Chapter 17

Quality Control

Quality Control

Purpose: monitor and maintain quality levels of products/services/processes, and try to improve product/service/process designs in ways that result in better quality products, services, and processes

Quality Control Departments:• Traditional focus inspections• Newer focus quality training, improvements,

working with suppliers, few inspections

Quality Control

Process variation causes a process to be less consistent, resulting in lower quality

W. Edwards Deming 2 causes of variationCommon causes: normal (typical) variation, inherent to the

process, difficult/expensive to reduce; example– a machine is not very accurate because it is old

Special causes: due to a specific problem, not inherent to process, usually easy/cheap to fix; example– a machine’s quality level is lower one morning, and after you investigate you discover that operator has hangover

To improve quality, identify and fix special causes of variation first (low hanging fruit)

Process Variation

10,000 units of a gear shaft needed – set up machine and do test run of 100 units.

2 different machines can do the same operation. Which should be used?

9.00 9.05 9.1 9.158.958.98.85

specs

diameter (mm)

machine A 20% out of spec

Process Variation

9.00 9.05 9.1 9.158.958.98.85

specs

diameter (mm)

machine B 50% out of spec

Which should be used, machine A or machine B?

Quality Control Throughout Productive Systems

Raw Materials,Parts, and Supplies

Production Processes

Products and Services

AcceptanceTests

Control ChartsAcceptance

Tests

Quality ofInputs

Monitoring Quality ofPartially Completed Products

Quality ofOutputs

Inputs Conversion Outputs

Monitoring Process Quality

Run Diagrams useful when starting a process

(most likely time for errors)

– measure every piece– plot measurements– look for outliers and patterns to investigate– process is in-control if no outliers or patterns

(just typical randomness)

Run Diagram—1st AttemptOuter Diameters of 30 Pieces

4.9

4.95

5

5.05

5.1

5.15

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Piece number

Cen

timet

ers

Run Diagram—2nd AttemptOuter Diameters of 30 Pieces

4.9

4.95

5

5.05

5.1

5.15

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Piece number

Cen

timet

ers

GP4890 ROSEBURG FOREST PRODUCTSSHIPPING TEMPERATURE 1/21/93 – 2/15/93

10

15

20

25

30

35

0 1 2 3 4 5 6 7 8 9101112131415161718192021222324252627282930313233343536373839404142434445464748

trucks

tem

pe

ratu

re

Control Charts

X chart and R chart

– when measuring a variable (e.g., length, weight, volume, viscosity)

– assumes normal distribution of sample means– X is the measurement of one unit– X is the mean measurement of one sample– X is the expected value of the measurement– R is the range of one sample (high – low)– R is the expected value of the range

Control Charts

p chart

– when measurement has only two outcomes (e.g., yes/no, defective/nondefective, good/bad)

– assumes binomial distribution– p is fraction or percent of bad parts in a

sample– p is the expected value of p

Control Charts

c chart

– when measuring the total number of defects in a sample

– sample size is 2 or more units– assumes Poisson distribution– c is number of defects in a sample– c is the expected value of c

Control Charts

u chart

– when measuring the number of defects on one unit

– sample size is one unit– assumes Poisson distribution– u is number of defects on one unit– u is the expected value of u– only difference between u and c charts is

sample size (1 or many)

Control Limits

X chart – for sample means

Upper control limit (UCL) = X + AR

Lower control limit (LCL) = X – AR

X = expected value of X (average over many samples)

R = expected value of R (average over many samples)

A = a constant from Table

Control Limits

R chart – for sample ranges

UCL = D2R

LCL = D1R

D1 and D2 are constants from Table

Control Limits

p chart – for fraction/percent defectives in sample

fraction percent

p = expected fraction/percent defectives in samples

n = size of one sample (number of units)

n)p(100p3pLCL or n)p(1p3pLCL

n)p(100p3pUCL or n)p(1p3pUCL

Control Limits

c chart – for total number of defects in a sample

c = expected number of defects in samples

c3cLCL

c3cUCL

X and R chart example: Suppose a company wants to startusing X and R control charts. They have collected 25samples of 5 units in each sample to estimate X and R.

