing the following sub-questions.

3a. Why do the MSD project at all?j According to a judgment sample of 3 employees and 2

managers from the PSD, team members determined thatMSDs that cannot withstand 4 or more bends are

unacceptable because they are unlikely to remain intactthroughout the paper shuffling processes and will not holdpapers tightly; this is called durability.


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j Defective MSDs create costs for POI, for example: papers from different clients may get mixed together if

not properly bound requiring additional processing time employees may have to use multiple MSDs for one

project creating additional material costs

employees get frustrated and do not perform their jobsefficiently and productively increasing labor costs.

j Additionally, team members discovered that alarge proportion of the boxes containing MSDsarrive to the PSD with 5 or more broken MSDs;this is called functionality.


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j This creates additional processing costs for POI,for example

increased unit costs frustrated and non-productive employees and

managers.

j Team members used the same judgment sampleas above and determined that approximately 60%

of individual MSDs do not meet durability criteriaand 60% of MSD boxes do not meet functionalitycriteria. They used the following surveyquestionnaire and the data matrix.


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SurveyName: ____________________________1. Please estimate the percentage of MSDs that cannot withstand 4 or more bends. _____

2. Please estimate the percentage of MSD boxes that contain greater than 5 broken MSDs. _____

Survey Number ResponseQ1 Response Q2

1 55 70

2 50 55

3 60 65

4 65 60

5 70 50

Average 60 60


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3b. Why do the MSD project now?

j The Paper Shuffling Department is experiencingvery high monthly production costs.j Also, internal customers, including managers and

hourly employees, are submitting an increasednumber of complaints as recorded in the

Purchasing Departments complaint log for thefiscal year 2000: 14 in the first quarter 18 in the second quarter 32 in the third quarter

j There are 100 hourly workers in the PaperShuffling Department.


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3c. What business objectives are supported by the MSDproject?

j The MSD project is most strongly related to theminimize production costs and eliminate employeecomplaints business objectives.


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3d. What are the consequences of not doing theproject?

j The consequences of not doing the project aredecreased profit margins due to higher productioncosts and increased employee complaints due tofrustration with materials.

3e. What projects have higher or equal priority?j At this time, the MSD quality project has the

highest priority.


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4. What is the problem statement? What is the pain?

j Low quality MSDs create additional production

costs and employee frustration.

5. What is the goal (desired state) for this project?

j The Champion and Process Owner of the MSDprocess initially determined that a 100-foldimprovement in MSD quality (durability andfunctionality) should be the goal for the Six Sigmaproject.

j They derived the concept of a 100-foldimprovement from Motorolas 1986 statedimprovement rate of 10-fold every 2 years, or a100-fold every 4 years during the kickoff of the SixSigma effort.


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j Since 100-fold improvement means the DPMO woulddecrease from 600,000 to 6,000, and a DPMO of

6210 represents a 4-sigma process, team membersdecided to use 4-sigma as the goal for the MSDproject.


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6. What is the project scope?

j Question 6 is answered by answering the following

sub-questions.6a. What are the process boundaries?

j The starting point for the project is when thePurchasing Department receives purchase ordersfrom the PSD.

j The stopping point for the project is when the PSDplaces MSDs into inventory.

6b. What, if anything, is out-of-bounds?

j The project team cannot change the way

employees handle or use MSDs.


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6c. What resources are available for the project?

j The budget for the MSD project is $30,000.00.

This includes estimated hourly salaries of projectparticipants.

j Team members, Brian Mercurio and JeremyPressman, are the only project participants that willincur additional job responsibilities as result of the

project.j Budget estimates show opportunity cost and

hard costs. The estimated hard costs ($10,500)and total costs ($26,040) are less than the budgetof $30,000.


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NAME POSITION EstimatedSalary /Hour

ExpectedNumber of

Hours

Per Week

ExpectedOpportunityCosts for 21weeks

Expected

HardCosts for21 weeks

(directlaborcosts)

Howard Gitlow Champion $100 2 $4,200

Dana Rasis Process Owner $50 2 $2,100

Bettina Arguelles Black Belt $50 5 $5,250

Brian Mercurio Team Member $25 10 $0 $5,250

Jeremy Pressman Team Member $25 10 $0 $5,250

Lindsey Barton Finance Rep. $45 2 $1,890

Mary Montano ITRep. $50 2 $2,100

TOTAL $15,540 $10,500


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6d. Who can approve expenditures?

j Only the Process Owner, Dana Rasis, can approve

expenditures.

6e. How much can the team spend beyond $30,000.00without seeking additional authority?

j Nothing.

6f. What are the obstacles and constraints of theproject?

j The team must work within a $30,000 budget and

a 21week time constraint.


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6g. What time commitment is expected of teammembers?

j Team members are expected to be present atweekly Friday morning meetings from 8:00 a.m.until 9:00 a.m.

j Team members are also expected to provideprogress of project tasks at each meeting.

Completion of project tasks may require additionalhours of work per week.

6h. What will happen to each team members regularjob while he or she is working on the project?

j If any, overtime hours will be compensated forteam members and support staff. Note: Theestimated rate for overtime labor is 1.5 timesnormal labor. Overtime labor is not included in thebudget.


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6i. Is there a Gantt chart for the project?

j Yes.

Steps Resp. Week

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

16

17

18

19

20

21

Define BA X X X X X X

Mesure BA X X

Analyze BA X X X

Improve BA X X X X X X

Control BA X X X X


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7. What are the benefits of the project?

j The soft benefits of the project include eliminatingcomplaints from the Paper Shuffling Departmentand increasing employee morale.

j The hard (financial) benefits of the project areminimizing labor costs and material costs. The

hard cost benefits are estimated from the following:


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100 employees in the Paper Shuffling Departmentx 40 hours/week/paper shuffling employeex 10% of time devoted to clipping

@ 400 hours/week devoted to clipping in PSDx $25/hour/paper shuffling employee$10,000/week devoted to clippingx 50 weeks/year$500,000/year devoted to clippingx .60 defective clips (judgment sample estimate of durability of thecurrent system)Broken clips are not selected for use on jobs. This

makes 0.6 a conservative estimate of the percentage of defective clips inthe current system. Note: This conservative estimate does not includeproblems arising from defective clips not detected until after they havebeen used and have caused failure on the job.$300,000/year on defective clipping for current system

x .0062 defective clips (durability of the proposed system)Again, broken

clips are not selected for use on jobs.$3100/year on defective clipping for proposed system


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j Hence, the annual savings on labor costs fromimproving MSD purchasing process is $296,900

($300,000 - $3,100).j The PSD incurs a 10% annual employee turn over.

j To capitalize on savings in labor costs, thedepartment will now higher 4 new employees

instead of 10 new employees, for a savings of 6full-time employees ($296,900/$25 11,876 hours;11,876/40 hours per week/50 weeks per year5.938 ~ 6 employees saved).

