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A Process Control Screen for Multiple Stream Processes. An Operator Friendly Approach. Richard E. Clark Process & Product Analysis. Injection Molding Extrusion Blow Molding Reheat Stretch Blow Molding Thermoforming Multilayer Sheet Extrusion. Double Seaming Filling Machines - PowerPoint PPT Presentation
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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