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Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

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Page 1: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Managing Quality

CHAPTER SIX

McGraw-Hill/Irwin

Statistical Process control

Page 2: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Basics of Statistical Process Basics of Statistical Process ControlControl

Basics of Statistical Process Basics of Statistical Process ControlControl

• Statistical Process Control (SPC) developed by

Walter A. Shewhart at Bell Lab in 1920.– monitoring production process to

detect and prevent poor quality

• Sample– subset of items produced to use

for inspection

• Control Charts– process is within statistical control

limits

UCLUCL

LCLLCL

Page 3: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

SPC in TQMSPC in TQMSPC in TQMSPC in TQM

• SPC–tool for identifying problems and make

improvements–contributes to the TQM goal of

continuous improvements

• Real world Example: Honda

Page 4: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Control ChartControl ChartControl ChartControl Chart

• Control Chart

–Purpose: to monitor process output to see if it is random deciding whether the process is in control or not

–A time ordered plot represents sample statistics obtained from an ongoing process (e.g. sample means)

–Upper and lower control limits define the range of acceptable variation

Page 5: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

VariabilityVariabilityVariabilityVariability

• Random–common causes–inherent in a process–can be eliminated only

through improvements in the system

• Non-Random–special causes–due to identifiable

factors–can be modified

through operator or management action

Page 6: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Process Control Process Control ChartChart

Process Control Process Control ChartChart

11 22 33 44 55 66 77 88 99 1010Sample numberSample number

UpperUppercontrolcontrol

limitlimit

ProcessProcessaverageaverage

LowerLowercontrolcontrol

limitlimit

Out of controlOut of control

Page 7: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Quality MeasuresQuality MeasuresQuality MeasuresQuality Measures

• Variable–a product characteristic that is continuous and can be

measured–weight - length

• Attribute–a product characteristic that can be evaluated with a

discrete response–good – bad; yes - no

Page 8: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Control ChartsControl ChartsControl ChartsControl Charts

• Types of charts–Variables

•mean (x bar – chart)•range (R-chart)*Note: mean and range charts are used together

–Attributes•p-chart•c-chart

Page 9: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Control Charts for VariablesControl Charts for VariablesControl Charts for VariablesControl Charts for Variables

• Mean control charts

–Used to monitor the central tendency of a process.

–X bar charts

• Range control charts

–Used to monitor the process variability

–R charts

Page 10: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Using x- bar and R-Charts TogetherUsing x- bar and R-Charts TogetherUsing x- bar and R-Charts TogetherUsing x- bar and R-Charts Together

Process average and process variability must be in control

It is possible for samples to have very narrow ranges, but their averages are beyond control limits

It is possible for sample averages to be in control, but ranges might be very large

Page 11: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Mean and Range ChartsMean and Range ChartsMean and Range ChartsMean and Range Charts

UCL

LCL

UCL

LCL

R-chart

x-Chart Detects shift

Does notdetect shift

(process mean is shifting upward)Sampling

Distribution

Page 12: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

10-10-1212

x-Chart

UCL

Does notreveal increase

Mean and Range ChartsMean and Range ChartsMean and Range ChartsMean and Range Charts

UCL

LCL

LCL

R-chart Reveals increase

(process variability is increasing)

SamplingDistribution

Page 13: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

x-bar Chartx-bar Chartx-bar Chartx-bar Chart

xx = = xx11 + + xx22 + ... + ... xxkk

kk==

UCL = UCL = xx + + AA22RR LCL = LCL = xx - - AA22RR== ==

WhereWhere

xx = average of sample means= average of sample means==

Page 14: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

R- ChartR- ChartR- ChartR- Chart

UCL = UCL = DD44RR LCL = LCL = DD33RR

RR = = RRkk

wherewhere

RR = range of each sample= range of each samplekk = number of samples= number of samples

Page 15: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Example Example Example Example

• measuring the weight/packet in grams

• Packet

• Sample 1 2 3 Ri x-bari

• 1 42 40 44

• 2 35 40 45

• 3 44 44 44

• 4 40 40 43

• 5 41 41 38

Total ___ ___

Average ___ ___

 

Page 16: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Example (cont.)Example (cont.)Example (cont.)Example (cont.)

• # of samples = k =

• Sample size = n =

Page 17: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Example (cont.)Example (cont.)Example (cont.)Example (cont.)

• X-bar chart

Page 18: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Example (cont.)Example (cont.)Example (cont.)Example (cont.)

• R chart

Page 19: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Example (cont.)Example (cont.)Example (cont.)Example (cont.)

