Statistical Process Control

Transcript Statistical Process Control

Chapter 3 Statistical Process Control

Lecture Outline

• Basics of Statistical Process Control • Control Charts • Control Charts for Attributes • Control Charts for Variables • Control Chart Patterns • SPC with Excel and OM Tools • Process Capability Copyright 2011 John Wiley & Sons, Inc.

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Statistical Process Control (SPC)

• Statistical Process Control • 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

UCL LCL

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Process Variability

• Random • inherent in a process • depends on equipment and machinery, engineering, operator, and system of measurement • natural occurrences • Non-Random • special causes • identifiable and correctable • include equipment out of adjustment, defective materials, changes in parts or materials, broken machinery or equipment, operator fatigue or poor work methods, or errors due to lack of training Copyright 2011 John Wiley & Sons, Inc.

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SPC in Quality Management

• SPC uses • Is the process in control?

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Quality Measures: Attributes and Variables

• Attribute • A characteristic which is evaluated with a discrete response • good/bad; yes/no; correct/incorrect • Variable measure • A characteristic that is continuous and can be measured • Weight, length, voltage, volume Copyright 2011 John Wiley & Sons, Inc.

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SPC Applied to Services

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SPC Applied to Services

• Hospitals • timeliness & quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance & checkouts • Grocery stores • waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors • Airlines • flight delays, lost luggage & luggage handling, waiting time at ticket counters & check-in, agent & flight attendant courtesy, accurate flight information, cabin cleanliness & maintenance Copyright 2011 John Wiley & Sons, Inc.

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SPC Applied to Services

• Fast-food restaurants • waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy • Catalogue-order companies • order accuracy, operator knowledge & courtesy, packaging, delivery time, phone order waiting time • Insurance companies • billing accuracy, timeliness of claims processing, agent availability & response time Copyright 2011 John Wiley & Sons, Inc.

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Where to Use Control Charts

• Process • Has a tendency to go out of control • Is particularly harmful and costly if it goes out of control • Examples • At beginning of process because of waste to begin production process with bad supplies • Before a costly or irreversible point, after which product is difficult to rework or correct • Before and after assembly or painting operations that might cover defects • Before the outgoing final product or service is delivered Copyright 2011 John Wiley & Sons, Inc.

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Control Charts

• A graph that monitors process quality • Control limits • upper and lower bands of a control chart • Attributes chart • p-chart • c-chart • Variables chart • mean (x bar – chart) • range (R-chart) Copyright 2011 John Wiley & Sons, Inc.

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Process Control Chart

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Normal Distribution

• Probabilities for Z= 2.00 and Z = 3.00

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A Process Is in Control If …

… no sample points outside limits … most points near process average … about equal number of points above and below centerline … points appear randomly distributed Copyright 2011 John Wiley & Sons, Inc.

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Control Charts for Attributes

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p-Chart

UCL =

LCL =



p z p



= number of standard deviations from process average = sample proportion defective; estimates process mean = standard deviation of sample proportion 

p = p

(1 -

)

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Construction of p-Chart

SAMPLE # 1 2 3 : : 20 NUMBER OF DEFECTIVES 6 0 4 : : 18 200 PROPORTION DEFECTIVE .06

.00

.04

: : .18

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Construction of p-Chart

p = total defectives total sample observations = 200 / 20(100) = 0.10

UCL =

z p

(1 -

n p

) = 0.10 + 3 0.10(1 - 0.10) 100 UCL = 0.190

LCL =

z p

(1 -

) = 0.10 - 3

0.10(1 - 0.10) 100 LCL = 0.010

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0.20

0.18

Construction of p-Chart

UCL = 0.190

0.16

0.14

0.12

0.10

= 0.10

0.08

0.06

0.04

0.02

LCL = 0.010

4 6 8 10 12 Sample number 14 16 18 20 3-19

p-Chart in Excel

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c-Chart

UCL =

LCL =



c z



where

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c-Chart

Number of defects in 15 sample rooms SAMPLE NUMBER OF DEFECTS 1 12 2 8 3 16

: : : :

15 15 190

190 = = 12.67

15 UCL =



= 12.67 + 3 12.67

= 23.35

LCL = c - z  c = 12.67 - 3 12.67

= 1.99

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c-Chart

9 6 3 24 21 18 15 12

UCL = 23.35

= 12.67

LCL = 1.99

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Control Charts for Variables



Range chart ( R-Chart )

 Plot sample range (variability) 

Mean chart ( x -Chart )

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x-bar Chart:



Known

UCL = x + z LCL = x - z   -

x x

Where = X = x 1 + x 2 + ... + x k k   x = process standard deviation = standard deviation of sample means = k = number of samples (subgroups)  / n = sample size (number of observations) n Copyright 2011 John Wiley & Sons, Inc.

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x-bar Chart Example:



Known

Observations(Slip-Ring Diameter, cm) n Sample k 1 2 3 4 5 x

We know σ = .08

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x-bar Chart Example:



Known

= 5.09

 -

= X = 10 = 5.01

= 4.93



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x-bar Chart Example:



Unknown

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Control Chart Factors

Factor for X-chart A2 1.880

1.023

0.729

0.577

0.483

0.419

0.373

0.337

0.308

0.285

0.266

0.249

0.235

0.223

0.212

0.203

0.194

0.187

0.180

0.173

0.167

0.162

0.157

0.153

Factors for R-chart D3 0.000

0.000

0.076

0.136

0.184

0.223

0.256

0.283

0.307

0.328

0.347

0.363

0.378

0.391

0.404

0.415

0.425

0.435

0.443

0.452

0.459

D4 3.267

2.575

2.282

2.114

2.004

1.924

1.864

1.816

1.777

1.744

1.717

1.693

1.672

1.653

1.637

1.622

1.609

1.596

1.585

1.575

1.565

1.557

1.548

1.541

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x-bar Chart Example:



Unknown

SAMPLE

1 2 3 4 5 6 7 8 9 10 OBSERVATIONS (SLIP- RING DIAMETER, CM)

1 2 3 4 5 x R

5.02

5.01

4.99

5.03

4.95

4.97

5.05

5.09

5.14

5.01

5.03

5.00

4.91

4.92

5.06

5.01

5.10

4.98

4.94

5.07

4.93

5.01

5.03

5.06

5.10

5.00

4.99

5.08

4.99

4.95

4.92

4.98

5.05

4.96

4.99

5.08

5.07

4.96

4.99

4.89

5.01

5.03

4.99

5.08

5.09

4.99

4.98

5.00

4.97

4.96

4.99

5.01

5.02

5.05

5.08

5.03

0.08

0.12

0.08

0.14

0.13

0.10

0.14

0.11

0.15

0.10

Totals 50.09

1.15

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x-bar Chart Example:



Unknown

_ R = k = 10 = 0.115

___

k x

10 _ = UCL = x + A 2 R = 5.01 + (0.58)(0.115) = 5.08

_ = LCL = x - A 2 R = 5.01 - (0.58)(0.115) = 4.94

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x- bar Chart Example

5.10 – 5.08 – 5.06 – 5.04 – 5.02 – 5.00 – 4.98 – 4.96 – 4.94 – 4.92 – UCL = 5.08

= 5.01

LCL = 4.94

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R- Chart

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SAMPLE

1 2 3 4 5 6 7 8 9 10

R-Chart Example

OBSERVATIONS (SLIP- RING DIAMETER, CM)

1 2 3 4 5 x R

5.02

5.01

4.99

5.03

4.95

4.97

5.05

5.09

5.14

5.01

5.03

5.00

4.91

4.92

5.06

5.01

5.10

4.98

4.94

5.07

4.93

5.01

5.03

5.06

5.10

5.00

4.99

5.08

4.99

4.95

4.92

4.98

5.05

4.96

4.99

5.08

5.07

4.96

4.99

4.89

5.01

5.03

4.99

5.08

5.09

4.99

4.98

5.00

4.97

4.96

4.99

5.01

5.02

5.05

5.08

5.03

0.08

0.12

0.08

0.14

0.13

0.10

0.14

0.11

0.15

0.10

Totals 50.09

1.15

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R-Chart Example

_ UCL = D 4 R = 2.11(0.115) = 0.243

_ LCL = D 3 R = 0(0.115) = 0

Retrieve chart factors D 3 and D 4

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R-Chart Example

0.28 – 0.24 – 0.20 – 0.16 – 0.12 – 0.08 – 0.04 – 0 – UCL = 0.243

= 0.115

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X-bar and R charts – Excel & OM Tools

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Using x- bar and R-Charts Together

• Process average and process variability must be in control • Samples can have very narrow ranges, but sample averages might be beyond control limits • Or, sample averages may be in control, but ranges might be out of control • An R-chart might show a distinct downward trend, suggesting some nonrandom cause is reducing variation Copyright 2011 John Wiley & Sons, Inc.

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Control Chart Patterns

• Run • sequence of sample values that display same characteristic • Pattern test • determines if observations within limits of a control chart display a nonrandom pattern Copyright 2011 John Wiley & Sons, Inc.

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Control Chart Patterns

• To identify a pattern look for: • 8 consecutive points on one side of the center line • 8 consecutive points up or down • 14 points alternating up or down • 2 out of 3 consecutive points in zone A (on one side of center line) • 4 out of 5 consecutive points in zone A or B (on one side of center line) Copyright 2011 John Wiley & Sons, Inc.

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UCL

Control Chart Patterns

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UCL

Control Chart Patterns

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Zones for Pattern Tests

UCL Zone A Zone B = 3 sigma =

= 2 sigma =

2 3

(

) = 1 sigma =

+ (

| 5 | 6 | 7 | 8 Sample number | 9 | 10 | 11 | 12 | 13 =

= 1 sigma =

1 3

(

) 2 sigma = =

2 3

(

) = 3 sigma =

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Performing a Pattern Test

SAMPLE 8 9 10 1 2 3 4 5 6 7

4.98

5.00

4.95

4.96

4.99

5.01

5.02

5.05

5.08

5.03

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Sample Size Determination

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Process Capability

• Compare natural variability to design variability • Natural variability • What we measure with control charts • Process mean = 8.80 oz, Std dev. = 0.12 oz • Tolerances • Design specifications reflecting product requirements • Net weight = 9.0 oz  • Tolerances are  0.5 oz 0.5 oz Copyright 2011 John Wiley & Sons, Inc.

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Process Capability

Design Specifications (a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time.

Process Design Specifications (b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time.

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Process Capability

Design Specifications Process Design Specifications (d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification.

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Process Capability Ratio

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Computing C

p Net weight specification = 9.0 oz  Process mean = 8.80 oz 0.5 oz Process standard deviation = 0.12 oz C p = upper specification limit lower specification limit 6  9.5 - 8.5

= = 1.39

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Process Capability Index

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Computing C

pk Net weight specification = 9.0 oz  Process mean = 8.80 oz 0.5 oz Process standard deviation = 0.12 oz C pk = minimum = x - lower specification limit 3  , = upper specification limit - x 3  8.80 - 8.50

9.50 - 8.80

= minimum , = 0.83

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Process Capability With Excel

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Process Capability With OM Tools

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