CONTROL CHARTS MORE THAN MEETS THE EYE Wayne

CONTROL CHARTS MORE THAN MEETS THE EYE Wayne Gaul, Ph. D. , CHP, CHMM Tidewater Environmental Columbia, SC SRHPS Technical Seminar, April 15, 2011 n. Daily Background Check Alpha n 2. 0 n 1. 5 n. Counts n 1. 0 n 0. 5 n 0. 0 n-0. 5 n-1. 0 n-1. 5 n 1 n 2 n 3 n 4 n 5 n+ 3 SD n 6 n 7 n 8 n. Date n+ 2 SD n 9 n 10 n 11 n. Mean n 12 n 13 n 14 n 15

Control Charts Used to determine whether or not the process in question is stable. “Stable” refers to a state of statistical control “Control” monitors a condition which exists when the process is affected by only random variation n 2

Control Charts � Assumes that the process is stable � The estimate of used in the calculation must be reliable � Several tests for stability have been developed which use statistical probability to determine the likelihood that certain patterns of variation are the result of chance (random variation) or assignable causes (non-random variation; a sign of instability). n 3

Caution with Standard Deviations Standard deviation of a population: Standard deviation of small sample size: (Used in Excel) n 4

Lets Develop an Example Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Alpha Background 2. 4 2. 2 2. 55 3. 0 3. 2 2. 9 2. 10 2. 44 2. 0 1. 6 2. 3 2. 4 2. 95 2. 6 Avg = 2. 503 σ = 0. 435 n 5

n Alpha Background Control Chart n 3. 65 n 3. 49 n. UCL n. Alpha Background (cpm) n 3. 15 n 2. 65 n. Average n 2. 50 n 2. 15 n 1. 65 n 1. 52 n. LCL n 1. 15 n 1 n 2 n. Alpha Bkgd n 3 n 4 n. UCL n 5 n +2 Sigma n 6 n 7 n 8 n 9 n. Date/Time/Period n +1 Sigma n. Average n 10 n 11 n -1 Sigma n 12 n n 13 -2 Sigma n 14 n 15 n. LCL n 6

Want to Monitor Trends The Control Chart monitors repeated measurements to ensure they are within limits. The X-axis is typically time but can be batches, groups, tests, anything to compare. n 7

Trends Monitored with Statistical Accuracy The simplest and best known indicator is the presence of a point beyond the 3 control limits. Because in a normal distribution 99. 73% of the population will fall within 3 of the mean. This means only a. 27% chance that a point will fall outside those limits. In other words, there is a 99. 73% chance that the points outside the limits are the result of non-random causes. n 8

Conditional Testing Additional tests are also based on the same sort of reasoning— There is a significantly small probability that any of the phenomena are the result of chance alone. n 9

Additional Tests � One point outside the 3 limits � Two out of three consecutive points more than 2 away from the mean on one side. � Four out of five consecutive points more than 1 away from the mean on one side n 10

Additional Tests � Seven consecutive points on one side of the mean � Six consecutive points trending up or down � Fourteen consecutive points alternating up or down n 11

Control Chart Areas of Interest n 22. 90 n. UCL +3 n 22. 80 Zone A Zone B Zone C n. Average n 22. 70 n 22. 60 Mean n. CL n 22. 50 n 22. 53 Zone B Zone A n 22. 40 n. LCL -3 n 22. 30 n 22. 78 n 22. 29 n 22. 20 n 1 n 2 n 3 n 4 n 5 n 6 n 7 n 8 n 9 n 10 n 11 n 12 n 13 n 14 n 15 n. Date/Time/Period n 16 n 17 n 18 n 19 n 20 n 21 n 22 n 23 n 24 n 25 n 12

Different Control Chart Rules Nelsn AIAG Juran Mont West- Hlth gmery Elec Care Points above UCL or below LCL 1 1 1 Zone A n of n+1 points above /below 2 2 2 2 Zone B n of n+1 points above /below 1 4 4 n points in a row above or below center 9 7 8 8 Trends of n points in a row incre or decr 6 6 Zone C n points in a row inside Zone C 15 15 n points in a row alternating up or down 14 14 14 Zone C – n points in row outside Zone 8 8 n 13