R Chart

| | | | |

x-bar Chart

| | | | |

Page 20: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

FaFactoctorsrs

FaFactoctorsrs

n A2 D3 D4

SAMPLE SIZE FACTOR FOR x-CHART FACTORS FOR R-CHART

2 1.88 0.00 3.273 1.02 0.00 2.574 0.73 0.00 2.285 0.58 0.00 2.116 0.48 0.00 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.44 0.18 1.82

10 0.11 0.22 1.7811 0.99 0.26 1.7412 0.77 0.28 1.7213 0.55 0.31 1.6914 0.44 0.33 1.6715 0.22 0.35 1.6516 0.11 0.36 1.6417 0.00 0.38 1.6218 0.99 0.39 1.6119 0.99 0.40 1.6120 0.88 0.41 1.59

Appendix: Determining Control Limits for x-bar and R-Charts

Page 21: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Control Charts for AttributesControl Charts for AttributesControl Charts for AttributesControl Charts for Attributes

p-charts uses portion defective in a sample

c-charts uses number of defects in an item

Page 22: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

p-Chartp-Chartp-Chartp-Chart

UCL = p + zp

LCL = p - zp

z = number of standard deviations from process averagep = sample proportion defective; an estimate of process averagep= standard deviation of sample proportion

pp = = pp(1 - (1 - pp))

nn

Page 23: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

p-Chart Examplep-Chart Example(assume the sample size of (assume the sample size of

100)100)

p-Chart Examplep-Chart Example(assume the sample size of (assume the sample size of

100)100)

NUMBER OFNUMBER OF PROPORTIONPROPORTIONSAMPLESAMPLE DEFECTIVESDEFECTIVES DEFECTIVEDEFECTIVE

11 1313

22 77

33 2020

44 00

5 105 10

totaltotal

averageaverage

Page 24: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

PP-Chart -Chart Example (cont.)Example (cont.) PP-Chart -Chart Example (cont.)Example (cont.)

Step 1: get sigma

Step 2: get UCL and LCL

n

ppp

1

pp pUCL 3

pp pLCL 3

Page 25: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

C-ChartC-ChartC-ChartC-Chart

UCL = UCL = cc + + zzcc

LCL = LCL = cc - - zzcc

where

c = number of defects per sample

cc = = cc

Page 26: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

C-Chart (cont.)C-Chart (cont.)C-Chart (cont.)C-Chart (cont.)

Measuring number of fouls called on a team per gameMeasuring number of fouls called on a team per game

1 371 372 92 93 223 224 254 255 325 32TotalTotalAvg. Avg.

SAMPLESAMPLE

NUMBER OF FOULS

Page 27: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

C-Chart (cont.)C-Chart (cont.)C-Chart (cont.)C-Chart (cont.)

UCLUCL = = cc + + zzcc

LCLLCL = = cc - - zzcc

Page 28: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Control Chart PatternsControl Chart PatternsControl Chart PatternsControl Chart Patterns

UCLUCL

LCLLCL

Sample observationsSample observationsconsistently above theconsistently above thecenter linecenter line

LCLLCL

UCLUCL

Sample observationsSample observationsconsistently below theconsistently below thecenter linecenter line

Page 29: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Control Chart Patterns (cont.)Control Chart Patterns (cont.)Control Chart Patterns (cont.)Control Chart Patterns (cont.)

LCLLCL

UCLUCL

Sample observationsSample observationsconsistently increasingconsistently increasing

UCLUCL

LCLLCL

Sample observationsSample observationsconsistently decreasingconsistently decreasing

Page 30: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Homework for Ch 6-IIHomework for Ch 6-II

6–6–3030

• Computer upgrade problem

Computer upgrades take 80 minutes. Six samples of five observations each have been taken, and the results are as listed. Determine if the process is in control. You have to use appropriate chart(s)

• 1 2 3 4 5 6• 79.2 80.5 79.6 78.9 80.5 79.7• 78.8 78.7 79.6 79.4 79.6 80.6• 80.0 81.0 80.4 79.7 80.4 80.5• 78.4 80.4 80.3 79.4 80.8 80.0• 81.0 80.1 80.8 80.6 78.8 81.1

Page 31: Managing Quality CHAPTER SIX McGraw-Hill/Irwin Statistical Process control

Homework for Ch 6-IIHomework for Ch 6-II

6–6–3131

• Wrong account problem• The operations manager of the booking services department of

hometown bank is concerned about the number of wrong customer account numbers recorded by hometown personnel. Each week a random sample of 2,500 deposits is taken, and the number of incorrect account numbers is recorded. The results for the past 12 weeks are shown in the following table. Is the process out of control? Use appropriate control chart and use three sigma control limit, ie. Z=3.

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

• wrong account 15 12 19 2 19 4 24 7 10 17 15 3


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