Note: Alternatively, the PSD may now serve morecustomers with their current employee base.


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Material Costs:

100 employees in the Paper Shuffling Department

x60 projects/week/paper shuffling employee

x50 weeks/year

@ 300,000 projects/year requiring 3,000,000 MSDs (10 clips per project on average)

x.60 defective clips (judgment sample estimate of current system).

7,500,000* clips must be used to complete 300,000 projectsx.01/clip

@ $75,000/year on clips in current system

x.0062 defective clips (proposed system)

3,018,000** clips must be used to complete 300,000 projects

x.01/clip

@ $30,180/year on clips in proposed system


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Material Costs:

Note: * 1/(1-.6) 2.5 clips needed to get a good

clip. So, 3,000,000 x 2.5 7,500,000Note: ** 1/(1-.0062) 1.006 clips needed to get agood clip. So, 3,000,000 x 1.006 3,018,000.

j Hence, the annual savings on material costs fromimproving MSD purchasing process is $44,820($75,000 - $30,180).

j This yields an annual total hard benefit savings of

$341,720.00.


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8. What are the roles and responsibilities of team members?

ProjectName: MSD Purchasing Process

Role Responsibility Stakeholder SupervisorsSignature

Signature Date

Champion Howard Gitlow HG 9/1/2000

Process Owner Dana Rasis DR 9/1/2000

Team Leader Bettina Arguelles BA 9/2/2000

Team Member 1 Bryan Mercurio BM 9/3/2000

Team Member 2 Jeremy Pressmen JP 9/3/2000

FinanceRep Lindsey Barton LB 9/4/2000

ITRep Michelle Montano MM 9/4/2000


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Do a SIPOC Analysisj The second part of the define phase requires that

team members perform a SIPOC analysis.j A SIPOC analysis is a simple tool for identifying

the Suppliers and theirInputs into a Process, thehigh level steps of a process, the Outputs of theprocess, and the Customers segments interestedin the outputs.

Start


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Purchasingreceives order from

Paper ShufflingDepartment

Purchasing agentcalls vendor

Does vendorhave MSDin stock?

Place order withvendor

Receive order fromvendor

Store productreceived into

inventory (newboxes go on bottom

back of shelf)

PSD removesproducts from

inventory

PSD uses Product

Stop

No

Yes


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Team members analyze the Voice of theCustomer data by market segment.

Next, they use all the raw Voice of the Customerdata points to create affinity diagram.

Themes, called focus points using numbers linkingcolumns 2 and 3 in column 3 in the following tableare identified.

Next, team members identify the engineering issueunderlying each focus point, called cognitiveissues.

Then, team members convert each cognitive issueinto one or more quantitative engineeringvariables, called Critical-To-Quality (CTQ)

variables. Finally, team members develop technical

specifications for each CTQ.


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SelectedMarketSegment

Raw Voice of the Customerdata

AffinityDiagramtheme (FocusPoint)

Engineeringissue(Cognitiveissue) CTQ

Tech.Spec.

Paperorganizingmanagers

My employees are frustratedabout the MSDs. They complain

that they break too fast 1&2

Variation indurability (1) Durability Ability towithstandbending

> 4 bendswithoutbreaking

My employees are complainingthat the MSDs are not holdingup during the organizingprocess. 1

Variation incolor(2)

Color Thenumber ofdifferentMSD colors

1 color ofMSDs

The employees arecomplaining that the color of theMSDs change from one day tothe next. It seems to beconfusing them. 2

Variation infunctionality(3)

Functionality Thenumber ofbrokenMSDs in abox

< 5brokenMSDs in abox

My employees are veryunhappy with the purple andblue MSDs. They would preferonly one color of MSDs be usedconsistently 2

My employees say that morethan 5 MSDs per box arrivebroken. 3

Ive heard from numerousemployees that the MSDscoming straight from inventoryare already broken. 3

. . .


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SelectedMarketSegment

Raw Voice of the Customerdata

AffinityDiagramtheme (FocusPoint)

Drivingissue(Cognitiveissue) CTQ

Tech.Spec.

Hourly

employees

"The MSDs are falling apart

before we are ready to file thepapers in to binders. An MSDshould be able to take at least 4bends." 1

Variation in

durability (1)

Durability Ability to

withstandbending

> 4 bends

withoutbreaking

"The MSDs aren't helping us todo our work efficiently." 1 & 2

Variation incolor(2)

Color Thenumber ofdifferentMSD colors

1 color ofMSDs

I would prefer if we only usedone color of MSDs. 2

Variation infunctionality

(3)

Functionality Thenumber of

brokenMSDs in abox

< 5broken

MSDs in abox

I dont understand why we usedifferent colors of MSDs. 2

"The MSDs just break whentrying to bend them over thepaper stacks. They should takeat least 4 bends" 1

It is very frustrating when youopen a brand new box of MSDsand find that more than 5 of theclips are already broken. 3

It is very time consuming to siftout the broken MSDs from abrand new box coming straightfrom inventory. 3

. . .


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Returning to the first part of the define phase, team memberscan now define the projects objectives.

Project Objective 1: Decrease (direction) the percentage ofMSDs that can not withstand 4 or more bends without breaking(measure) bought by the Purchasing Department (process) to00.62% (goal) by January 1, 2003 (deadline). Go for 4-sigma!

Project Objective 2: Decrease (direction) the percentage of

boxes of MSDs with more than 5 broken clips (measure)bought by the Purchasing Department (process) to 00.62%(goal) by January 1, 2003 (deadline). Go for 4-sigma!

