a process control screen for multiple stream processes

A Process Control Screen for Multiple Stream Processes

An Operator Friendly Approach

Richard E. Clark

Process & Product Analysis

Multiple Stream Processes

• Injection Molding• Extrusion Blow

Molding• Reheat Stretch Blow

Molding• Thermoforming• Multilayer Sheet

Extrusion

• Double Seaming• Filling Machines• Heat Sealing

Machines• Labelers

History

Year 1978 1993

Number of Stations 4 48

Production Rate 2400 48000

Number of Characteristics Monitored

6 10+

Number of Charts Monitored 24 480+

Method of Collection and Analysis Manual Computer

The Object of This Paper is to Describe a System of Charts

to Be Used by Operators and/or Inspectors to Control Multiple Stream Processes.

The Operator Needs to Know

– That the process is adjusted so that the average of the characteristic being monitored is equal to the targeted mean.

– That the means and variation of the individual streams are being maintained within an acceptable range.

– That the pattern of variation among streams is stable.

– That the individual items from all stations are conforming to internal or customer specification limits.

Process Model

Yijk = + Ti + Pj + k(ij)

i = 1, 2, …, t j = 1, 2, …, p K = 1, 2, …, n

represents the process mean.

Ti is an independently and normally distributed random variable with mean 0 and variance t

2 which represents the process variation with time. By definition, TI equals 0 for an in control process.

Pj is a fixed value representing the effect of station j. In order for the process average to = , the sum of the Pj over the j stations must be 0.

Process Model (cont.)

k(ij) is an independently and normally distributed random variable with mean 0 and variance 2 resulting from random variation in the process and measurement system. For this paper, 2 is assumed to be constant for all positions and times.

Observations from an “In Control” 5 Station Machine are Shown in the Table

Below

Station Value

1 Yi11 = + 0 + P1 + 1(I,1)

2 Yi21 = + 0 + P2 + 1(I,2)

3 Yi31 = + 0 + P3 + 1(I,3)

4 Yi41 = + 0 + P4 + 1(I,4)

5 Yi51 = + 0 + P5 + 1(I,5)

Average Computation

The average value for time i is calculated using the following equation._

Yi.. = (5* + P1 + P2 + P3 + P4 + P5 + 1(I,1) + 1(I,2) +

1(I,3) + 1(I,4) + 1(I,5))/5

By definition P1 + P2 + P3 + P4 + P5 = 0 and the expected

values for 1(i,j)’s is 0. Therefore;

_

Yi.. =

And is an unbiased estimate of the population mean.

Confidence Intervals

The random component in each observation, k(ij), is

independent of other observations and randomly distributed with mean 0 and variance 2 . _Therefore, the confidence intervals for the means and observations from this process at time i are as follows.

The mean at time i

_Yi.. ± 3*/√5

The mean for each position is:_

Y.j. = + Pj

Confidence Intervals (cont.)

And the confidence intervals for control limits for the measurements from each position for an “in control” process are:

_ YK(ij) = Y.j. ± 3*

Distributions Used to Generate Data for Examples

Station Average Standard Deviation

19 19.0 1.00

20 20.0 1.00

21 21.0 1.00

22 22.0 1.00

23 23.0 1.00

DataStation

Set 19 20 21 22 23 Ave. Range2 19.4 20.2 20.4 22.6 22.8 21.08 3.43 18.6 21 20.8 22.2 23.2 21.16 4.64 20.6 19.4 20.8 22.2 22.4 21.08 35 17.4 20.6 19.2 22.2 24 20.68 6.66 21.8 21 21.6 22.6 23.2 22.04 2.27 20.6 19.8 20.4 22.2 23.6 21.32 3.88 19 19.4 19.2 23 22.8 20.68 49 19.4 20.2 22.6 23 22.8 21.6 3.6