Sample # 1st unit 2nd unit 3rd unit 4th unit 5th unit Average X-bar Range R

1 10.60 10.40 10.30 9.90 10.20 10.28 .70

2 9.98 10.25 10.05 10.23 10.33 10.17 .35

3 9.85 9.90 10.20 10.25 10.15 10.07 .40

4 10.20 10.10 10.30 9.90 9.95 10.09 .40

5 10.30 10.20 10.24 10.50 10.30 10.31 .30

6 10.10 10.30 10.20 10.30 9.90 10.16 .40

7 9.98 9.90 10.20 10.40 10.10 10.12 .50

8 10.10 10.30 10.40 10.24 10.30 10.27 .30

9 10.30 10.20 10.60 10.50 10.10 10.34 .50

10 10.30 10.40 10.50 10.10 10.20 10.30 .40

11 9.90 9.50 10.20 10.30 10.35 10.05 .85

12 10.10 10.36 10.50 9.80 9.95 10.14 .70

13 10.20 10.50 10.70 10.10 9.90 10.28 .80

14 10.20 10.60 10.50 10.30 10.40 10.40 .40

15 10.54 10.30 10.40 10.55 10.00 10.36 .55

16 10.20 10.60 10.15 10.00 10.50 10.29 .60

17 10.20 10.40 10.60 10.80 10.10 10.42 .70

18 9.90 9.50 9.90 10.50 10.00 9.96 1.00

19 10.60 10.30 10.50 9.90 9.80 10.22 .80

20 10.60 10.40 10.30 10.40 10.20 10.38 .40

21 9.90 9.60 10.50 10.10 10.60 10.14 1.00

22 9.95 10.20 10.50 10.30 10.20 10.23 .55

23 10.20 9.50 9.60 9.80 10.30 9.88 .80

24 10.30 10.60 10.30 9.90 9.80 10.18 .80

25 9.90 10.30 10.60 9.90 10.10 10.16 .70

10.21X 0.60R R is R of Avg.and ;X is X of Avg.

Compute Control Limits

R

X chart: for n=5 in Table (p.671), A=0.577

XUCL,LCL = ± A( ) = =LCL = and UCL =

R

R chart: for n=5 in Table, D1=0 and D2=2.116

LCL = D1 =UCL = D2 =R

9.8

9.9

10

10.1

10.2

10.3

10.4

10.5

10.6

1 3 5 7 9 11 13 15 17 19 21 23 25

Sample Number

UCL 10.56

LCL 9.86

X=10.21

X Chart

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 3 5 7 9 11 13 15 17 19 21 23 25

Sample Number

LCL=0

UCL=1.27

R=0.6

R Chart

ControlChart

Problemsto

Investigate

GP4890 ROSEBURG FOREST PRODUCTS% CAUSTIC 1/15/93 – 2/13/93

5.7

5.8

5.9

6

6.1

6.2

6.3

6.4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

batches (n = 3)

%C

AU

STI

C

MOVING AVERAGE MOVING RANGE

UPPER CONTROL LIMIT

UPPER CONTROL LIMIT

LOWER CONTROL LIMIT

3

2.5

2

1.5

1

0.5

0

p Chart Example

Process placing labels on jeans

Label placement is either defective or non-defective.

Typically, about 1.5% of labels are considered defective.

Compute control limits for a p chart, with sample size = 200.

If a sample has 6 bad labels, is this in-control?

c Chart Example

Twice a day, Ford takes a sample of 5 cars after the painting operation to count the number of bad spots on the freshly painted surfaces. The typical number of defects per sample is 3.1 bad spots. Compute 3σ control limits.

Good/Bad & Investigate or Not

Above

UCL

Below

LCL

X chart

R chart

p chart

c chart

u chart

Guidelines for Determining Which Control Chart to Use

1. Identify the item or product to be evaluated for quality.

2. What characteristic is to be measured?

3. Should every item be checked, or should a random sample be taken?

4. Is the characteristic measured on a continuous scale?

5. Is the item either good or bad, or is the number of defects on one item important?

6. Should the random sample size be one unit, or should it be more than one unit?

Control Chart Examples

1. A local building contractor builds large custom homes. He wants to use a control chart to monitor the number of problems that customers find in the finished homes. What type of control chart should be used?

2. A manufacturer of semiconductors chips plans to use a control chart to monitor the quality of chips they produce. Due to the complexity and density of circuits on each chip, typically 5% to 15% of the chips are faulty, which is about normal for the industry. Faulty chips are returned by customers for a full refund or replacement. What type control chart should be used?

3. A professional proofreader checks manuscript pages for typing errors. What type of control chart should be used to monitor the quality of their proofreading?

4. As cereal boxes are filled in a factory they are weighed for their contents by an automatic scale. The target is to put 10 ounces of cereal in each box. What type of control chart should be used to monitor how well they are achieving their target?

5. What type of control chart should Microsoft use to monitor the quality of their software programmers in developing computer code for assigned portions of larger software products?

6. What type of chart should a business school use to monitor the quality of incoming MBA students based on GMAT scores?

Control Chart Examples