A correlation exists between the project objectives. A brokenMSD cannot withstand 4 or more bends because it is already

broken. Improving the percentage of functional MSDs per boxwill increase the percentage of MSDs that can withstand 4 ormore bends.

M Ph


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The measure phase has three steps: operationally define the CTQs perform a gage R&R study on each CTQ develop a baseline for each CTQ.

Operationally define the CTQs

First, team members operationally define durabilityand functionality by: establishing criteria for durability and

functionality developing a test for each set of criteria

formulating a decision rule for each criteria.

Measure Phase


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Test for a selected MSD

1. Select the top-front box of MSDs on the shelf in theinventory room.

2. Close your eyes, then open the box of MSDs, thenhaphazardly select one intact MSD. No switching isallowed.

3. Utilize the criteria for the selected MSD4. Count the number of bends until breaking

Decision for a selected MSD

If the number of bends is u 4, then MSD is conforming.If the number of bends is < 4, then MSD is defective.


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Operational Definition for CTQ2: Functionality

Criteria for a box of MSDs: Count the number ofbroken clips. Aclip is broken if it is in 2 pieces, regardless of the relative sizes ofthe pieces. Clips can be broken only into two pieces.

Testfor a box of MSDs:1. Select the top-front box of MSDs on the shelf in the inventory

room.2. Count the number ofbroken clips.

Decision for a box of MSDsIf the number of MSDs that are broken e 5, then the box of MSDs is

conforming.If the number of MSDs that are broken > 5, then the box of MSDs is

defective.

The same box of MSDs is used for both operational definitions.


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Perform a gage R&R study on each CTQ.

Team members conduct an attribute Gage R&R(Repeatability and Reproducibility) study on themeasurement system of each CTQ to determine if it isadequate for the needs of the project.

The measurement of durability requires a destructivetest, hence, a simple Gage R&R study was not done fordurability at this time.

In the near future, an operational definition of the testing

process for durability will be established and testing willbe audited to assure consistency.


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The measurement system for functionality is studied using thefollowing sampling plan.

1. A shelf in the storage area contains boxes of MSDs purchasedthroughout the week. There are different types of MSD boxes inthe storage area (different vendors, sizes, etc.).

2. The Gage R&R study required 2 inspectors to sample the same10 boxes of MSDs twice.

3. The top 10 boxes on the front of the shelf were selected for the

Gage R&R study.4. The study is repeated as is deemed necessary by PSDmanagement.

Two PSD managers have the responsibility of inspecting theMSDs for functionality; they are called Inspector 1 (Tom) and

Inspector 2 (Jerry). BothT

om and Jerry counted the number ofdefective MSDs, twice, in random order.

Box Inspector Count Functionality Box Inspector Count Functionality


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1 1 1 10

1 1 2 10

1 2 1 10

1 2 2 10

2 1 1 9

2 1 2 9

2 2 1 9

2 2 2 9

3 1 1 5

3 1 2 5

3 2 1 5

3 2 2 5

4 1 1 4

4 1 2 4

4 2 1 4

4 2 2 4

5 1 1 5

5 1 2 5

5 2 1 5

5 2 2 5

6 1 1 9

6 1 2 9

6 2 1 9

6 2 2 9

7 1 1 6

7 1 2 6

7 2 1 6

7 2 2 6

8 1 1 6

8 1 2 6

8 2 1 6

8 2 2 6

9 1 1 9

9 1 2 9

9 2 1 9

9 2 2 9

10 1 1 11

10 1 2 11

10 2 1 11

10 2 2 11

Date of study:

Gage name:

Runchart of Fuctionality by Box Inspector


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Misc:

Tolerance:

Reported by:

11

10

9

8

7

6

5

4

54321Box

Fuctionality

1

2

1110

9

8

7

6

5

4

109876Box

Fuctionality

Runchart of Fuctionality by Box, Inspector

A Gage Run chart shows that there is no variation within inspectors orbetween inspectors. All the variation is between the 10 boxes ofMSDs. Hence, the measurement system is acceptable to measurefunctionality.


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Develop a baseline for each CTQ.

At the beginning of each hour, one box of MSDs isselected from the storage area.

The procedure for selecting a box of MSDs is simply to

select the top-front most box on the shelf.T

he selectionprocess was not altered during a sampling period of two8-hour shifts.

Baseline capability data is as follows.


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Th i ld f d bilit d f ti lit b th 0 375


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The yield for durability and functionality are both 0.375 asdetermined by the number of tests out of 16 trials shown in theprevious table that met their respective CTQs (i.e., at least 4bends for durability, no more than 5 broken MSDs per box forfunctionality).

This indicates very poor levels of durability and functionalityfor the MSDs received into the Paper Shuffling department andsupports the initial yield estimates of 40.0%, or 60% defectiveMSDs.

An individuals and moving range (I-MR) chart for thedurability baseline data indicates that the variability ofdurability is not stable over time, see bottom panel of thefollowing chart.

An investigation of the range between the eight and ninthMSDs did not reveal any obvious special cause of variationthat could be used to improve the durability of MSDs.


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15105Subgroup 0

15

10

5

0

-5IndividualValue

Mean 3.875

UCL 12.21

LCL -4.458

10

5

0M

ovingRange

1

R=3.133

UCL=10.24

LCL=0

I and MR Chart for Durability

Note: Use of the I-MR chart assumes approximate normality of the CTQ (durability). Thedurability data is clearly not normally distributed, see dot plot that follows.


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Hence, use of the durability I-MR chart is not advisedat this time.

However, the distribution of durability mayapproximate a Poisson distribution. Consequently, team members constructed a c-chart

for the count of bends before each MSD breaks,see next slide.

Note: If the durability were measured using a continuousmeasurement system allowing for fractional number of bends beforebreaking, then a log or similar transformation of the distribution may beappropriate before using an Individuals-Moving Range chartingprocedure.


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The c chart indicated a possible special cause during Shift 2 - Hour 1 when 12bends was observed for the durability test. Further investigation and notes relatedto the test did not reveal any obvious differences between the MSD tested and theothers, although during the first hour the tester indicated that he may have bent theMSD slower than usual during the test which may have caused less stress andconsequently more bends.


