OM-09-QualityCapabilitySPC.ppt

8/10/2019 OM-09-QualityCapabilitySPC.ppt

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Six-Sigma Quality, Process Capability,

and Statistical Process ControlSelected Slides from Jacobs et al, 9thEdition

Operations and Supply Management

Chapter 9 and 9AEdited, Annotated and Supplemented by

Peter Jurkat


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Total Quality Management (TQM)

Total qualitymanagementis definedas managing the entireorganization so that it

excels on all dimensionsof products and servicesthat are important to thecustomer

Design quality: Inherentvalue of the product inthe marketplace

Dimensions include:Performance, Features,Reliability/Durability,Serviceability, Aesthetics,and Perceived Quality.

Conformance quality:Degree to which theproduct or service designspecifications are met


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Six Sigma Quality

A philosophy and set of methods

companies use to eliminate defects

in their products and processes Seeks to reduce variation in the

processes that lead to product

defects

9-3


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McGraw-Hill/Irwin Copyright 2009 by The McGraw-Hill Companies, Inc. All rights reserved.

Gurus and their wisdom


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Consensus

Gurus had considerable differences

After 30 years get some consensus

Senior level leadership

Customer focus

Work force involvement

Process analysis

Continuous improvement


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Costs of Quality

External Failure

Costs

Appraisal Costs

Prevention Costs

Internal Failure

Costs

Costs of

Quality

9-6


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9-7

Cost of Quality Example

At 20% of sales, represents about $2M sales, at 2.5% about $73M sales


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Six Sigma Quality Measurement

Six Sigma allows managers to readily describe process

performance using a common metric: Defects Per MillionOpportunities (DPMO)

Defect associated with a critical-to-quality characteristic: a

measurable quantity used to identify failure

Statistical six sigma goal is 3.4 failures per 1,000,000 opportunities 1

failure in about 300,000 DPMO (actually 1 in 294,118)

1,000,000x

unitsofNo.x

unitpererrorfor

iesopportunitofNumber

defectsofNumber

DPMO

9-8


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9A-9Process Capability

Shows to what extent (probability) parts are produced that meet and fall

outside of specifications

Achieved when process variation (s.d.) is so small that an acceptable

proportion are defectsSix-Sigma goal is 3.4 out of one million

Bearing Diameter


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Why 3.4 DPMO?

Six sigma between mean and, say, upper

specification limit results 1 defect in100,000,000 (see SixSigmaOrigin.xls)

Experience has shown that in long term

processes have a wider variation than in shortterm studies, which results in defects with

probability beyond 4.5 sigma, i.e.3.4 DPMO

(1.5 sigma less than 6 sigma) See origin of this at http://en.wikipedia.org/wiki/Six_Sigma ( which bases

above on Tennant, Geoff (2001). SIX SIGMA: SPC and TQM in

Manufacturing and Services. Gower Publishing, Ltd., p. 25. ISBN

0566083744.)
http://en.wikipedia.org/wiki/Six_Sigmahttp://books.google.com/books?id=O6276jidG3IC&printsec=frontcoverhttp://books.google.com/books?id=O6276jidG3IC&printsec=frontcoverhttp://en.wikipedia.org/wiki/Special:BookSources/0566083744http://en.wikipedia.org/wiki/Special:BookSources/0566083744http://en.wikipedia.org/wiki/Special:BookSources/0566083744http://en.wikipedia.org/wiki/Special:BookSources/0566083744http://books.google.com/books?id=O6276jidG3IC&printsec=frontcoverhttp://books.google.com/books?id=O6276jidG3IC&printsec=frontcoverhttp://en.wikipedia.org/wiki/Six_Sigma


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9A-11

Mean shift during process improvement

Still an improvement but capability is now measured against closest of LTL and UTL

LTL = lower tolerance limit UTL = upper tolerance limit


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Measure Example

Example of Defects Per MillionOpportunities (DPMO) calculation.Suppose we observe 200 letters deliveredincorrectly to the wrong addresses in asmall city during a single day when atotal of 200,000 letters were delivered.