Common Types of Control Charts Often classified according to the type of quality characteristic that they are supposed to monitor: There are quality control charts for variables, and Quality control charts for attributes. n 14

Control Charts for Variables X-bar chart. The sample means are plotted in order to control the mean value of a variable. R chart. The sample ranges are plotted in order to control the variability of a variable. S chart. The sample standard deviations are plotted in order to control the variability. Moving Average chart. The moving average of successive samples is plotted. n 15

Control Charts for Attributes These are more for production processes. C chart – plot the number of defectives per batch, day, per machine, etc, Poisson assumed. U chart – plot the rate of defectives. # defects per # units. Good for different batch sizes. Np chart, similar to C chart, use binomial dist. P chart, similar to U chart, uses proportions. n 16

n. Gross Alpha n 7 2/ 3/ 08 1/ 3/ 08 7 /3 /0 12 n n /3 /0 11 /0 7 /3 7 3/ 0 9/ 07 8/ 3/ 10 n n /0 7 7/3 7 3/ 0 6/ n n 7 3/ 0 5/ 7 3/ 0 4/ n n 3/ 3/ 07 2/ 3/ 07 n n 3/ 07 1/ n. Counts per Minute n Actual Weekly Air Sample Data n. Environmental Air Sample Data n 70 n 60 n 50 n 40 n 30 n 20 n 10 n 0 n. Gross Beta n 17

n 2/ 3/ 08 1/ 3/ 08 7 /3 /0 12 n n 7 /3 /0 11 /0 7 /3 7 3/ 0 9/ 07 8/ 3/ 10 n n /0 7 7/3 7 3/ 0 6/ n. Counts per Minute n 16 n n 7 3/ 0 5/ 7 3/ 0 4/ n n 3/ 3/ 07 07 3/ 07 1/ 2/ 3/ n n n Lets Look at Just the Alpha n. Gross Alpha n 14 n 12 n 10 n 8 n 6 n 4 n 2 n 0 n. Gross Alpha n 18

n. Gross Alpha X-bar Control Chart n 16 n 14 n. Gross Alpha (cpm) n 12 n 10 n. UCL n 9. 32 n. CL n 3. 62 n 8 n 6 n 4 n 2 2/ 3/ 08 n 1/ 3/ 08 n n 12 /3 /0 7 7 /3 /0 11 n n 10 /3 /0 7 7 3/ 0 9/ n 07 8/ 3/ n /0 7 7/3 n n 6/ 3/ 0 7 7 3/ 0 5/ n 7 3/ 0 4/ n 3/ 3/ 07 n 2/ 3/ 07 n n 1/ 3/ 07 n 0 n. Date n. Gross Alpha n. UCL n +2 Sigma n +1 Sigma n. Average n -1 Sigma n -2 Sigma n. LCL n 19

9/ n 08 3/ 2/ n 08 3/ 1/ 3/ 07 07 3/ 07 3/ n 12 / 8/ n n 7/ n 11 / 6/ n n 5/ n 10 / 4/ n n 3/ n 07 n 2 3/ 2/ n 07 3/ 1/ n n. Range n Gross Alpha Range Control Chart n 14 n 12 n 10 n 8 n 6 n 4 n. UCL n 6. 3 n. CL n 1. 9 n 0 n. Date n 20

n. Gross Alpha Moving Average Trend Control Chart n 19. 1 n 14. 1 n 11. 4 n. Average n 9. 1 n. UCL n 6. 3 n. CL n 1. 1 n 4. 1 Fit (R^2) < 0. 80 Ryx = 0. 580 Slope = 0. 090 Sigma = 1. 713 Probability = 0. 273 n-0. 9 n. LCL 08 3/ 2/ n 08 n 1/ 3/ 7 n 12 /3 /0 7 /0 /3 11 n n 10 /3 /0 7 07 3/ 9/ n 07 3/ 8/ n 07 3/ 7/ n 07 3/ 6/ n 07 3/ 5/ n 07 3/ 4/ n n 3/ 3/ 07 07 3/ 2/ n n 1/ 3/ 07 n-5. 9 n. Date n 21

n. Gross Alpha Different ROI's n 16 n 14 n 12 n 10 n 8 n 6 n 4 n 2 n 0 n 1/3/07 n 2/3/07 n. Alpha n 3/3/07 n 4/3/07 n. UCL n 5/3/07 n 6/3/07 n +2 Sigma n 7/3/07 n +1 Sigma n 8/3/07 n 9/3/07 n. Average n 10/3/07 n 11/3/07 n -1 Sigma n 12/3/07 n 1/3/08 n -2 Sigma n 2/3/08 n. LCL n 22