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A c-chart forfunctionality indicates that is stable overtime.


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The functionality data appears to be approximately Poissondistributed (due to a Goodness of Fit test). Hence, use ofthe functionality c-chart is acceptable at this time.

Finally team members estimate the current process


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Finally, team members estimate the current processperformance for each CTQ in the following table.

Notice the desired 100-fold improvement shown in the DPMO

columns (Current = 625,000 and Desired = 6,210). This isconsistent with the goals stated in question 5 of the Define Phaseof the DMAIC model.

CTQs Yield DPMO Process Sigma

Current Desired Current Desired Current Desired

Durability 37.50% 99.38% 625,000 6210 ~1.2 4.0

Functionality 37.50% 99.38% 625,000 6210 ~1.2 4.0

Analyze Phase


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The Analyze phase has five steps:

1. Develop a more detailed process map (that is, moredetailed than the process map developed in theSIPOC analysis of the Define phase)

2. Construct operational definitions for each input orprocess variable (called Xs)

3. Perform a gage R&R study on each X (test theadequacy of the measurement system)

4. Develop a baseline for each X5. Develop hypotheses between the Xs and Ys. The Ys

are the output measures used to determine if theCTQs are met.

First, team members prepare a detailed process mapidentifying and linking the Xs and Ys.

Analyze Phase

Start


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Purchasingreceives order from

Paper ShufflingDepartment

Purchasing agentcalls vendor

Does vendorhave MSDin stock?

Place order with

vendor

Receive order fromvendor

MSDs placed intoinventory (new boxes

go on the bottomback of shelf)

PSD removesbox frominventory

PSD uses MSDs

Stop

No

Yes

X1 Vendor (Ibix or Office Optimum)X2 Size (Small or Large)X3 Ridges (With or Without)X4 = Cycle time from order to receipt for MSDsX5 = Discrepancy in count from order placed andorder received

X6 = Cycle time to place product in inventory

X7 = Inventory shelf time (in days)

X8 =Type of usage (Large stack of paper or Smallstack of paper)

D l ti l d fi iti f h X


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Develop an operational definition for each X.

Team members develop an operational definition for each X

variable identified on the process map. The operationaldefinitions for X1, X2, X3 and X8 relate to individual MSDs andare shown below.

Criteria: Each X conforms to either one or the other of the options.

Test: Select MSD.Decision: Determine X1, X2, X3, and X8 options for the selectedMSD.

X1 Vendor Ibix Office Optimum

X2 Size Small (stock size) Large (stock size)

X3 Ridges With ridges Without ridges

X8 Type of Usage Large stack of paper (# papers is 10 or more)

Small stack ofpaper(# papers is 9 or

less)


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The operational definitions for the procedures used tomeasure X4, X5, X6 and X7 are:

Criteria: Compute cycle time in days by subtracting theorder date from the date on the bill of lading.

Test: Select a box of MSDs upon receipt of shipment

from vendor. Compute the cycle time.Decision: Determine X4 for the selected box of MSDs.

X4 Cycle time from order toreceipt for MSDs

In days


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Criteria: Count the number of boxes of MSD received fora given order. Subtract the number of boxes ordered

from the number of boxes received for the order understudy.

Test: Select a particular purchase order for MSDs.

Decision: Compute the value of X5 in number of boxesfor the selected purchase order.

X5 Discrepancy in count fromorder placed and orderreceived

In boxes of MSDs by order

Criteria: Compute cycle time in days to place a shipment of MSDs in


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Criteria: Compute cycle time in days to place a shipment of MSDs ininventory by subtracting the date the shipment was received from thedate the order was place in inventory.

Test: Select a particular purchase order.

Decision: Compute the value of X6 in days for the selected purchaseorder.

Criteria: Compute inventory shelf-time in days for a box of MSDs bysubtracting the date the box was placed in inventory from the datethe box was removed from inventory.

Test: Select a box of MSDs.

Decision: Compute the value of X7 in days for the selected box ofMSDs.

X6 Cycle time to place product in inventory In days

X7 Inventory shelf time In days


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Conduct Gage R&R studies on Xs.

Recall, that the purpose of a Gage R&R study is todetermine the adequacy of the measurement system foran X.

In this case, the measurement systems for all of the Xsare known to be reliable and reproducible, hence, GageR&R studies were not conducted by team members.

Collect baseline data for each X


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Collect baseline data for each X.

Team members gathered baseline data on durability(Y1) and functionality (Y2), and relevant Xs using thefollowing sampling plan:

For a two-week period the first box of MSDs broughtto the PSD each hour was selected as a sample; thisyielded a sample of 80 boxes of MSDs

For each sampled box, team members determined thedurability (Y1) and functionality (Y2) measurement.Furthermore, they collected information concerning

the vendor (X1), size of the MSD (X2), whether or notthe MSD has ridges (X3), and inventory shelf life willbe recorded (X7).


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Note that Purchasing Department will separately studycycle time from order to receipt of order (X4), discrepancy

between ordered and received box counts (X5), and cycletime from receipt of order to placement in inventory (X6). These last factors may influence such concerns aschoice of vendor, ordering procedures, and inventorycontrol, but they do not impact durability and functionality.

Furthermore, the MSDs are not tested after they areused so the type of usage (X8) is not studied here.As was indicated in the Define phase, certain variables(e.g., X4, X5, X6, and X8) can be addressed in subsequentGreen Belt projects.

The following show the baseline data for the Xs.