10 19.4 20.2 19.2 21 21.2 20.2 211 18.2 21 22.8 22.6 21.2 21.16 4.612 18.6 19.4 20.4 22.2 21.6 20.44 3.613 18.6 21 20.4 20.2 25.2 21.08 6.614 19.4 20.6 21.6 21.4 22 21 2.615 20.2 21.4 22.8 22.6 22.4 21.88 2.616 17 19 20 23 22.8 20.36 617 19.8 20.2 21.2 22.2 24.4 21.56 4.618 19.8 21 20 22.2 23.6 21.32 3.819 18.6 20.6 20 22.2 22.4 20.76 3.820 18.2 18.6 21.2 22.6 22 20.52 4.421 18.6 19.4 20 22.6 23.2 20.76 4.622 18.6 18.2 20 23.8 22.4 20.6 5.623 19 19 20.4 23 24 21.08 524 17.8 19.4 20.8 22.6 22.8 20.68 525 17.8 19 20.8 22.2 23.2 20.6 5.426 19 19.8 20.8 24.2 22.8 21.32 5.227 19.4 20.2 20 21.4 21.6 20.52 2.228 19.4 19.8 22.4 23.8 22.8 21.64 4.429 19 19.4 22 23.4 23.2 21.4 4.430 18.6 20.6 21.6 20.2 20.8 20.36 331 19 20.6 20.8 20.6 23.2 20.84 4.232 17.8 19.4 20 22.6 24 20.76 6.233 20.2 20.2 22.4 23 23.2 21.8 334 21 20.2 21.6 21.4 20.4 20.92 1.435 18.2 19.4 22.4 21.8 22.8 20.92 4.636 19 19.4 21.2 21.8 22 20.68 337 19.4 20.6 20.8 22.2 24 21.4 4.638 18.2 19.8 19.6 23.8 22 20.68 5.639 18.2 19.4 19.6 21.8 23.2 20.44 540 17.4 20.6 20.8 23 22 20.76 5.641 20.6 19.8 22 23 24.4 21.96 4.642 20.2 20.6 21.2 24.6 25.6 22.44 5.443 18.2 19.8 19.6 20.6 25.6 20.76 7.444 19.4 19 21.2 23.4 22 21 4.445 19.8 19.8 20 23.4 23.6 21.32 3.846 18.2 21 21.6 21.8 23.2 21.16 547 19 19.8 21.6 21.8 24 21.24 548 19 21.4 20.8 22.2 23.6 21.4 4.649 17.8 19 20 23.4 23.6 20.76 5.850 17.8 20.2 21.6 21.8 23.2 20.92 5.4

Average 18.984 19.988 20.861 22.396 22.980 21.042R-bar MR(2) 1.05 0.9 1.15 1.02 1.17 1.058

DataStation

Set 19 20 21 22 23 Ave. Range38 18.2 19.8 19.6 23.8 22 20.68 5.639 18.2 19.4 19.6 21.8 23.2 20.44 540 17.4 20.6 20.8 23 22 20.76 5.641 20.6 19.8 22 23 24.4 21.96 4.642 20.2 20.6 21.2 24.6 25.6 22.44 5.443 18.2 19.8 19.6 20.6 25.6 20.76 7.444 19.4 19 21.2 23.4 22 21 4.445 19.8 19.8 20 23.4 23.6 21.32 3.846 18.2 21 21.6 21.8 23.2 21.16 5

Note: Sample 42 – All Values above mean with two by moreThan 2 std. Dev.

Proposed Screen

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Parameters Required to Calculate Control Limits for the Proposed Charts

• Within Station Standard Deviation Inherent in the Process

• Position Allowance for Maximum Position• Position Allowance for Minimum Position

Estimation of Within Position Inherent Standard Deviation

• Estimate from Within Position Moving Range Data

• Estimate from Analysis of Variance Residual after Removing Effects of Time and Position

• Estimate from Analysis of Sample Means

• Compare to Historical Data

Estimate of Standard Deviation based on RangeParameter 19 20 21 22 23 Ave.Average 18.984 19.988 20.861 22.396 22.980 21.042R-bar MR(2) 1.05 0.9 1.15 1.02 1.17 1.058d2 1.128 1.128 1.128 1.128 1.128 1.128Est. Sigma 0.931 0.798 1.020 0.904 1.037 0.938

Estimates of Standard Deviation Based on Within Positon Moving Range

Analysis of Variance for Values - Type III Sums of Squares--------------------------------------------------------------------------------Source Sum of Squares Df Mean Square F-Ratio P-Value--------------------------------------------------------------------------------MAIN EFFECTS A:Set 56.5433 48 1.17799 1.34 0.0868 B:Station 537.441 4 134.36 152.80 0.0000

RESIDUAL 168.831 192 0.87933--------------------------------------------------------------------------------TOTAL (CORRECTED) 762.815 244--------------------------------------------------------------------------------All F-ratios are based on the residual mean square error.

Factor SS df MS sError 168.831 192 0.87933 0.938Time 56.5433 48Pooled Error 225.3743 240 0.939059583 0.969

Since Time is not significant, the SS for Time and Error can be pooled to improve the estimate of s.