What is the DPMO in this situation?

000,1 1,000,000x

200,000x1

200DPMO

So, for every onemillion letters

delivered thiscitys postalmanagers canexpect to have1,000 lettersincorrectly sent to

the wrongaddress.

Cost of Quality: What might that DPMO mean in terms ofover-time employment to correct the errors?

9-12


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8-13Service Blueprint, Failure Anticipation, and Poka-Yokes

Complete blueprint (p262-3)identifies 16 failure opportunities


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Toyota Dealer Service Example

Blueprint identified 16 failure opportunitiesper customer

Assume 20 customers /day => 80,000

customers/year for 250 working days per year At 3.4 failures per 1,000,000 opportunities this

would allow .272 failures/year, or 3 2/3 years

between failures What is the critical-to-quality characteristic of

the first identified failure? Second failure?


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DMAIC Cycle

GE developedmethodology

Overall focus is tounderstand andachieve what the

customer wants (Juran) Identifies defects and

variation in processesas underlying cause ofdefects (Deming)

A 6-sigma programseeks to reduce thevariation in theprocesses that lead tothese defects

Define customers andtheir priorities

Measure process and itsperformance

Analyze causes ofdefects

Improve by removingcauses

Control to maintainquality


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DMAIC in Action

We are the maker of acereal. Consumer Reportshas just published an articlethat shows that wefrequently have less than 16

ounces of cereal in a box. What should we do?

1. Define

a. What is the critical-to-quality characteristic?

b. The CTQ (critical-to-quality) characteristic inthis case is the weight ofthe cereal in the box.

2. Measurea. How would we measure to

evaluate the extent of theproblem?

b. What are acceptable limitson this measure?

c. Lets assume that thegovernment says that wemust be within 5 percentof the weight advertised onthe box.

d. Upper Tolerance Limit = 16 +.05(16) = 16.8 ouncese. Lower Tolerance Limit = 16

.05(16) = 15.2 ouncesf. Survey: 1000 boxes have

mean weight = 15.875 ozwith s.d. = .529

9 17


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Upper Tolerance

= 16.8Lower Tolerance

= 15.2

Process

Mean = 15.875

Std. Dev. = .529

What percentage of boxes are defective (i.e. less than 15.2 oz)?

Z = (xMean)/Std. Dev. = (15.215.875)/.529 = -1.276

NORMSDIST(Z) = NORMSDIST(-1.276) = .100978

Approximately, 10 percent of the boxes have less than 15.2

Ounces of cereal in themway out of six-sigma specs

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DMAIC in Action

3. Analyze - how can we

improve the

capability of our cereal

box filling process?a. Decrease Variation

b. Center Process

c. Tighten Specifications

4. ImproveHow good is

good enough?

a. Set center spec at goal

(16 oz in this case)b. Set controls so that a

deviation of 6 s.d.

occurs only 3.4 times

out of a million


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DMAIC in Action

5. Statistical ProcessControl

a. Use data from actualprocess

b. Estimate distributions

c. Calculate capabilitydobetter if not adequate(actually do better all thetime)

d. Statistically monitor the

process over time

e. Tools1) Process flow charts (e.g.,

Toyota service blueprint)

2) Run charts

3) Pareto charts

4) Check sheets5) Cause-and-effect

diagrams

6) Opportunity flowdiagrams

7) Failure mode and effect

analysis (FMEA)8) Statistical Process Control(SPC) and Control charts

9) Design of Experiments(DOE)

9-20


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9-20

9-21


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9 21

9-22


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9 22

9-23


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9 23

Severity: cost of damage, rating number

Occurrence: observed relative frequency,

predicted probability

Detection: probability of detection

RPN = Occurrence X Severity X Detection

Failure Mode and Effect Analysis

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9 24

Part of Statistical Process Control

Uses statistical theory and practice to follow processes in order to determine if they are

within specification/control

Also used to predict if a process might be going out of control while still within specs

General approach is to sample a process at intervals, plot the results and compare

these to control limits

Upper

Control

Limit

Lower

ControlLimit

9A-25


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Statistical Process Control

Assignable variationis causedby factors that can be clearlyidentified and possiblymanaged

Common variationis inherentin the production process

Example: A poorly trained

employee that creates

variation in finished product

output.