Sample Day Hour X1 X

2 X3 X7 Durability Function


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Sample Day Hour X1 X2 X3 X7 Durability Function1 Mon 1 1 0 0 7 2 52 Mon 2 0 1 0 7 2 93 Mon 3 0 0 1 7 10 74 Mon 4 0 1 0 7 1 4

5 Mon 5 0 0 0 7 7 36 Mon 6 0 1 1 7 2 57 Mon 7 0 1 1 7 1 98 Mon 8 0 0 0 7 7 59 Tue 1 0 1 0 8 2 810 Tue 2 0 1 0 8 1 711 Tue 3 0 1 0 8 1 1312 Tue 4 1 1 1 8 9 513 Tue 5 1 1 0 8 9 9

14T

ue 6 1 1 1 8 10 1115 Tue 7 1 1 1 8 10 1116 Tue 8 0 0 1 8 8 917 Wed 1 1 1 1 9 8 1118 Wed 2 1 0 0 9 1 1119 Wed 3 1 1 1 9 10 1120 Wed 4 0 0 0 9 7 1121 Wed 5 1 1 1 9 9 922 Wed 6 0 0 1 9 9 523 Wed 7 1 0 1 9 2 1124 Wed 8 1 0 0 9 1 1025 Thu 1 1 0 1 10 1 1426 Thu 2 0 1 1 10 1 1027 Thu 3 1 1 1 10 8 1328 Thu 4 0 0 1 10 10 1229 Thu 5 0 0 0 10 7 1430 Thu 6 0 1 1 10 3 13


2 X3 X7 Durability Function31 Thu 7 0 0 0 10 9 13


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31 Thu 7 0 0 0 10 9 1332 Thu 8 1 1 1 10 8 1133 Fri 1 0 1 0 1 2 034 Fri 2 0 1 0 1 2 135 Fri 3 0 1 0 1 1 6

36 Fri 4 0 1 0 1 3 337 Fri 5 0 1 0 1 2 238 Fri 6 1 1 0 1 10 639 Fri 7 0 0 1 1 10 040 Fri 8 0 1 0 1 2 041 Mon 1 0 1 1 4 3 442 Mon 2 0 1 0 4 3 743 Mon 3 0 1 1 4 3 344 Mon 4 0 0 0 4 10 2

45 Mon 5 1 1 0 4 8 546 Mon 6 0 1 1 4 3 447 Mon 7 1 0 0 4 1 448 Mon 8 0 0 1 4 10 549 Tue 1 1 1 1 5 11 650 Tue 2 1 0 1 5 3 451 Tue 3 1 1 0 5 10 652 Tue 4 1 0 1 5 3 553 Tue 5 1 0 0 5 2 454 Tue 6 0 0 0 5 9 555 Tue 7 0 0 1 5 9 556 Tue 8 0 1 0 5 3 757 Wed 1 0 0 1 6 9 558 Wed 2 1 1 0 6 9 759 Wed 3 0 0 0 6 9 560 Wed 4 1 0 0 6 2 6


2 X3 X7 Durability Function


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p y 1 2 3 7 y61 Wed 5 1 0 1 6 2 562 Wed 6 1 1 1 6 10 563 Wed 7 0 1 0 6 1 764 Wed 8 0 1 0 6 2 5

65 Thu 1 0 0 1 7 10 766 Thu 2 1 1 0 7 9 567 Thu 3 1 0 0 7 1 768 Thu 4 0 1 0 7 2 569 Thu 5 1 0 1 7 1 670 Thu 6 0 1 0 7 1 571 Thu 7 1 0 0 7 1 872 Thu 8 1 1 1 7 10 573 Fri 1 0 1 1 8 3 7

74 Fri 2 1 1 1 8 9 775 Fri 3 1 0 0 8 1 1376 Fri 4 0 1 1 8 2 877 Fri 5 0 1 1 8 3 978 Fri 6 1 1 1 8 8 1079 Fri 7 1 0 1 8 3 1180 Fri 8 0 0 1 8 10 11

Legend:X1 = Vendor (0 = Office Optimum and 1 = Ibix)X2 = Size (0 = Small and 1 = Large)X3 =Ridges (0 = Without and 1 = With)X7 = Inventory shelf time, in days

Collect Baseline Data for Each X


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Collect Baseline Data for Each X.

The baseline data revealed that the yield for durabilityis 0.4625 (37/80) and the yield for functionality is0.425 (34/80), see the next table.

As before, this indicates very poor levels for the CTQsin the Paper Shuffling Department.

For comparison purposes the judgment samplecarried out by the team during the Define phaseshowed that the yield was approximately 40% (i.e., theteam assumed the failure rate was approximately

60%) for both durability and functionality.

Th li ht i d i ld i thi t d b d t


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The slight increased yields in this study can be due tonatural variation in the process.

The baseline data also showed that 56.25% of allMSDs are from Office Optimum (X1), 42.50% ofMSDs are small (X2), 50.00% of all MSDs are withoutridges (X3), and the average shelf time for boxes of

MSDs (X7) is 6.5 days, with a standard deviation of2.5 days, see the next table.


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Basic statistics on baseline data

Variable Proportion Mean Standarddeviation

Y1: Durability 4or morebends/clip

0.4625 5.213 3.703

Y2: Functionality 5 or fewer broken/box

0.4250 7.025 3.438

X1: Vendor 0=OfficeOptimum1=Ibix

0.56250.4375

X2: Size 0=Small1=Large

0.42500.5750

X3: Ridges 0=Without

Ridges1=WithRidges

0.5000

0.5000

X7: Inventory ShelfTime

Shelf time indays

6.5000 2.5160

Develop hypothesis between Xs and Ys.


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Team members develop hypotheses [Y=f(X)] about the

relationships between the Xs and the Ys to identify the Xsthat are critical to improving the center, spread and shapeof the Ys in respect to customer specifications.

This is accomplished through data mining. Data mining isa method used to analyze passive data; that is, data that is

collected as a consequence of running a process. In this case, the baseline data is the passive data set thatwill be subject to data mining procedures.

Dot plots or box plots of durability (Y1) and functionality (Y2)stratified by X1, X2, X3 and X7 can be used to generatesome hypotheses about main effects (i.e., the individual

effects of each X on Y1 and Y2).


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Interaction plots can be used to generate hypotheses aboutinteraction effects (i.e., those effects on Y1 orY2 for which

the influence of one X variable depend on the level or valueof another X variable) if all combinations of levels of Xvariables are studied.

If all combinations of levels of X variables are not studied,then often interaction effects are not discovered.Frequently, screening designs are utilized to uncoverinteraction effects.

Team members constructed dot plots from the baselinedata to check if any of the Xs (i.e., main effects) impactdurability (Y1) and functionality (Y2).

