Statistical Process Control PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh Edition Principles of Operations Management,

Statistical Process Control

PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh EditionPrinciples of Operations Management, Ninth

Edition

PowerPoint slides by Jeff Heyl

66

© 2014 Pearson Education, Inc.

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Learning Objectives1. Apply quality management tools for

problem solving

2. Identify the importance of data in quality management

6S–6S–22

Introduction

Statistical Quality Control

Statistical Process Control (SPC)

Acceptance Sampling (AS)

Statistical process control is a statistical technique that is widely used to ensure that the process meets standards.

Acceptance sampling is used to determine acceptance or rejection of material evaluated by a sample.

6S–6S–33

Introduction

FiringPreparing

the clay for throwing

Wedging Throwing Pinching pots

Painting

Pottery Making Process

6S–6S–44

Introduction

6S–6S–55

Statistical Process Control Chart (SPC)

Variability is inherent in every process.

Natural variation – can not be eliminated Assignable variation -- Deviation that can be

traced to a specific reason: machine vibration, tool wear, new worker.

Variation

Natural Variation

Assignable Variation

6S–6S–66


The essence of SPC is the application of statistical techniques to prevent, detect, and eliminate defective products or services by identifying assignable variation.

6S–6S–77

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

UCL

LCL

Sample number

Mean

Out ofcontrol

Natural variationdue to chance

Abnormal variationdue to assignable sources

Abnormal variationdue to assignable sources

A control chart is a time-ordered plot obtained from an ongoing process

6S–6S–88



Control Charts

Control Charts for Variable Data

Control Charts for Attribute Data

-charts (for controlling central tendency)x

R-charts (for controlling variation)

p-charts (for controlling percent defective)

c-charts (for controlling number of defects)

Attribute Data (discrete): qualitative characteristic or condition, such as pass/fail, good/bad, go/no go.

Variable Data (continuous): quantifiable conditions along a scale, such as speed, length, density, etc.

6S–6S–99

1. Take random samples

2. Calculate the upper control limit (UCL) and the lower control limit (LCL)

3. Plot UCL, LCL and the measured values

4. If all the measured values fall within the LCL and the UCL, then the process is assumed to be in control and no actions should be taken except continuing to monitor.

5. If one or more data points fall outside the control limits, then the process is assumed to be out of control and corrective actions need to be taken.


6S-10

x-Charts

Lower control limit Lower control limit (LCL)(LCL) = x - A = x - A22RR

Upper control limit Upper control limit (UCL)(UCL) = x + A = x + A22RR

wherewhere RR ==average range of the samplesaverage range of the samples

AA22 ==control chart factor from Table control chart factor from Table S6.1(page 241) S6.1(page 241)

xx ==average of the sample meansaverage of the sample means

6S–6S–1111

Range=18-13=5

Hour 1Hour 1

BoxBox Weight ofWeight ofNumberNumber Oat FlakesOat Flakes

11 1717

22 1313

33 1616

44 1818

55 1717

66 1616

77 1515

88 1717

99 1616

x-Charts

6S–6S–1212

Range=17-14=3

Hour 2Hour 2


11 1414

22 1616

33 1515

44 1414

55 1717

66 1515

77 1515

88 1414

99 1717

RR ==(5+3)/2 = 4(5+3)/2 = 4

x-Charts




AA22 ==control chart factor from Table control chart factor from Table S6.1 (page241) S6.1 (page241)


6S–6S–1313

Average=(17+13+…+16)/9=16.11

Hour 1Hour 1


11 1717

22 1313

33 1616

44 1818

55 1717

66 1616

77 1515

88 1717

99 1616

x-Charts

6S–6S–1414

Average=(14+16+…+17)/9=15.22

Hour 2Hour 2


11 1414

22 1616

33 1515

44 1414

55 1717

66 1515

77 1515

88 1414

99 1717

xx ==(16.11+15.22)/2 = 15.665(16.11+15.22)/2 = 15.665

x-Charts






6S–6S–1515

x-Charts Sample Size Sample Size Mean Factor Mean Factor Upper Range Upper Range Lower Lower RangeRange

n n AA22 DD44 DD3322 1.881.88 3.273.27 00

33 1.021.02 2.582.58 00

44 .73.73 2.282.28 00

55 .58.58 2.122.12 00

66 .48.48 2.002.00 00

77 .42.42 1.921.92 0.080.08

88 .37.37 1.861.86 0.140.14

99 .34.34 1.821.82 0.180.18

1010 .31.31 1.781.78 0.220.22

1111 .29.29 1.741.74 0.260.26

6S–6S–1616

x-Charts






6S–6S–1717

x-Charts Example S6.1: Eight samples of seven tubes were taken at random intervals. Construct the x-chart with 3- control limit. Is the current process under statistical control? Why or why not? Should any actions be taken?