Conclusion from the Alpha Possibly two separate contamination events n 23

n 2/ 3/ 08 1/ 3/ 08 7 /3 /0 12 n n 7 /3 /0 11 /0 7 /3 7 3/ 0 9/ 07 8/ 3/ 10 n n /0 7 7/3 7 3/ 0 6/ n n 7 3/ 0 5/ 7 3/ 0 3/ 3/ 07 4/ n n 3/ 07 1/ 2/ 3/ 07 n n. Counts per Minute n. Gross Beta n 60 n 50 n 40 n 30 n 20 n 10 n 0 n. Gross Beta n 24

9/ n 3/ 2/ n 3/ 1/ 08 08 7 /0 /3 7 /0 7 07 /0 /3 n 07 07 07 3/ 3/ 3/ /3 12 8/ n n 7/ n 11 6/ n n 5/ n 10 4/ n n 3/ n n-6. 8 07 07 Beta (cpm) n 63. 2 3/ 2/ n 3/ 1/ n n. Gross Beta X-bar Control Chart n 73. 2 n 53. 2 n 43. 2 n 33. 2 n 23. 2 n 13. 2 n. UCL n 61. 0 n. CL n 27. 7 n. LCL n-5. 7 n-16. 8 n. Date n 25

9/ n 3/ 2/ n 08 08 3/ 1/ n 7 /0 /3 7 07 /0 3/ 07 07 3/ 3/ /3 12 8/ n n 7/ n 11 6/ n n 5/ n 10 4/ n n 3/ n 07 07 n. Range n 40 3/ 2/ n 3/ 1/ n n. Gross Beta Range Control Chart n 45 n 30 n 25 n 20 n 15 n. UCL n 41. 0 n. CL n 12. 5 n 10 n 5 n 0 n. Date n 26

n. Gross Beta Moving Average Control Chart n 77. 8 n 67. 8 n 57. 8 n 66. 3 n. UCL n 37. 8 n 33. 0 n 27. 8 n. CL n 17. 8 n-12. 2 n-0. 4 Fit (R^2) < 0. 80 Ryx = 0. 260 Slope = 0. 181 Sigma = 11. 121 Probability = 0. 273 n-2. 2 n. LCL n 2/ 3/ 08 08 n 1/ 3/ 07 /3 / 12 n n 11 /3 /0 7 /3 10 n 3/ 07 n 9/ 07 n 8/ 3/ 7 7/3 /0 n 3/ 07 6/ n 7 /0 5/ 3 n 3/ 07 4/ n 7 3/ 0 3/ n 07 2/ 3/ n 1/ 3/ 07 n-22. 2 n n. Average (cpm) n 47. 8 n. Date n 27

n Gross Beta Different ROI's n 74. 8 n 70. 0 n 64. 8 n. UCL n 50. 6 n 44. 8 n 34. 8 n 24. 8 n 31. 9 n. CL n 23. 7 n. LCL n-3. 3 n 14. 8 n-5. 2 n-6. 2 8 3/ 0 2/ n 08 3/ 1/ n 12 /3 / 07 7 n /0 /3 11 n 10 /3 /0 7 7 n n 9/ 3/ 0 7 3/ 0 8/ n n 7/3 /0 7 7 3/ 0 6/ n 7 3/ 0 5/ n n 4/ 3/ 07 7 3/ 0 3/ n 3/ 07 2/ n 1/ 3/ 0 7 n-15. 2 n n. Gross Beta (cpm) n 54. 8 n. Date n 28

Conclusions for Beta No specific event possible to identify. Moving average trend line gives indication an upward trend of some kind. n 29

Conclusion Control charts can provide meaningful information. Must be properly used. Multiple types may be necessary to identify possible problems. n 30