The dot plots for durability an functionality are:


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Dot plot for durability by X1 (i.e., vendor)


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Dot plot for durability by X2 (i.e., size)


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Dot plot for durability by X3 (i.e., ridges)


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Dot plot for durability by X7 (i.e., shelf life)


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Dot plot for functionality by X1 (i.e., vendor)


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Dot plot for functionality by X2 (i.e., size)


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Dot plot for functionality by X3 (i.e., ridges)


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Dot plot for functionality by X7 (i.e., shelf life)


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The dot plots for durability (Y1) indicate:

1.T

he values of durability tend to be low or high with a significantgap between 4 and 6 for X1, X2, X3 and X7, and2. The variation in durability is about the same for all levels of X1,

X2, X3 and X7.

The dot plots for functionality (Y2) indicate:

1. The values of functionality tend to be lower when X1 = 0 thanwhen X1 = 1

2. The variation in functionality is about the same for all levels of X2and X3

3. The values of functionality tend to be lower for low values of X7.

Discussion of the Analysis ofDurability.


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Since there are no clear differences in variation (i.e.,

spread) of durability for each of the levels of X1, X2, X3and X7, the team wondered if there might bedifferences in the average (i.e., center) for each levelof the individual Xs.

Team members constructed a main effects plot fordurability to study differences in averages, seefollowing figure.


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Main effects plot for durability by X1, X2, X3, and X7.



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p yp

The main effects plot for durability indicates that:

For the range of shelf lives observed there is no clearpattern for the relationship of shelf life (X7) to theaverage Durability.

On the other hand, it appears that ridges (i.e., X3 = 1)

has a positive relationship to the average Durability. At first glance it would seem that the better results for

the average Durability are seen when the vendor Ibixis chosen using small MSDs (i.e., X1 = 1 and X2 = 0),while using large MSDs from Office Optimum

(i.e., X1 = 0 and X2 = 1) yield worse results.


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While discussing the dot plots and main effects plot itwas suggested that it is dangerous to make any

conclusions without knowing if there are interactioneffects.

An interaction effect is present when the amount ofchange introduced by changing one of the Xs

depends on the value of another X.

In that case, it is misleading to choose the best valueof the Xs individually without first considering theinteractions between the Xs.

Consequently, team members did an interactions plot


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Consequently, team members did an interactions plotfor X1, X2, and X3.

X7 was not included in the interactions plot becausethe main effects plot indicated no clear pattern orrelationship with durability (Y1).

All combinations of levels of the X variables must be

present to draw an interactions plot.

This is often not the case with passive data (i.e., noplan was put in place to insure all combinations wereobserved in the data gathering phase).

Fortunately, although not all combinations wereobserved equally often they were all present.

Interaction effects plot for durability by X1, X2, and X3


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Interestingly, the interaction plot indicates that there isa possible interaction between X1 (i.e., vendor) and

X2 (i.e., size).

How is this known?

When there is no interaction the lines should be

parallel to each other indicating the amount of changein average Durability when moving from one level ofeach X variable to another level should be the samefor all values of another X variable.

This plot shows the lines on the graph of X and X


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This plot shows the lines on the graph of X1 and X2not only are not parallel, but they cross.

The average Durability is the highest when eitherlarge Ibix MSDs (i.e., X1 = 1 and X2 = 1) or smallOffice Optimum MSDs (i.e., X1 = 0 and X2 = 0) areused.

This means the choice of vendor may depend on thesize of MSD required.

The main effects plot suggests that the best results


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for average Durability would occur when small MSDsfrom Ibix are used, but the interactions plot suggests

this combination would yield a bad average Durability.

In order to study all this further the team decides thatduring the Improve phase they will run a full factorialdesign to examine the relationship of X1, X2, and X3

on Durability (Y1) since the main effects plot indicatespotential patterns.

Again, there does not appear to be a relationshipbetween Durability (Y1) and X7.

Discussion of the Analysis of Functionality


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Discussion of the Analysis ofFunctionality

Main effects plot for functionality by X1, X2, X3, and X7.

Interaction effects plot for functionality by X1, X2, and X3


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The main effects plot indicates that higher values ofh lf lif (X ) i ld hi h l f F ti lit (Y )


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shelf life (X7) yield higher values for Functionality (Y2).

The team surmised that the longer a box of MSDs sitsin inventory (i.e., higher values of shelf life), thehigher the count of broken MSDs (i.e., functionalitywill be high).

From a practical standpoint, the team felt comfortablewith this conclusion.

They decided the Purchasing Department should puta Six Sigma project in place to investigate whether

the potential benefit of either a just in time MSDordering process or establishing better inventoryhandling procedures will solve the problem.

The interaction effects plot indicate a potentialinteraction between the X (i e size) and X (i e


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interaction between the X2 (i.e., size) and X3 (i.e.,ridges).

The better results for functionality (i.e., low values)were observed for large MSDs without ridges(i.e., X2 = 1 and X3 = 0). Why this may be the casewould need to be studied further.

Also, there may be an interaction between X1 (i.e.,vendor) and X2 (i.e., size), but it appears that betterresults are observed whenever Office Optimum isused (i.e., X1 = 0).

In other words, the average count of broken MSDs islower (i.e., functionality average is lower) wheneverOffice Optimum is the vendor.

Analyze Phase Summary.


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The Analyze Phase resulted in the following hypotheses:

Hypothesis 1: Durability =f(X1=Vendor, X2=Size,X3=Ridges) with a strong interaction effect betweenX1 and X2.

Hypothesis 2: Functionality =f (X1=Vendor, X2=Size,

X3 =Ridges, X7=Shelf Life) with the primary driverbeing X7 with some main effect due to X1 and aninteraction effect between X2 and X3.

X7 is the main driver of the distribution of Functionality(Y2) and is under the control of the employees of POI.

Hence, team members restructured Hypothesis 2 asfollows:

Functionality =f(X1=Vendor, X2=Size, X3=Ridges) foreach fixed level of X7 (Shelf Life).

Improve Phase


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The improve phase involves:

Designing experiments to understand the relationshipbetween the Ys and the vital few Xs and major noisevariables

Generating the actions needed to implement thelevels of the vital few Xs that optimize the shape,spread and center of the distributions of the Ys

Developing action plans

Conducting pilot test of the action plans.

Conduct Experiments.