Example: A molding process

that always leaves burrs or

flaws on a molded item.

Based on statistical theory of variation (dispersion)

Defines process capability

Establishes process control limits

Controls process bases on periodic sampling (small samples

as opposed to inspecting/measuring everything)

Variation

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Taguchis View of Variation

Incremental

Cost of

Variability

High

Zero

Lower

Spec

Target

Spec

Upper

Spec

Traditional View

Incremental

Cost of

Variability

High

Zero

Lower

Spec

Target

Spec

Upper

Spec

Taguchis View

Traditional view is that quality within the LS and US is good and that

the cost of quality outside this range is constant, Taguchi views costs as

increasing as variability increases, so seek to achieve zero defects and

that will truly minimize quality costs.

Upper and lower specs are also called upper and lower tolerance limits (UTL and LTL)

9A-27


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Process Capability Index, Cpk

3X-UTLor

3LTLXmin=Cpk

Shifts in Process Mean

Capability Index shows

how well parts being

produced fit into design

limit specifications.

As a production process

produces items small

shifts in equipment or

systems can cause

differences inproduction

performance from

differing samples.

LTL/UTL = lower/upper tolerance limit

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The Cereal Box Example

We are the maker of this cereal. Consumer reports hasjust published an article that shows that we frequentlyhave less than 16 ounces of cereal in a box.

Lets assume that the government says that we must

be within 5 percent of the weight advertised on thebox.

Upper Tolerance Limit = 16 + .05(16) = 16.8 ounces

Lower Tolerance Limit = 16.05(16) = 15.2 ounces

We go out and buy 1,000 boxes of cereal and find thatthey weight an average of 15.875 ounces with astandard deviation of .529 ounces.

9A-29


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Cereal Box Process Capability

Specification or Tolerance

Limits Upper Spec = 16.8 oz

Lower Spec = 15.2 oz

Observed Weight

Mean = 15.875 oz

Std Dev = .529 oz

3

;3

XUTLLTLXMinCpk

)529(.3

875.158.16;

)529(.3

2.15875.15MinCpk

5829.;4253.MinCpk

4253.pkC

9A-30


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What does a Cpkof .4253 mean?

An index that shows how well theunits being produced fit within the

specification limits. This is a process that will produce a

relatively high number of defects.

Many companies look for a Cpkof 1.3or better 6-Sigma company wants2.0!

9A-31


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Types of Statistical Sampling in SPC

Attribute (overall acceptable or not)

Defectives refers to the acceptability of product across arange of characteristics.

Defects refers to the number of defects per unit whichmay be higher than the number of defectives.

p-chart application (p for proportion)

Variable (Continuous)

Usually actual dimensions (length, weight, hardness, )

Usually measured by the mean and the standarddeviation.

X-bar and R chart applications (x-bar for mean and R forrangemuch easier to measure than s.d.)

9A-32


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Control Charts

9A-33


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Statistical Process Control Formulas:

Attribute Measurements (p-Chart)

p =T o t al N u m b e r o f D e fe c tiv e s

T o ta l N u m b e r o f O b s e rv a tio n s

n

s

)p-(1p=p

p

p

z-p=LCL

z+p=UCL

s

s

Given:

Compute control limits:

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1. Calculate the sample

proportions, p (these

are what can be plotted

on thep-chart) for each

sample

Sample n Defectives p

1 100 4 0.04

2 100 2 0.02

3 100 5 0.05

4 100 3 0.03

5 100 6 0.06

6 100 4 0.04

7 100 3 0.03

8 100 7 0.07

9 100 1 0.01

10 100 2 0.02

11 100 3 0.03

12 100 2 0.02

13 100 2 0.02

14 100 8 0.0815 100 3 0.03

Example of Constructing ap-chart

2. Calculate theaverage and s.d. of the

sample proportions

0.036=1500

55=p

.0188=

100

.036)-.036(1=

)p-(1p=p

n

s

E l f C t ti Ch t9A-35


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Example of Constructing ap-Chart

