1. A Process Control Screen for Multiple Stream Processes An Operator Friendly Approach Richard E. Clark Process & Product Analysis

2. Multiple Stream Processes Injection Molding Extrusion Blow Molding Reheat Stretch Blow Molding Thermoforming Multilayer Sheet Extrusion Double Seaming Filling Machines Heat Sealing Machines Labelers

3. History Year19781993 Number of Stations448 Production Rate240048000 Number of Characteristics Monitored 610+ Number of Charts Monitored24480+ Method of Collection and AnalysisManualComputer

4. 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.

5. 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.

6. Process Model Y ijk =  + T i + P j +  k(ij) i = 1, 2, …, t j = 1, 2, …, p K = 1, 2, …, n  represents the process mean. T i is an independently and normally distributed random variable with mean 0 and variance  t 2 which represents the process variation with time. By definition, T I equals 0 for an in control process. P j is a fixed value representing the effect of station j. In order for the process average to = , the sum of the P j over the j stations must be 0.

7. 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.

8. Observations from an “In Control” 5 Station Machine are Shown in the Table Below StationValue 1 Y i11 =  + 0 + P 1 +  1(I,1) 2 Y i21 =  + 0 + P 2 +  1(I,2) 3 Y i31 =  + 0 + P 3 +  1(I,3) 4 Y i41 =  + 0 + P 4 +  1(I,4) 5 Y i51 =  + 0 + P 5 +  1(I,5)

9. Average Computation The average value for time i is calculated using the following equation. _ Y i.. = (5*  + P 1 + P 2 + P 3 + P 4 + P 5 +  1(I,1) +  1(I,2) +  1(I,3) +  1(I,4) +  1(I,5) )/5 By definition P 1 + P 2 + P 3 + P 4 + P 5 = 0 and the expected values for  1(i,j) ’s is 0. Therefore; _ Y i.. =  And is an unbiased estimate of the population mean.

10. 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 _ Y i.. ± 3*  /√5 The mean for each position is: _ Y.j. =  + P j

11. Confidence Intervals (cont.) And the confidence intervals for control limits for the measurements from each position for an “in control” process are: _ Y K(ij) = Y.j. ± 3* 

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

15. Proposed Screen

16. 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

17. 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

18. Estimates of Standard Deviation Based on Within Positon Moving Range

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

21. Moving Range Chart for Sample Averages

22. Estimate of Standard Deviation Based on Analysis of Sample Averages

23. Individuals Control Chart of Sample Averages

24. Estimation of Position Effects P Max & P Min Historical Position Averages when Process is Stable Analysis of Variance – Position Means Engineering Judgment of Reasonable Ranges

25. Mean = 21.0  = 1 P min = P max = 2

26. Data from “In Control” Process

28. Average for All Stations Increased by 1 for the Last Point

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

31. Average for All Stations Increased by 1 for Last 10 Points

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

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

35. Std. Dev. Of Station 20 Increased to 2 for last 23 Points

36. Average for Station 21 Increased to 22 for last 10 points

38. Average for Station 21 Increased to 22 for last 24 points

40. Average for Station 21 Increased by 3 for last 5 points

42. Average for Station 21 Increased by 3 for last 6 points

44. Average for Station 21 Increased by 3 for last 24 points

46. “Real World” Chart

48. Data Through Set 35

50. Data Through Set 47

52. Last 48 Data Sets

54. 24 Station Machine

56. 24 Station Rotary Machine

58. Evaluation of Screen Change Robust Container Relatively Low Production Rate Stable Process with Minimal Problems Before ~ 3300 Observation After 1 Year ~ 3300 Observations

59. Comparison of Probability Distributions Section B Before and After

60. Comparison of Frequency Histograms Section B

61. Comparison of Statistics for Section B

62. Comparison of Probability Distributions Section A

63. Comparison of Frequency Histograms Section A

64. Comparison of Statistics for Section A

65. Compare Probability Distributions Height

67. Comparison of Statistics for Height

68. 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

69. 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

70. Process & Product Analysis Richard E. Clark (630) 584 0566 r.clark@worldnet.att.net