Sample size = n = 7

A2 = ?

Sample number Mean Range

1 6.36 0.16 2 6.38 0.18 3 6.35 0.17 4 6.40 0.20 5 6.32 0.15 6 6.34 0.16 7 6.39 0.16 8 6.34 0.18

6S–6S–1818

x-Charts

6S–6S–1919

Sample Size Sample Size Mean Factor Mean Factor Upper Range Upper Range Lower Lower RangeRange

n n AA22 DD44 DD3322 1.881.88 3.273.27 00

33 1.021.02 2.582.58 00

44 .73.73 2.282.28 00

55 .58.58 2.122.12 00

66 .48.48 2.002.00 00

77 .42.42 1.921.92 0.080.08

88 .37.37 1.861.86 0.140.14

99 .34.34 1.821.82 0.180.18

1010 .31.31 1.781.78 0.220.22

1111 .29.29 1.741.74 0.260.26

x-Charts

oz 29.6)17.0(42.036.62 RAxLCL

oz 36.68

34.6...38.636.6

x

oz 43.6)17.0(42.036.62 RAxUCL

oz 17.08

18.0...18.016.0

R

Example S6.1: Eight samples of seven tubes were taken at random intervals. Construct the x-chart with 3- control limit. Is the current process under statistical control? Why or why not? Should any actions be taken?

A2 = 0.42


1 6.36 0.16 2 6.38 0.18 3 6.35 0.17 4 6.40 0.20 5 6.32 0.15 6 6.34 0.16 7 6.39 0.16 8 6.34 0.18

6S–6S–2020

x-Charts Control Chart Control Chart for sample of for sample of 7 tubes7 tubes

6.43 = UCL6.43 = UCL

6.29 = LCL6.29 = LCL

6.36 = Mean6.36 = Mean

Sample numberSample number

|| || || || || || || || || || || ||11 22 33 44 55 66 77 88 99 1010 1111 1212

It is assumed that the central tendency of process is in control with 99.73% confidence. No actions need to be taken except to continuously monitor this process.

6S–6S–2121

Steps in Creating Charts

1. Take samples from the population and compute the appropriate sample statistic

2. Use the sample statistic to calculate control limits

3. Plot control limits and measured values

4. Determine the state of the process (in or out of control)

5. Investigate possible assignable causes and take actions

6S–6S–2222

R-Charts

Lower control limit Lower control limit (LCL)(LCL) = D = D33RR

Upper control limit Upper control limit (UCL)(UCL) = D = D44RR

wherewhere

RR ==average range of the samplesaverage range of the samples

DD33 and D and D44==control chart factors from control chart factors from Table S6.1 (Page 241) Table S6.1 (Page 241)

6S–6S–2323

R-Charts

6S–6S–2424


n n AA22 DD44 DD3322 1.881.88 3.273.27 00

33 1.021.02 2.582.58 00

44 .73.73 2.282.28 00

55 .58.58 2.122.12 00

66 .48.48 2.002.00 00

77 .42.42 1.921.92 0.080.08

88 .37.37 1.861.86 0.140.14

99 .34.34 1.821.82 0.180.18

1010 .31.31 1.781.78 0.220.22

1111 .29.29 1.741.74 0.260.26

R-Charts

Average range R Average range R = 5.3 = 5.3 poundspoundsSample size n Sample size n = 5= 5From From Table S6.1Table S6.1 D D44 = ? = ? DD33 = ? = ?

