Analysis Phase

Client, Enterprise & Competitive Intelligence for Product, Process & Systems Innovation

Dr. Rick L. Edgeman, University of Idaho

Six Sigma

IXCUSTOMER & COMPETITIVE INTELLIGENCE

FOR SYSTEMS INNOVATION & DESIGN

S IGMAS DEPARTMENT OF

STATISTICSDR. RICK EDGEMAN, PROFESSOR & CHAIR – SIX SIGMA BLACK BELT

[email protected] OFFICE: +1-208-885-4410



Six Sigma

IXS IGMAS DEPARTMENT OF

STATISTICS

DMAIC: The Analyze

Phase



Six Sigma

IXS IGMAS

DEPARTMENT OF

STATISTICS

a highly structured strategy for acquiring, assessing, and applying customer, competitor, and enterprise intelligence for the purposes of product, system or enterprise innovation and

design.



Six Sigma

Alternative Six Sigma Definitions• “Six Sigma is a business improvement

approach that seeks to find and eliminate causes of mistakes or defects in business processes by focusing on process outputs that are of critical importance to customers.” (Snee, 2004).

• “Six Sigma is a useful management philosophy and problem-solving methodology but it is not a comprehensive management system. “ (McAdam & Evans, 2004)



Six Sigma

Alternative Six Sigma Definitions• “A Six Sigma initiative is designed to change

the culture in an organisation by the way of breakthrough improvement in all aspects of the business.” (Breyfogle III et al., 2001)

• “Six Sigma is a programme that combines the most effective statistical and non-statistical methods to make overall business.” (Pearson, 2001)



Six Sigma

Alternative Six Sigma Definitions• “Six Sigma is a highly disciplined process that helps

us focus on developing and delivering near-perfect products and services. The central idea behind Six Sigma is that you can measure how many defects you have in a process, you can systematically figure out how to eliminates them and get as close to ‘zero defects’ as possible. Six Sigma has changed the DNA of GE – it is the way we work - in everything we do in every product we design” (General Electric at www.ge.com)



Six Sigma

Define

Control

Improve Analyze

Measure

Six Sigma Innovation & the DMAIC

Algorithm

Define the problem and customerrequirements.

Measure defect rates and documentthe process in its current incarnation.

Analyze process data and determinethe capability of the process.Improve the process and removedefect causes.

Control process performance andensure that defects do not recur.



Six Sigma

Analyze: Where are we now? Where are we going?

What can prevent us from reaching our goals?

At this stage we determine the process sigma level and regardvariation as an enemy. We must determine process capability,

that is, the ability of the process to meet customer requirements.

We require several “z-scores” to make this evaluation.

ZBENCH Zst ZLT ZLSL ZUSL

Where “BENCH” = benchmark, “st” = short term, “LT” = long term “LSL” = lower specification limit, and “USL” = upper specification limit.



Six Sigma

Analyze: Where are we now? Where are we going? What can prevent us from reaching our goals?

ZST = best performance that can be expected from a process

ZLT = allows for drift through time (1 to 2 sigma drift is typical)

ZLSL= (X – LSL) / S then determine PLSL(d)

ZUSL= (USL – X) / S then determine PUSL(d)

P(d) = PLSL(d) + PUSL(d) then apply inverse use of the Z-table to findZBENCH (long-term)

P(d) * 1,000,000 = DPMO or PPM

0.0X

Zx.y P(d) ZBENCH



Six Sigma

Analyze: Where are we now? Where are we going? What can prevent us from reaching our goals?

ZSHIFT = ZST – ZLT drift over time (DPMO tables assume 1.5)

ZST = (Specification Limit – Target) / ST * process sigma is determined here * indicates potential process performance if only common cause variation is present.

ZLT = (Specification Limit - ) / LT

* reveals long-term process capability

* used to estimate DPMO or PPM (“parts per million” same as DPMO) * includes special cause variation

^

^



Six SigmaAnalyze:

An Alternative Means of Approximating the Sigma Capability for Your Process

StepAction Equations Your Calculations

1 What process do you want to consider? N/A Billing & Charging

2 How many units were put through the N/A 2,000process?

3 Of the units that went into the process, N/A 1,800how many were OK?

4 Compute process yield (step 3)/(step 2) 0.90005 Compute defect rate 1.0 – (step 4) 0.10006 Determine the number of potential N = number of 16

things that could create a defect critical-to-quality characteristics

7 Compute the defect rate per CTQ (step 5)/(step 6) 0.00625characteristic

8 Compute DPMO (step 7)*(1 million) 6,250

9 Convert DPMO to value conversion chart About 4.010 Draw conclusions JUST ABOUT INDUSTRY AVERAGE



Six Sigma

Process Capability:The Control Chart Method for Variables Data

1. Construct the control chart and remove all special causes.NOTE: special causes are “special” only in that they come and

go, not because their impact is either “good” or “bad”.

2. Estimate the standard deviation. Used approach depends on whether an R or S chart is used to monitor process variability.

^ _ ^ _

= R / d2 = S / c4

Several capability indices are provided on the following slide.

NOTE: Control Charts arepresented in later slidesets.



