1

Quality and Education

Business has made progress toward quality over the past several years. But I don’t believe we can truly make quality a way of life … until we make quality a part of every student’s education

Edwin Artzt, Chairman and CEO, Proctor & Gamble Co., Quality Progress, October 1992, p. 25

2

Quality and Competitive Advantage

• Better price– The better customers judge the quality of a

product, the more they will pay for it• Lower production cost

– It is cheaper to do a job right the first time than do it over

• Faster response– A company with quality processes for handling

orders, producing products, and delivering them can provide fast response to customer requests

3

Quality and Competitive Advantage

• Reduced Inventory– When the production line runs smoothly with

predictable results, inventory levels can be reduced

• Improved competitive position in the marketplace– A customer who is satisfied with quality will tell 8

people about it; a dissatisfied customer will tell 22 (A.V. Feigenbaum, Quality Progress, February 1986, p. 27)

4

TQMWheel

Customer

satisfaction

5

Customer-Driven Definitions of Quality

• Conformance to specifications– Conformance to advertised level of performance

• Value– How well the purpose is served at a particular

price. – For example, if a $2.00 plastic ballpoint pen lasts

for six months, one may feel that the purchase was worth the price.

6

Customer-Driven Definitions of Quality

• Fitness for use– Mechanical feature of a product, convenience of a

service, appearance, style, durability, reliability, craftsmanship, serviceability

• Support– Financial statements, warranty claims, advertising

• Psychological Impressions– Atmosphere, image, aesthetics– “Thanks for shopping at Wal-Mart”

7

Defectives and Defect

• In the popular sense, a defect is some characteristic that makes a product unsatisfactory for its intended purpose

• Technically, a defect is a failure to conform to some specification e.g., 0.140 0.003 in.

• To avoid ambiguity, following words are suggested– Nonconformity or Nonconformance: defect– Nonconforming: defective

8

Quality Costs

• Prevention costs– Customer requirements/expectations market

research – Product design/development reviews– Quality education programs– Equipment and preventive maintenance– Supplier-rating program administration

9

Quality Costs

• Appraisal costs– Testing/inspection equipment – Inspection costs– Audits

10

Quality Costs

• Internal failure costs– Rework, scrap, repair

• External failure costs– Returned goods, warranty costs, liability costs,

penalties• Intangible costs

– Customer dissatisfaction, company image, lost sales, loss of customer goodwill

11

Costs of Detecting Defects

Co

st o

f d

etec

tio

n (

do

llar

s)

Process Final testing Customer

When defect is detected

12

Statistical Quality ControlIntroduction

• Control charts and sampling• Simple and R charts• Variation• Common and assignable causes

X

13

Control Chart Viewpoint

• Variation due to – Common or chance causes– Assignable causes

• Control chart may be used to discover “assignable causes”

14

Scientific Sampling

• Inspection– Incoming materials, in-process products, finished

goods• JIT inventory control makes formal sampling

impractical except for quality audit purposes– The supplier performs sampling inspection and

provides statistical evidence of conformance to specifications

• 100% inspection may be impractical or uneconomical

15

Some Terms

• Run chart - without any upper/lower limits• Specification/tolerance limits - not statistical• Control limits - statistical

16

Weakness of Plotting Individual Measurements against Specification/Tolerance Limits

• If individual measurements are plotted against specification/tolerance limits, following problems may occur– If specification/tolerance limits are too wide, the

systems may fail to detect some variations that are less likely to be caused by chance and more likely to be caused by some problems in the production system (see Example 1.1)

– If specification/tolerance limits are too narrow, unavoidable random variations may be considered as defects and too many items may be rejected (see Example 1.2)

17

Control Charts

• Take periodic samples from a process

• Plot the sample points on a control chart

• Determine if the process is within limits

• Correct the process before defects occur

18

Types of Data

• Variable data• Product characteristic that can be measured

• Length, size, weight, height, time, velocity

• Attribute data• Product characteristic evaluated with a discrete

choice• Good/bad, yes/no

19

Process Control Chart

1 2 3 4 5 6 7 8 9 10

Sample number

Uppercontrollimit

Processaverage

Lowercontrollimit

20

Constructing a Control Chart

• Decide what to measure or count• Collect the sample data• Plot the samples on a control chart• Calculate and plot the control limits on the control chart• Determine if the data is in-control • If non-random variation is present, discard the data (fix the

problem) and recalculate the control limits

21

Control Charts For Variables

• Mean chart (X-Bar Chart)–Measures central tendency of a sample

• Range chart (R-Chart)–Measures amount of dispersion in a sample

• Each chart measures the process differently. Both the process average and process variability must be in control for the process to be in control.