Example S6.2Example S6.2

6S–6S–2525

R-Charts

6S–6S–2626


n n AA22 DD44 DD3322 1.881.88 3.273.27 00

33 1.021.02 2.582.58 00

44 .73.73 2.282.28 00

55 .58.58 2.122.12 00

66 .48.48 2.002.00 00

77 .42.42 1.921.92 0.080.08

88 .37.37 1.861.86 0.140.14

99 .34.34 1.821.82 0.180.18

1010 .31.31 1.781.78 0.220.22

1111 .29.29 1.741.74 0.260.26

R-Charts

UCLUCLRR = D= D44RR

= (2.12)(5.3)= (2.12)(5.3)= 11.2 = 11.2 poundspounds

LCLLCLRR = D= D33RR

= (0)(5.3)= (0)(5.3)= 0 = 0 poundspounds

Average range R Average range R = 5.3 = 5.3 poundspoundsSample size n Sample size n = 5= 5From From Table S6.1Table S6.1 D D44 = 2.12, = 2.12, DD33 = 0 = 0

UCL = 11.2UCL = 11.2

Mean = 5.3Mean = 5.3

LCL = 0LCL = 0

Example S6.2Example S6.2

6S–6S–2727

R-Charts

oz 17.08

18.0...18.016.0

R

n=7

Example S6.3: Refer to Example S6.1. Eight samples of seven tubes were taken at random intervals. Construct the R-chart with 3- control limits. Is the current process under statistical control? Why or why not? Should any actions be taken?

D3 =? D4 = ?


1 6.36 0.16 2 6.38 0.18 3 6.35 0.17 4 6.40 0.20 5 6.32 0.15 6 6.34 0.16 7 6.39 0.16 8 6.34 0.18

6S–6S–2828

R-Charts

6S–6S–2929


n n AA22 DD44 DD3322 1.881.88 3.273.27 00

33 1.021.02 2.582.58 00

44 .73.73 2.282.28 00

55 .58.58 2.122.12 00

66 .48.48 2.002.00 00

77 .42.42 1.921.92 0.080.08

88 .37.37 1.861.86 0.140.14

99 .34.34 1.821.82 0.180.18

1010 .31.31 1.781.78 0.220.22

1111 .29.29 1.741.74 0.260.26

R-Charts

oz 17.08

18.0...18.016.0

R


1 6.36 0.16 2 6.38 0.18 3 6.35 0.17 4 6.40 0.20 5 6.32 0.15 6 6.34 0.16 7 6.39 0.16 8 6.34 0.18

6S–6S–3030

Example S6.3: Refer to Example S6.1. Eight samples of seven tubes were taken at random intervals. Construct the R-chart with 3- control limits. Is the current process under statistical control? Why or why not? Should any actions be taken?

oz 01.0)17.0(08.03 RDLCL

oz 33.0)17.0(92.14 RDUCL

D3 =0.08, D4 = 1.92

R-ChartsControl Chart Control Chart for sample of for sample of 7 tubes7 tubes

0.33 = UCL0.33 = UCL

0.01 = LCL0.01 = LCL


|| || || || || || || || || || || ||11 22 33 44 55 66 77 88 99 1010 1111 1212

0.17 = R0.17 = R

The variation of process is in control with 99.73% confidence.

6S–6S–3131

Mean and Range Charts

R-chartR-chart(R-chart detects (R-chart detects increase in increase in dispersion)dispersion)

UCLUCL

LCLLCL

(a) The central tendency of process is in control, but its variation is not in control.

x-chartx-chart(x-chart does not (x-chart does not detect dispersion)detect dispersion)

UCLUCL

LCLLCL

6S–6S–3232

Mean and Range Charts(b) The variation of process is in control, but its central tendency is not in control.

R-chartR-chart(R-chart does not (R-chart does not detect changes in detect changes in mean)mean)

UCLUCL

LCLLCL

x-chartx-chart(x-chart detects (x-chart detects shift in central shift in central tendency)tendency)

UCLUCL

LCLLCL

6S–6S–3333

R-Chart and X-ChartExample S6.4: Seven random samples of four resistors each are taken to establish the quality standards. Develop the R-chart and the x-chart both with 3- control limits for the production process. Is the entire process under statistical control? Why or why not?

Sample Number Sample Range Sample Mean

1 3 100.5 2 2 101.5 3 4 100.0 4 1 99.5 5 2 99.0 6 5 97.0 7 4 101.0

D3 = 0, and D4 = 2.28

n = 4

R = (3 + 2 + … + 4)/7 = 3.0

0)0.3(03 RDLCL

6.84)0.3(28.24 RDUCL

6S–6S–3434

R-Chart and X-ChartControl Chart Control Chart for sample of for sample of 4 resistors4 resistors

6.84 = UCL6.84 = UCL

0 = LCL0 = LCL


|| || || || || || || || || || || ||11 22 33 44 55 66 77 88 99 1010 1111 1212

3.0 = R3.0 = R

The variation of process is in control with 99.73% confidence.