Six Sigma

Process Capability Indices: Variables Data ^

^CP = (engineering tolerance)/6 = (USL – LSL) /

6

This index is generally used to evaluate machine capability. It

compares tolerance to the engineering requirements. Assuming

that the process is (approximately) normally distributed and that

the process average is centered between the specifications, an

index value of “1” is considered to represent a “minimally

capable” process. HOWEVER … allowing for a drift, a minimum

value of 1.33 is ordinarily sought … bigger is better. A true “Six

Sigma” process that allows for a 1.5 shift will have Cp

= 2.



Six Sigma

Process Capability Indices: Variables Data

^ ^CR = 100*6 / (Engineering Tolerance) = 100* 6/(USL

– LSL)

This is called the capability ratio. Effectively this is the reciprocal of Cp so that a value of less than 75% is

generallyneeded and a Six Sigma process (with a 1.5 shift) will

lead to aCR of 50%.



Six Sigma

Process Capability Indices: Variables Data ^

^CM = (engineering tolerance)/8 = (USL – LSL) /

8

This index is generally used to evaluate machine capability.

Note … this is only MACHINE capability and NOT the capability of the full process. Given that there will be additional sources of variation (tooling, fixtures, materials, etc.) CM uses an 8 spread,

rather than 6. For a machine to be used on a Six Sigma process, a 10 spread would be used.



Six Sigma

Process Capability Indices: Variables Data = ^ = ^

ZU = (USL – X) / ZL = (X – LSL) /

Zmin = Minimum (ZL , ZU)

Cpk = Zmin / 3

This index DOES take into account how well or how poorly centered

a process is A value of at least +1 is required with a value of at least

+1.33 being preferred. Cp and Cpk are closely related. In some sense

Cpk represents the current capability of the process whereas Cp

represents the potential gain to be had from perfectly centering the

process between specifications.



Six SigmaProcess Capability: ExampleAssume that we have conducted a capability analysis using X-bar

and R chartswith subgroups on size n = 5. Also assume the process is in

statistical controlwith an average of 0.99832 and an average range of 0.02205. A

table of d2

values gives d2 = 2.326 (for n = 5). Suppose LSL = 0.9800 and USL = 1.0200

^ _ = R / d2 = 0.02205/2.326 = 0.00948

Cp = (1.0200 – 0.9800) / 6(.00948) = 0.703

CR = 100*(6*0.00948) / (1.0200 – 0.9800) = 142.2%

CM = (1.0200 – 0.9800) / (8*(0.00948)) = 0.527

ZL = (.99832 - .98000)/(.00948) = 1.9

ZU = (1.02000 – .99832)/(.00948) = 2.3 so that Zmin = 1.9

Cpk = Zmin / 3 = 1.9 / 3 = 0.63



Six SigmaProcess Capability: Interpretation

Cp = 0.703 … since this is less than 1, the process is not regarded as being capable.

CR = 142.2% implies that the “natural tolerance” consumes 142% of the specifications (not a good situation at all).

CM = 0.527 = Being less than 1.33, this implies that – if we were dealing with a machine, that it would be incapable of meeting requirements.

ZL = 1.9 … This should be at least +3 and this value indicates that approximately 2.9% of product will be undersized.

ZU = 2.3 should be at least +3 and this value indicates that approximately 1.1% of product will be oversized.

Cpk = 0.63 … since this is only slightly less that the value of Cp the indication is that there is little to be gained by centering and that the need is to reduce process variation.



Six Sigma

Analyze: Setting Performance Objectives

Critical to the Setting of Performance Objectives are the Concepts of‘Baseline’, ‘Process Entitlement’, ‘Benchmark’ and ‘Benchmarking’

BASELINE: This is the process performance level at the start of the Six Sigma Project.

PROCESS ENTITLEMENT: This is our best expectation for process performance(e.g., the ‘sigma level’) with the current technology – that is, without

substantial reengineering or investment. This can be estimated from Zst.

BENCHMARK: This is the current ‘best in class’ performance level.

BENCHMARKING: The process of finding the benchmark performancelevel and then matching or exceeding that performance.



Six Sigma

Analyze: Sources of Variation

This is the search for the Vital X’s – the factors that drive the customer CTQs.

Various statistical and quality methods are useful in this effort. Among these are:

HYPOTHESIS TESTING, which can • Reveal Significant Differences in Performance Between Processes

• Validate Process Improvements• Identify Factors that Impact the Process Mean and Variation.

FISHBONE or CAUSE-AND-EFFECT DIAGRAMS



Six Sigma

Analyze: Sources of Variation:

The Hypothesis Testing Algorithm

1. Formulate the Null and Alternative Hypotheses, H0 and HA.

2. Specify the Sample Size and Significance Level of the Test, n and 3. Determine Which Type of Test Should be Employed.

4. State the Critical Value(s) & the Test Statistic & Specify the Decision Rule. 5. Collect and Validate Process Data.

6. Determine the Calculated Value of the Test Statistic (Data Based)7. As Appropriate, Construct and Interpret Confidence Intervals.

8. Determine and Pursue a Course of Action.

Key Vocabulary: Type I and II Errors, and



Six Sigma

IXS IGMAS DEPARTMENT OF

STATISTICS

End of Session

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Analysis Phase