OPSM 501: Operations Management

Week 7:

Quality

Koç University Graduate School of BusinessMBA Program

Zeynep Aksinzaksin@ku.edu.tr

The Ottoman Catapult

Lord of the Rings: Mordor Catapult

Lord of the Rings: Gondor Catapult

Angry Birds Catapult

The OPSM Catapult!

Process Capability Cp = (design tolerance width)/(process width) = (max-spec – min-spec)/ /6

x

Example:

– Plane is “on time” if it arrives between T – 15min and T + 15min.

– Design tolerance width is therefore 30 minutes

x of arrival time is 12 min

– Cp = 30/6*12 = 30/72 = 0.42

A “capable” process can still miss target if there is a shift in the mean.

Motorola “Six Sigma” is defined as Cp = 2.0

– I.e., design tolerance width is +/- 6x or 12

x

3 3

process width

min acceptable

max acceptable

Design tolerance width

There are multiple solutions to most parametric design problemsAnalytical Expression for Brownie Mix “Chewiness”

Chewiness = FactorA + FactorB

Where FactorA = 600(1-exp(-7T/600)) + T/10

And FactorB = 10*TimeFactorA

Temperature

FactorB

Time200F 400F 20 min26 min

Option 1

Option 2

HYPOTHETICAL

Options 1 and 2 deliver the same value of “chewiness.” Why might you prefer one option over the other?

Taguchi Methods

1. Any deviation from the target value is “quality lost.”

Minimum acceptable value

Maximum acceptable value

Target value

Quality

Good

Bad

Performance Metric

Target value

QualityLoss

Performance Metric, x

Loss = C(x-T)2

Who is the Better Target Shooter?

• The mean is important, but the variance is very important as well.

• Need to look at the distribution.

• What are the sources of variability?

• How can obvious sources be eliminated?

Take Aways Products and processes are causal systems

– Typically have lots of variables

• Internal variables are set by the manufacturer/provider

– Target settings and associated variance

• External variables are set by the environment or the user

– Target settings and associated variance (variance often much harder to control than with internal variables)

Impossible to eliminate all variability

– GOAL: find target settings for variables such that variability in other values of these variables has minimal effect on output/performance….a “robust design.”

Methodology for achieving robust design

– Causal model, even if not explicitly analytical

– Early exploratory experimentation

– Control of variability and increased robustness through design changes

– Focused experimentation to refine settings

Statistical Quality Control Objectives

1.Reduce normal variation (process capability)– If normal variation is as small as desired, Process is

capable– We use capability index to check for this

2.Detect and eliminate assignable variation (statistical process control)– If there is no assignable variation, Process is in

control– We use Process Control charts to maintain this

Natural Variations

Also called common causes

Affect virtually all production processes

Expected amount of variation, inherent due to:- the nature of the system - the way the system is managed - the way the process is organised and operated

can only be removed by- making modifications to the process - changing the process

Output measures follow a probability distribution

For any distribution there is a measure of central tendency and dispersion

Assignable Variations

Also called special causes of variation

Exceptions to the system

Generally this is some change in the process

Variations that can be traced to a specific reason

considered abnormalities

often specific to a

certain operator

certain machine

certain batch of material, etc.

The objective is to discover when assignable causes are present

Eliminate the bad causes

Incorporate the good causes

Natural and Assignable Variation

1. Process Capability

Design requirements:Diameter: 1.25 inch ±0.005 inch

Specification Limits

Lower specification Limit:LSL=1.25-0.005=1.245Upper Specification Limit:USL=1.25+0.005=1.255

Example:Producing bearings for a rotating shaft

Relating Specs to Process LimitsProcess performance (Diameter of the products produced=D):Average 1.25 inchStd. Dev: 0.002 inch

Frequency

Frequency

DiameterDiameter1.25

Question:What is the probability That a bearing does not meet specifications?(i.e. diameter is outside (1.245,1.255) )

006.0)5.2(1)5.2()002.0

25.1255.1()255.1(

006.0)5.2()5.2()002.0

25.1245.1()245.1(

NORMSDISTzPzPDP

NORMSDISTzPzPDP

P(defect)=0.006+0.006=0.012 or 1.2% This is not good enough!!