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

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

Observation

p

UCL

LCL

Calculate control limits and plot the individual sample proportions, the

average of the proportions, and the control limits 3(.0188).036

UCL = 0.0924

LCL = -0.0204 (or 0)

9A-36


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Example of x-bar and R charts: Steps: Calculate x-bar Chart and Plot Values

10.601

10.856

=).58(0.2204-10.728RA-x=LCL

=).58(0.2204-10.728RA+x=UCL

2

2

10.550

10.600

10.650

10.700

10.750

10.800

10.850

10.900

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

S a m p l e

Means

UCL

LCL

9A-37


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Example of x-bar and R charts: Calculate R-chart and Plot Values

0

0.46504

)2204.0)(0(RD=LCL

)2204.0)(11.2(RD=UCL

3

4

0 . 0 0 0

0 . 1 0 0

0 . 2 0 0

0 . 3 0 0

0 . 4 0 0

0 . 5 0 0

0 . 6 0 0

0 . 7 0 0

0 . 8 0 0

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

S a m p l e

RUCL

LCL

9A-38


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Common criteria for concluding

process is out of control or in

danger of being so


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Advantages Economy Less handling damage Fewer inspectors Upgrading of the

inspection job Applicability to destructive

testing Entire lot rejection

(motivation forimprovement)

Disadvantages

Risks of accepting badlots and rejecting goodlots

Added planning anddocumentation

Sample provides less

information than 100-percent inspection

Acceptance Sampling

PurposesDetermine quality level of acquired goods or services(after the fact) when no sampling of productionprocess is availableEnsure quality is within predetermined level

9A-40


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Risk

Acceptable Quality Level (AQL)

Max. acceptable percentage of defectives defined

by producer

The (Producers risk)

The probability of rejecting a good lot

Probability of Type I error based on consumersnull hypothesis that lot is good

Lot Tolerance Percent Defective (LTPD)

Percentage of defectives that defines consumers

rejection point

The (Consumers risk)

The probability of accepting a bad lot

Probability of Type II error based on consumers

null hypothesis that lot is good

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Operating Characteristic Curve

n = 99

c = 4

AQL LTPD

00.1

0.2

0.3

0.4

0.50.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10 11 12

Percent defective

Probabilityofacceptinglots

withgive%o

fdefectives

=.10(consumers risk = accept bad lot)

= .05 (producers risk

= reject good lot)

The OCC brings the concepts of producers risk, consumers

risk, sample size, and maximum defects allowed together

The shape

or slope of

the curve is

dependent

on a

particular

combination

of the four

parameters

n = sample size

c = acceptance number (max

defectives allowed before lotis rejected)

H0: Lot is good

Ha: Lot is bad

9A-42


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Example: Acceptance Sampling Problem

Zypercom, a manufacturer of video interfaces,

purchases printed wiring boards from an outside

vender, Procard. Procard has set an acceptable

quality level of 1% and accepts a 5% risk of rejecting

lots at or below this level. Zypercom considers lots

with 3% defectives to be unacceptable and will assume

a 10% risk of accepting a defective lot.

Develop a sampling plan for Zypercom and determine

a rule to be followed by the receiving inspection

personnel.


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9A-44


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Example: Step 2. Determine c

First divide LTPD by AQL

LTPDAQL

= .03.01

= 3

Then find the value for c by selecting the value in the QA-12 (on disk)

n(AQL)column that is equal to or just greater than the ratio above.

Exhibit QA-12

c LTPD/AQL n AQL c LTPD/AQL n AQL

0 44.890 0.052 5 3.549 2.6131 10.946 0.355 6 3.206 3.286

2 6.509 0.818 7 2.957 3.981

3 4.890 1.366 8 2.768 4.695

4 4.057 1.970 9 2.618 5.426

So, c = 6.

LTPD = Lot tolerant percent defective (buyers)

AQL = Acceptable quality level (seller)

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OM-09-QualityCapabilitySPC.ppt