6S–6S–3535

R-Chart and X-Chart

X= (100.5 + 101.5 + … + 101.0)/7 99.79

Sample Number Sample Range Sample Mean

1 3 100.5 2 2 101.5 3 4 100.0 4 1 99.5 5 2 99.0 6 5 97.0 7 4 101.0

n = 4, A2 = 0.73

R = (3 + 2 + … + 4)/7 = 3.0

97.6)0.3(73.079.992 RAxLCL

101.98)0.3(73.079.992 RAxUCL

6S–6S–3636

R-Chart and X-ChartsControl ChartControl Chart

101.98 = UCL101.98 = UCL

97.6 = LCL97.6 = LCL

99.79 = Mean99.79 = Mean


|| || || || || || || || || || || ||11 22 33 44 55 66 77 88 99 1010 1111 1212

The central tendency of process is not in control with 99.73% confidence.

In conclusion, with 99.7% confidence, the entire resistor production process is not in control since its central tendency is out of control although its variation is under control.

6S–6S–3737

EX 1 in classA part that connects two levels should have a distance between the two holes of 4”. It has been determined that x-bar chart and R-chart should be set up to determine if the process is in statistical control. The following ten samples of size four were collected. Calculate the control limits, plot the control charts, and determine if the process is in control

No. of Sample Mean Range

1 4.01 0.04

2 3.98 0.06

3 4.00 0.02

4 3.99 0.05

5 4.00 0.06

6 3.97 0.02

7 4.02 0.02

8 3.99 0.04

9 3.98 0.05

10 4.01 0.066S–6S–3838

R-Chart and X-Chart

6S–6S–3939

Example S6.5: Resistors for electronic circuits are manufactured at Omega Corporation in Denton, TX. The head of the firm’s Continuous Improvement Division is concerned about the product quality and sets up production line checks. She takes seven random samples of four resistors each to establish the quality standards. Develop the R-chart and the chart both with 3- control limits for the production process. Is the entire process under statistical control? Why or why not?

# of sample Readings of Resistance (ohms)

1 99 100 102 101

2 101 103 101 101

3 98 102 101 99

4 99 100 99 100

5 99 99 98 100

6 95 100 97 96

7 101 99 101 103

R-Chart and X-Chart# of Sample 1 2 3 4 5 6 7

Sample range 3 2 4 1 2 5 4

Sample mean 100.5 101.5 100.0 99.5 99.0 97.0 101.0

3.07

4...23

R n=4 D3 =0 D4 = 2.28

03 RDLCL

84.60.328.24 RDUCL

6.84 = UCL6.84 = UCL

0 = LCL0 = LCL


|| || || || || || || || || || || ||11 22 33 44 55 66 77 88 99 1010 1111 1212

3.0 = R3.0 = Rvariation of process is in control with 99.73% confidence.

6S–6S–4040

R-Chart and X-Chart# of Sample 1 2 3 4 5 6 7

Sample range 3 2 4 1 2 5 4

Sample mean 100.5 101.5 100.0 99.5 99.0 97.0 101.0

3.07

4...23

R

n=4

102.0 = UCL102.0 = UCL

97.6 = LCL97.6 = LCL


|| || || || || || || || || || || ||11 22 33 44 55 66 77 88 99 1010 1111 1212

99.8 = X99.8 = X

central tendency of process is not in control with 99.73% confidence.

Thus, entire process is not in control.

6S–6S–4141

A2 =0.73

X= (100.5 + … + 101.0)/7 99.8

97.6)0.3(73.08.992 RAxLCL

102.0)0.3(73.08.992 RAxUCL

EX 2 in classA quality analyst wants to construct a sample mean chart for controlling a packaging process. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below. Set up control charts to determine if the process is in statistical control

Day Package 1 Package 2 Package 3 Package 4

Monday 23 22 23 24

Tuesday 23 21 19 21

Wednesday 20 19 20 21

Thursday 18 19 20 19

Friday 18 20 22 20

6S–6S–4242


Control Charts

Control Charts for Variable Data

Control Charts for Attribute Data

-charts (for controlling central tendency)x

R-charts (for controlling variation)

p-charts (for controlling percent defective)

c-charts (for controlling number of defects)

Attribute Data (discrete): qualitative characteristic or condition, such as pass/fail, good/bad, go/no go.

Variable Data (continuous): quantifiable conditions along a scale, such as speed, length, density, etc.