Example: Control Charts for Variable Data

Slip Ring Diameter (cm)

Sample 1 2 3 4 5 X R

1 5.02 5.01 4.94 4.99 4.96 4.98 0.08

2 5.01 5.03 5.07 4.95 4.96 5.00 0.12

3 4.99 5.00 4.93 4.92 4.99 4.97 0.08

4 5.03 4.91 5.01 4.98 4.89 4.96 0.14

5 4.95 4.92 5.03 5.05 5.01 4.99 0.13

6 4.97 5.06 5.06 4.96 5.03 5.01 0.10

7 5.05 5.01 5.10 4.96 4.99 5.02 0.14

8 5.09 5.10 5.00 4.99 5.08 5.05 0.11

9 5.14 5.10 4.99 5.08 5.09 5.08 0.15

10 5.01 4.98 5.08 5.07 4.99 5.03 0.10

50.09 1.15

23

Normal Distribution Review

• If the diameters are normally distributed with a mean of 5.01 cm and a standard deviation of 0.05 cm, find the probability that the sample means are smaller than 4.98 cm or bigger than 5.02 cm.

24

• If the diameters are normally distributed with a mean of 5.01 cm and a standard deviation of 0.05 cm, find a lower value and an upper value of the sample means such that 97% sample means are between the lower and upper values.

Normal Distribution Review

25

• Define the 3-sigma limits for sample means as follows:

• What is the probability that the sample means will lie outside 3-sigma limits?

Normal Distribution Review

94345

0503015

3

07755

0503015

3

.).(

. Limit Lower

.).(

. Limit Upper

n

n

26

Normal Distribution Review

• Note that the 3-sigma limits for sample means are different from natural tolerances which are at 3

27

Constructing a Range Chart

).)((LCL

.).)(.(UCL

R

R

011500

4321150112

3

4

RD

RD

), of values the for App., Table Text or 29 p. see(

range

10samples of number

././R where

43

115010151

DDD

R

k

kR

Note: The control limits are only preliminary with 10 samples.It is desirable to have at least 25 samples.

28

Constructing A Mean Chart

94341150580015

07751150580015

2

2

.).(.).(LCL

.).(.).(UCL

X

X

RAX

RAX

) of value the for 3 App., Table Text or 29 p. see(

range

10samples of number

././R

././X where

2

115010151

015100950

AD

R

k

kR

kX

29

3-Sigma Control Chart Factors

Sample size X-chart R-chart

n A2 D3 D4

2 1.88 0 3.27

3 1.02 0 2.57

4 0.73 0 2.28

5 0.58 0 2.11

6 0.48 0 2.00

7 0.42 0.08 1.92

8 0.37 0.14 1.86

30

Common Causes

31

Assignable Causes

(a) MeanGrams

Average

32

Assignable Causes

(b) SpreadGrams

Average

33

Assignable Causes

(c) ShapeGrams

Average

34

The NormalDistribution

-3 -2 -1 +1 +2 +3Mean

68.26%95.44%99.74%

= Standard deviation

35

Control Charts

UCL

Nominal

LCL

Assignable causes likely

1 2 3Samples

36

Control Chart Examples

Nominal

UCL

LCL

Sample number

Var

iati

on

s

37

Control Limits and Errors

LCL

Processaverage

UCL

(a) Three-sigma limits

Type I error:Probability of searching for a cause when none exists

38

Control Limits and ErrorsType I error:Probability of searching for a cause when none exists

UCL

LCL

Processaverage

(b) Two-sigma limits

39

Type II error:Probability of concludingthat nothing has changed

Control Limits and Errors

UCL

Shift in process average

LCL

Processaverage

(a) Three-sigma limits

40

Type II error:Probability of concludingthat nothing has changed

Control Limits and Errors

UCL

Shift in process average

LCL

Processaverage

(b) Two-sigma limits

41

Process Capability

• Range of natural variability in process– Measured with control charts

• Process cannot meet specifications if natural variability exceeds tolerances

• 3-sigma quality– specifications equal the process control limits.

• 6-sigma quality– specifications twice as large as control limits

42

Process Capability

Process cannot meet specifications Process can meet specifications

Process capability exceeds specifications

PR

OC

ES

S

PR

OC

ES

S

PR

OC

ES

SNaturalcontrollimits

Naturalcontrollimits

Naturalcontrollimits

Designspecs

Designspecs

43

Process Capability

• If the R chart shows control, estimate the standard deviation of items as

• If the R chart does not show control, remove the ones that showed lack of control, calculate a revised and new control limits for R. Repeat the process as long as it is needed. Estimate standard deviation of items as shown above.

• Process capability

d

R

R

33

XUSLLSLXC xxpk ,min

44

Process Capability

• By computing we can conclude whether the mean has shifted towards upper/lower specification limit and if it has shifted at all. If both the numbers are equal, the mean is at the center. If the first number is smaller, the mean has shifted towards LSLx. If the second number is smaller, the mean has shifted towards USLx.

• If then the process is capable of producing 99.74% items within the specification limits. Else, either the process needs improvement or the specification limits must be widened.

pkC

1pkC

45

Text Exercise 2.2: Is the following process capable?:

0200

320034041

20

4

.2.050 are limits ionSpecificat

. ,.

samples, of Number

size, Sample

RX

k

n

46

Reading and Exercises

• Chapter 1: – pp. 3-24

• Chapter 2: – pp. 37-54– Problems 2.5, 2.6, 2.10