10 20 30 40 50

0.0

0.5

1.0

1.5

2.0

Mo

vin

g R

ang

e

Summary

0.000

0.578

1.888

Sep 27, 2002 11:08:54

Moving Range Chart

Moving Range Chart for Sample Averages

R-bar - Moving Rande Set Averages 0.578d2 1.128sy-bar 0.512y-bar 21.043UCLy-bar 22.580LCLy-bar 19.506Sample Size 5.000s 1.146

Estimate of Standard Deviation Based on Analysis of Sample Averages

Individuals Control Chart of Sample Averages

10 20 30 40

19

20

21

22

23

MV

.Mea

n

Summary

19.504

21.042

22.580

Oct 6, 2002 16:39:38

Item Chart

Estimation of Position Effects PMax & PMin

• Historical Position Averages when Process is Stable

• Analysis of Variance – Position Means • Engineering Judgment of Reasonable Ranges

Chart Parameters

Parameter Calculation Value

Center Line Y-double bar 21.00

UCL Average Y-double bar + 3*/?5

22.34

LCL Average Y-double bar - 3*/?5

19.66

UCL Individual Y-double bar Pmax + 3*

26

LCL Individual Y-double bar+Pmin - 3*

16

Mean = 21.0 = 1 Pmin = Pmax = 2

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Data from “In Control” Process

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Out of Control

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A A

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Average for All Stations Increased by 1 for the Last Point

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A A A

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Average for All Stations Increased by 1 for the Last 10 Points

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Std. Dev. For Station 20 Increased to 2 for last 5 points

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A

B

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

HFI Out of Spec. Low

Summary

LSL

CLS

USLMin. & Max. Values

B

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Std. Dev. For Station 20 Increased to 2 for last 23 points

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Average for Station 21 Increased to 22 for last 10 points

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Average for Station 21 Increased to 22 for last 24 points

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Out of Control

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A A

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Average for Station 21 Increased by 3 for last 6 points

10 20 30 4019.019.520.020.521.021.522.022.523.0

Ave

rag

e

Out of Control

Summary

LCL

CL

UCL

Lid Holes Demonstration Data

A A A

4 8 12 16 20 24 28 32 36 40 44 4815171921232527

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary

19 20 21 22 23

Box Plot by Mold (Station)

15171921232527

Val

ues

Average for Station 21 Increased by 3 for last 24 points

“Real World” Chart

10 20 3014.5

15.0

15.5

16.0

16.5

17.0

Ave

rag

e

Summary

LCL

CL

UCL

Weigtht

B

A A

AA

A

B

AA

A

4 8 12 16 20 24 28 3214.014.515.015.516.016.517.017.518.0

Ind

.

Summary

LSL

CLS

USL

Min. & Max. Values

A

Summary

AAA A AA

1 2 3 4 5 6

Box Plot by Mold (Station)

14.014.515.015.516.016.517.017.518.0

wei

gh

t

Data Through Set 35

10 20 3016.016.517.017.518.018.519.019.5

Ave

rag

e

Out of Control

Summary

LCLCLUCL

Weight

AA A A

A AA

A AA A

AA

AA A A A A A A A

AA

A

4 8 12 16 20 24 28 3214

16

18

20

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary A A AAA

1 2 3 4 5 6 7 8 9 10

Box Plot by Mold (Station)

14

16

18

20

Bas

eWt

Last 48 Data Sets

10 20 30 4016.016.517.017.518.018.519.019.5

Ave

rag

e

Out of Control

Summary

LCLCLUCL

Weight

AA

AAA AAAAAA

AA

A

B

BBB B

BBB B

B

BB

AA

A

4 8 12 16 20 24 28 32 36 40 44 4814

16

18

20

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

BBBBBB BBBBBBBBBB

BB

B

BB

Summary AAA

1 2 3 4 5 6 7 8 9 10

Box Plot by Mold (Station)

14

16

18

20

Bas

eWt

10 20 30 401196.01196.51197.01197.51198.01198.51199.01199.51200.0

Ave

rag

e

Out of Control

Summary

LCL

CL

UCL

Fill

A

BB B

A

B

AA A A

A

A

4 8 12 16 20 24 28 32 36 40119011921194119611981200120212041206

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary A

1 2 34 5 6 78 9101112131415161718192021222324

Box Plot by Mold (Station)

119011921194119611981200120212041206

Fil

l

24 Station Machine

24 Station Rotary Machine

1 2 3 4 5 6 7 8 9 10 11 12118911901191119211931194119511961197

Ave

rag

e

Out of Control

Summary

LCLCLUCL

Fill

A

A

BB

A

4 8 121185

1189

1193

1197

1201

Ind

.