6S–6S–4343

Control Charts for Attribute Data Categorical variables

Good/bad, yes/no, acceptable/unacceptable Measurement is typically counting defectives Charts may measure

Percentage of defects (p-chart) Number of defects (c-chart)

6S–6S–4444

P-Charts

n

ppzpzpUCL p

)1(ˆ

wherewhere pp ==mean percent defective overall the mean percent defective overall the samplessampleszz ==number of standard deviations = 3number of standard deviations = 3nn ==sample sizesample size

n

ppzpzpLCL p

)1(ˆ

6S–6S–4545

P-Charts

SampleSample NumberNumber PercentPercent SampleSample NumberNumber PercentPercentNumberNumber of Errorsof Errors DefectiveDefective NumberNumber of Errorsof Errors DefectiveDefective

11 66 .06.06 1111 66 .06.0622 55 .05.05 1212 11 .01.0133 00 .00.00 1313 88 .08.0844 11 .01.01 1414 77 .07.0755 44 .04.04 1515 55 .05.0566 22 .02.02 1616 44 .04.0477 55 .05.05 1717 1111 .11.1188 33 .03.03 1818 33 .03.0399 33 .03.03 1919 00 .00.00

1010 22 .02.02 2020 44 .04.04

Total Total = 80= 80

Example S6.6: Data-entry clerks at ARCO key in thousands of insurance records each day. One hundred records entered by each clerk were carefully examined and the number of errors counted. Develop a p-chart with 3- control limits and determine if the process is in control.

6S–6S–4646

P-Charts

040.0)20)(100(

80

examined records ofnumber Total

errors ofnumber Totalp

099.0100

)04.01(04.0304.0

)1(

n

ppzpUCL

0019.0100

)04.01(04.0304.0

)1(

n

ppzpLCL

n = 100

Because we cannot have a negative percent defective

040.020

04.0...05.006.0

samples ofNumber

defectivefraction Total ,

por

6S–6S–4747

P-Charts.11 .11 –.10 .10 –.09 .09 –.08 .08 –.07 .07 –.06 .06 –.05 .05 –.04 .04 –.03 .03 –.02 .02 –.01 .01 –.00 .00 –


Per

cen

t d

efec

tive

Per

cen

t d

efec

tive

| | | | | | | | | |

22 44 66 88 1010 1212 1414 1616 1818 2020

UCL= 0.10UCL= 0.10

LCL= 0.00LCL= 0.00

p p = 0.04= 0.04

Possible assignable

causes present

Possible good assignable causes present

The process is not in control with 99.73% confidence.

6S–6S–4848

C-Charts A c-chart is used when the quality cannot be

measured as a percentage. Number of car accidents per month at a particular

intersection Number of complaints the service center of a hotel

receives per week Number of scratches on a nameplate Number of dimples found on a metal sheet

6S–6S–4949

C-Charts

wherewhere cc ==mean number defective overall the samplesmean number defective overall the samples

UCLUCL = c + = c + 33 c c LCLLCL = c - = c - 33 c c

6S–6S–5050

C-Charts

c c = 54 / 9= 54 / 9 = 6 = 6 complaints complaints //weekweek

|1

|2

|3

|4

|5

|6

|7

|8

|9

Week NumberWeek Number

Nu

mb

er o

f d

efec

tN

um

ber

of

def

ect14 14 –

12 12 –

10 10 –

8 8 –

6 6 –

4 –

2 –

0 0 –

UCLUCL = 13.35= 13.35

LCLLCL = 0= 0

c c = 6= 6

Example S6.7: Over 9 weeks, Red Top Cab company received the following numbers of calls from irate passengers: 3, 0, 8, 9, 6, 7, 4, 9, 8, for a total of 54 complaints. Determine the 3- control limits of a c-Chart.

Because we cannot have the negative number of defective records

UCLUCL = c + = c + 33 c c= 6 + 3 6= 6 + 3 6= 13.35= 13.35

LCLLCL = c - = c - 33 c c= 6 - 3 6= 6 - 3 6= - 1.35 => 0= - 1.35 => 0

The process is in control with 99.73% confidence.

6S–6S–5151

1. Effective quality management is data driven

2. There are multiple tools to identify and prioritize process problems

3. There are multiple tools to identify the relationships between variables

Managing Quality Summary

6S–6S–5252

Documents

Statistical Process Control PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh Edition Principles of Operations Management,