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First, team members conducted an experimental

design to determine the effect of X1 (Vendor), X2(Size), and X3 (Ridges), and their interactions, on theYs with X7 = 0 (no shelf life MSDs are testedimmediately upon arrival to POI before they areplaced in inventory).

A 23 full factorial design with 2 replications (8 trials)was performed for durability and functionality.

The factor conditions for Vendor (X1) are Office


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1

Optimum (-1) or Ibix (1); the factor conditions for Size

areSmall (-1) or

Large (1), and the factorsconditions forRidges (X3) are Without Ridges (-1)

orWith Ridges (1).

The experiment was setup in two blocks to increase

experimental reliability, with the first 8 runs conductedin the morning and the second 8 runs conducted inthe afternoon.

The runs were randomized within each block


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The runs were randomized within each block.

The purpose of the blocks and randomization is tohelp prevent lurking (background) variables that arerelated to time (e.g., time of day and order in whichdata is collected) from confusing the results.

Additional information can be gathered since 16 trials

were run, rather than the minimum of 8 trials,especially regarding potential interactions.

The data from the 23 full factorial design, with 2replications in run order with the first 8 runsconstituting the first replicate, is:

Std Order Run Order Vendor Size Ridges Durability Functionality

2 1 Ibix Small Without 1 8

4 2 Ibix Large Without 9 9


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3 3 Office Optimum Large Without 1 8

8 4 Ibix Large With 11 8

5 5 Office Optimum Small With 10 06 6 Ibix Small With 4 2

7 7 Office Optimum Large With 4 3

1 8 Office Optimum Small Without 10 2

16 9 Ibix Large With 9 3

10 10 Ibix Small Without 3 0


14 12 Ibix Small With 3 7

13 13 Office Optimum Small With 9 6

11 14 Office Optimum Large Without 2 4

9 15 Office Optimum Small Without 8 1

15 16 Office Optimum Large With 2 4

Pareto Chart of Effects for Durability


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The major effects (i.e., those that have significance level less than.10, in other words over 90% confidence level) for Durability are theinteraction of Vendor and Size and the main effect due to Ridges.

Pareto Chart of Effects for Functionality


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j There are no significant effects due to Vendor, Size,Rid t f F ti lit


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orRidges present for Functionality.j This indicates that since the effect of Shelf Life was

held constant in this designed experiment, while itwas shown to affect Functionality in the data mininganalysis, the team can restrict its attention toimproving Functionality by addressing Shelf Life first.

j As Durability is the only outcome influenced by

Vendor, Size, orRidges in this designed experiment,further consideration in this study will be restricted toDurability.

j Another project can address Shelf Life and its effecton Functionality.

Since interaction effects should be interpreted prior tostudying main effects the team decided to construct


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studying main effects the team decided to constructan interaction effect plot for Vendor and Size.

The interaction effect plot between Size and Vendor


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The interaction effect plot between Size and Vendorindicates that the best results for Durability are

obtained using small MSDs supplied by OfficeOptimum or large MSDs supplied by Ibix.

The reasons for this interaction may be due to factorssuch as materials used for each size MSD,

differences in supplier processes for each size MSD,or other supplier-dependent reasons.

Team members can ask each vendor why their sizesshow significant differences in average durability if


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show significant differences in average durability, ifthere is a preference to use only one vendor.

Otherwise, the Purchasing Department should buysmall MSDs from Office Optimum or large MSDsfrom Ibix to optimize Durability (Y1).

The only significant main effect not involved within asignificant interaction effect is X3 =Ridges.

The main effect forRidges on Durability is shownnext.


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The main effect ofRidges indicates that the averageDurability is about 6 5 5 4 = 1 1 more when an MSD


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Durability is about 6.5 5.4 1.1 more when an MSDwith Ridges is used rather than an MSD without

Ridges.

Therefore, since Ridges is a main effect independentof any interaction effects, then the right selection ofMSDs is to use Office Optimum for small MSDs with

ridges and Ibix for large MSDs with ridges.

If the experimental results are used, then the averageDurability for Office Optimums small MSDs withridges is (10 + 9) / 2 = 9.5 while the average

Durability for Ibixs large MSDs with ridges is (11 + 9)/ 2 = 10.0.

Both averages are well above the requireddi CTQ f t l t 4


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corresponding CTQ of at least 4.

As long as the variation (spread) of results is smallenough so that no individual Durability result is farfrom these averages, then the team is successfulwith respect to Durability.

The variation in these results can be monitored usingcontrol charts after changing the purchasing processfor selecting MSDs.

The team members decided to purchase all MSDs


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The team members decided to purchase all MSDsWith Ridges.

In addition, the choice of Vendor and Size will be asfollows: (Vendor= Office Optimum) and (Size =Small) or (Vendor= Ibix) and (Size = Large) tomaximize average durability.

In addition, the team decided to take on anotherproject to reduce Shelf Life to less than 5 days toaddress Functionality.

The revised flowchart for the Purchasing Departmentincorporating the findings of the Six Sigma project isshown next.

Start

Purchasing Department receives an orderfrom the Paper Shuffling Department


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Purchasing agent calls Ibix to place an order A

Are large MSDswith ridgesavailable

Yes

No

Place an order for MSDs with IbixPurchasing agent calls Office Optimum

Are small MSDswith ridgesavailable

YesPlace an order forMSDs with Office

Optimum

Receive order from vendor

No

Wait one day and call again

A

Store product received into inventory

PSD removes MSDs from inventory

PSD uses MSDs

Stop

Pilot Test.