Summary

LSL

CLS

USLMin. & Max. Values

Summary A

1 2 34 5 6 78 9101112131415161718192021222324

Box Plot by Mold (Station)

1185

1189

1193

1197

1201F

ill

Evaluation of Screen Change

• Robust Container• Relatively Low Production Rate• Stable Process with Minimal Problems• Before ~ 3300 Observation • After 1 Year ~ 3300 Observations

Comparison of Probability Distributions Section B Before and After

10.0 12.5 15.0 17.5 20.0

.01

.50

.99

SectionB

No

rmal

Pro

bab

ilit

y

.05

.95

.10

.90

.25

.75

Before

SectionBTheoretical

Test for Normality:Not applicable

Probability Plot

10.0 12.5 15.0 17.5 20.0

.01

.50

.99

SectionB

No

rmal

Pro

bab

ilit

y

.05

.95

.10

.90

.25

.75

After

SectionBTheoretical

Test for Normality:Not applicable

Probability Plot

Comparison of Frequency Histograms Section B

0100200300400500

600

Fre

qu

ency

After

10.0 12.5 15.0 17.5 20.0

0

100

200

300

400

Fre

qu

ency

Before

10.0 12.5 15.0 17.5 20.0

Comparison of Statistics for Section B

Statistic Before After

Average 15.98 16.003

Q3 16.65 16.5

Q1 15.4 15.55

Q3-Q1 Range 1.25 0.95

Std. Dev. (Not Normal)

0.943 0.749

Cpk (Not Normal)

0.787 1.003

Comparison of Probability Distributions Section A

9 10 11 12 13

.01

.50

.99

SectiionA

No

rmal

Pro

bab

ilit

y

.05

.95

.10

.90

.25

.75

Before

SectiionATheoretical

Probability Plot

9 10 11 12 13

.01

.50

.99

SectionA

No

rmal

Pro

bab

ilit

y

.05

.95

.10

.90

.25

.75

After

SectionATheoretical

Probability Plot

Comparison of Frequency Histograms Section A

0

200

400

600

800

Fre

qu

ency

After

9 10 11 12 13

0

100

200

300

400

Fre

qu

ency

Before

9 10 11 12 13

Statistic Before After

Average 11.013 11.232

Q3 11.25 11.35

Q1 10.75 11.1

Q3-Q1 Range 0.5 0.25

Std. Dev. (Not Normal)

0.393 0.232

Cpk (Not Normal)

0.477 1.123

Comparison of Statistics for Section A

Compare Probability Distributions Height

9.800 9.825 9.850 9.875 9.900 9.925

.01

.50

.99

Height

No

rmal

Pro

bab

ilit

y

.05

.95

.10

.90

.25

.75

After

HeightTheoretical

Test for Normality:Not applicable

Probability Plot

9.800 9.825 9.850 9.875 9.900 9.925

.01

.50

.99

height

No

rmal

Pro

bab

ilit

y

.05

.95

.10

.90

.25

.75

Before

heightTheoretical

Test for Normality:Not applicable

Probability Plot

0100200300400

500600

Fre

qu

ency

After

9.800 9.825 9.850 9.875 9.900 9.925

0100200300400

500600

Fre

qu

ency

Before

9.800 9.825 9.850 9.875 9.900 9.925

Comparison of Statistics for Height

Statistic Before After

Average 9.888 9.872

Q3 9.896 9.879

Q1 9.881 9.865

Q3-Q1 Range 0.015 0.014

Std. Dev. (Not Normal)

0.00118 0.01169

Cpk (Not Normal)

0.907 1.208

Conclusion

• Process control has improved substantially since the new screen was introduced on this line.

• Since there is no control, it is not possible to determine how much if any of the improvement was due to the change.

• “Hawthorne” Effect

Other Areas to Consider

• Add Hidden Tests to Determine when a Change Occurs Between or Within Stations. Display Message when an “Out of Control” Condition Occurs

• Replace Capability Index with and Index of Potential Process Improvement

• Statistics for Measurement and Control of Contaminates in Post-Consumer Flake

Process & Product Analysis

Richard E. Clark

(630) 584 0566

r.clark@worldnet.att.net