Process capability

What can we do to improve capability of our process? What should be to have Six-Sigma quality?

We want to have: (1.245-1.25)/ = 6 =0.00083 inch We need to reduce variability of the process. We cannot change specifications

easily, since they are given by customers or design requirements.

•If P(defect)>0.0027 then the process is not capable of producing according to specifications.

•To have this quality level (3 sigma quality), we need to have:•Lower Spec: mean-3 •Upper Spec:mean+3

If we want to have P(defect)0, we aim for 6 sigma quality, then, we need: Lower Spec: mean-6 Upper Spec:mean+6

Six Sigma Quality

Process Capability Index Cpk

Shows how well the parts being produced fit into the range specified by the design specifications

Want Cpk larger than one

3

X-USLor

3

LSLXmin=Cpk

183.0)002.03

25.1255.1,

002.03

245.125.1min(

xxC pk

For our example:

Cpk tells how many standard deviations can fit between the mean and the specification limits. Ideally we want to fit more, so that probability of defect is smaller

Process Capability Index Cp

Process Interval = 6

Specification interval = US –LS

Cp= (US-LS) / 6

Process Interval = 60

Specification Interval = US – LS = 60

Cp= (US-LS) / 6 = 60 / 60 = 1

Process IntervalSpecification Interval

99.73%

USLS

100 160

= 10

Process Capability Index Cp

Process Interval = 6 = 30

Specification Interval = US – LS =60

Cp= (US-LS) / 6 =2

Specification Interval6 Process Interval

3 Process Interval

USLS

100 160 = 5

99.73%

99.99998%

Process Mean Shifted

USLS

100 160

= 10

130

Cpk = min{ (US - )/3, ( - LS)/3 }

Cpk = min(2,0)=0

Specification

3 Process

70

2. Statistical Process Control: Control Charts

Can be used to monitor ongoing production process quality

Can be used to monitor ongoing production process quality

970

980

990

1000

1010

1020

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

LCL

UCL

Mean and Range ChartsMean and Range Charts

(a)(a)

These These sampling sampling distributions distributions result in the result in the charts belowcharts below

(Sampling mean is (Sampling mean is shifting upward but shifting upward but range is consistent)range is consistent)

R-chartR-chart(R-chart does not (R-chart does not detect change in detect change in mean)mean)

UCLUCL

LCLLCL

x-chartx-chart(x-chart detects (x-chart detects shift in central shift in central tendency)tendency)

UCLUCL

LCLLCL

Mean and Range ChartsMean and Range Charts

R-chartR-chart(R-chart detects (R-chart detects increase in increase in dispersion)dispersion)

UCLUCL

LCLLCL

(b)(b)

These These sampling sampling distributions distributions result in the result in the charts belowcharts below

(Sampling mean (Sampling mean is constant but is constant but dispersion is dispersion is increasing)increasing)

x-chartx-chart(x-chart does not (x-chart does not detect the increase detect the increase in dispersion)in dispersion)

UCLUCL

LCLLCL

Process Control and Improvement

LCL

UCL

Out of Control In Control Improved

Process Control and Capability: Review

Every process displays variability: normal or abnormal Do not tamper with process “in control” with normal variability Correct “out

of control” process with abnormal variability Control charts monitor process to identify abnormal variability Control charts may cause false alarms (or missed signals) by mistaking

normal (abnormal) for abnormal (normal) variability Local control yields early detection and correction of abnormal Process “in control” indicates only its internal stability Process capability is its ability to meet external customer needs Improving process capability involves changing the mean and reducing

normal variability, requiring a long term investment Robust, simple, standard, and mistake - proof design improves process

capability Joint, early involvement in design improves quality, speed, cost

For upcoming weeks Assignment: Turkish Airlines case-due week 8 (do with your

study team)– Discuss all, but answer only Question 2 and 6 for your written assignment– For question 6 submit excel sheet as well as explanation in writing

Littlefield simulation calendar (teams of 3)– Register groups by Friday Nov 9

http://lab.responsive.net/lt/koc/start.html

Code: operations– Screening begins right after all groups are registered: explore interface

and first 50 days’ data– Start simulation Monday Nov 12 @ 17:00– End simulation Monday Nov 20 @ 17:00– Report due-in class week 9