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The team members conducted a pilot test of therevised best practice (flowchart). Data for durabilityfrom the pilot test is:

HourVendor Size Ridges Durability

Shift 1 Hour 1 Office Optimum

Ibix

Small

Large

With

With

10

11Shift 1 Hour 2 Office Optimum

IbixSmallLarge

WithWith

711

Shift 1 Hour 3 Office OptimumIbix

SmallLarge

WithWith

1011


SmallLarge

WithWith

811

Shift 1 Hour 5 Office Optimum

Ibix

Small

Large

With

With

9

10


SmallLarge

WithWith

99


SmallLarge

WithWith

811


SmallLarge

WithWith

910

Shift 2 Hour 1

Office Optimum Small With 9


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Office OptimumIbix

SmallLarge

WithWith

911

Shift 2 Hour 2

Office OptimumIbix

SmallLarge

WithWith

810

Shift 2 Hour 3

Office OptimumIbix

SmallLarge

WithWith

109

Shift 2 Hour 4

Office OptimumIbix

SmallLarge

WithWith

79

Shift 2 Hour 5

Office OptimumIbix

SmallLarge

WithWith

710

Shift 2 Hour 6

Office OptimumIbix

SmallLarge

WithWith

911

Shift 2 Hour 7

Office OptimumIbix

SmallLarge

WithWith

109

Shift 2 Hour 8

Office OptimumIbix

SmallLarge

WithWith

811

RTY 32/32=1

The RTY for durability is 100%.

Functionality was also tested but not shown here


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Functionality was also tested, but not shown here,using Shelf Life = 0 days; that is, the MSDs weretested immediately upon arrival to POI before theywere placed in inventory.

It resulted in a RTY of 75% that is better than thebaseline RTY.

The effect on Functionality of Shelf Life and inventorycontrol procedures will be investigated in subsequentprojects if management decides these projects shouldbe chartered.

With all things being equal, large MSDs from Ibixshould have a higher average durability then smallMSDs from Office Optimum.


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Control Chart for Durability for small MSDs from OfficeOptimum


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Control Chart for Durability for Large MSDs from Ibix

I an MR Chart for Large MSDs f


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Subgrou

In

iiual

alue

Mean=

CL=

LCL=

Mo

ingRange

R=

CL=

LCL=

I an MR Chart for Large MSDs f

Durability (Y1) is in control, but it is dangerous tocompute any process capability statistics due to the

ll l i


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small sample sizes.

However, estimates for the mean and standarddeviation of Small MSDs from Office Optimum are8.625 and 1.05 (calculated from the data but thecalculation is not shown here), respectively.

The mean and standard deviation for Large MSDsfrom Ibix are 10.25 and 0.83, respectively.

Since the CTQ for durability requires the number ofbends to be 4 or more, then this requirement is 4.4


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qstandard deviations below the mean for Small MSDs

from Office Optimum and 7.5 standard deviationsbelow the mean for Large MSDs from Ibix.

Team members all agreed that as long as theprocess for both Small MSDs from Office Optimumwith ridges and Large MSDs from Ibix with ridgesremain in control, then it is extremely unlikely that theMSDs will fail the CTQ for Durability (Y1).


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Mistake Proof the Revised Process.

Team members identified and prioritized two


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Team members identified and prioritized twoproblems while mistake proofing the processimprovements discovered in the improve phase; theywere:

1. Purchasing agents do not specify with ridges on apurchase order

2. Purchasing agents do not consider that the choice ofvendor depends on the size of the MSDs beingrequested on the purchase order.

Team members created solutions that makeboth errors impossible; they are:


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both errors impossible; they are:

The purchase-order entry system does not processorder unless with ridges is specified on thepurchase order

The purchase-order entry system does not processan order unless Office Optimum is the selectedvendor for small MSDs and Ibix is the selected

vendor for large MSDs.

Develop a Risk Management Plan.

Team members use risk management to identify two


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Team members use risk management to identify tworisk elements, they are:

1. Failing to train new purchasing agents in the revisedpurchasing process

2. Office Optimum and Ibix are out of MSDs with ridges.

Team members assigned risk ratings to both riskelements.

Risk Elements Risk CategoryLikelihood ofoccurrence

Impact ofoccurrence

Riskelementscore

Failing to train new

purchasing agents Performance 5 5 25 High

Vendor out of MSDswith ridges Materials 2 5 10 Medium

Scale: 1-5 with 5 being the highest.

Both risk elements must be dealt with in riskabatement plans.


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The risk abatement plan forfailing to train newpurchasing agents is to document the revisedpurchasing process in training manuals.

The risk abatement plan forVendor out of MSDs with

ridges is for POI to request that both Office Optimumand Ibix manufacture only MSDs with ridges due totheir superior durability.

This is a reasonable and acceptable suggestion toPOI, Office Optimum and Ibix because the coststructures for manufacturing MSDs with and withoutridges are equal, and neither Office Optimum nor Ibixhas other customers requesting MSDs without ridges.

Office Optimum and Ibix agree to produce only MSDsith id ft i th t i l i d i hi h th


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with ridges after a six-month trial period in which they

check incoming purchase orders for requests forMSDs without ridges.

If the trial period reveals no requests for MSDswithout ridges, then the POI Purchasing Department

will revise the process and the appropriate ISO 9000documentation to reflect the possibility of purchasingonly MSDs with ridges.

Additionally, Office Optimum and Ibix thanked POI for

pointing out to them that average durability is higherfor MSDs with ridges than MSDs without ridges.

Both vendors claim that they are going to experimentwith possible different ridge patterns to increased bili d d


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durability and decrease costs.

Both vendors stated that they anticipate decreasecosts from only producing MSDs with ridges becauseof the lower amortized costs of having only oneproduction line.

Prepare ISO Documentation.


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Team members prepare ISO 9000 documentation for

the revisions to the training manual for the purchasingprocess.

Develop a Control Plan.

Thi i thl li f th b f


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This requires a monthly sampling of the boxes of

MSDs in inventory. The purpose of the sampling plan is to check if the

boxes of MSDs being purchased are either smallOffice Optimum MSDs with ridges or large Ibix MSDswith ridges.

The percentage non-conforming boxes of MSDs willbe plotted on a p-chart. PSD management will usethe p-chart to highlight violations of the new andimproved purchasing process.

The p-chart will be the basis for continuously turningthe PDSA cycle for the purchasing process.

Control Plan.


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Finally, team members checked the business

indicator from the PSD metric tracking system anddetermined that production costs in the PSDdecreased, probably due to the MSD Six Sigmaproject.

The MSD project took effect in month 73 as per thenext control chart.


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Turn over the Process to the Process Owner


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It is time for the Champion and Black Belt to disbandthe project team, turn the improved process over tothe Purchasing Department, and celebrate theprojects success with team members.

Documents

Chapter 20 Quality Control