History of Control Charts

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2 History of Control Charts 1920 s Walter Shewhart of Bell Labs working to improve reliability of telephone transmission systems W. Edward Demmings, U.S. Dept. of Agriculture and later U.S Census Bureau, promotes Shewart s work for next 50 years, becoming adopted widely in US WWII and post-war Japan industry for process control Handbook for Analytical Quality Control in Water and Wastewater Laboratories, USEPA, EPA-600/

3 What is a Control Chart? A control chart is a graph used to evaluate how a process changes over time. Some quality metric(s), representative of the process (e.g. product weight, measured value of a known standard, percent recovery), is selected for evaluation. There are many types of control charts. Charts may be uni- or multivariate. Univariate Shewhart-type (Levey-Jennings) control charts are commonly used in laboratories. Control charts typically plot an average of the metric, upper and lower warning limits (UWL, LWL) and/or control limits (UCL, LCL) for a predetermined number of events (n). Warning and control limits may be based on fixed values, or may be calculated based on arithmetic or statistical functions of the data.

4 % Recovery Fixed Limits Control Chart 140 % Recovery PO4-P % Recovery Mean LWL = 85% UWL = 115% 20 0 Run Date

5 % Recovery Fixed Limits Control Chart 140 % Recovery PO4-P % Recovery Mean LWL = 85% UWL = 115% 20 0 Run date

6 CaCO3 (mg/l) 95% and 99% Probability Limits (Means) Control Chart 650 SM 2340 C-1997 Hardness Standard (mg/l) Standard (mg/l) Mean LWL (mean-2sd) UWL (mean+2sd) LCL (mean-3sd) UCL (mean+3sd) 300 Run Date

7 RPD One Sided Precision Control Chart 45 RPD Duplicates SM NH3-D RPD Mean UWL UCL 5 0 Run Date

8 KCl (ppm) Cusum Control Chart P. promelas Chronic SRT (Growth) EPA Method SRT IC25 Mean IC25 Lower Limit Upper Limit SRT Test Number

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10 KCl (ppm) Same Data in a Traditional Control Chart P. promelas Chronic SRT (Growth) EPA Method SRT IC25 Mean IC25 Lower Limit Upper Limit SRT Test Number

11 Control Chart Interpretation 1 in 20 points should exceed 95% warning limits and 1 in 100 should exceed 99% control limits. These are not necessarily out of limits but may be Type 1 statistical errors. Specific guidelines regarding interpretation may be included in the test method. A control chart evaluates changes in your system. It does not evaluate the validity of data per se. A highly proficient lab may have much narrower control limits than a lab of lesser proficiency. Compare lab precision with method-specific intra-laboratory precision data, if available

12 Lab A Lab B

13 Control Chart Interpretation

14 Control Chart Interpretation WECO (Western Electric Company) Rules for Identifying Out-of- Control Data Points Any point above or below 3 SD 2 out of last 3 above or below 2 SD 4 out of last 5 above or below 1 SD 8 consecutive points on one side of the control line (e.g. mean) Trend Rules 6 in a row trending up or down 14 in a row alternating up and down

15 Control Chart Interpretation Standard Methods (1020 B.13.c) Any point above or below 3 SD: Repeat analysis; if repeat exceeds 3 SD discontinue analyses and correct problem. 2 out of last 3 above or below 2 SD: Analyze another sample; if exceeds 2 SD evaluate bias and correct problem. 4 out of last 5 above or below 1 SD, or are in decreasing or increasing order: Analyze another sample; if exceeds 1 SD or in same order, discontinue analyses and correct problem. 7 consecutive points on one side of the control line (e.g. mean): Discontinue analyses and correct problem. After correcting problem: Reanalyze samples analyzed between last in-control measurement and the out-of-control measurement.

16 Control Chart Construction Essentials Generally there are no rigid requirements on control chart construction (See EPA, Standard Methods, ASTM guidance). Methods often define WLs, CLs and n. The typical control chart based on the mean and standard deviation assumes the data are normally distributed. The charts are not robust to non-normal data and interpretations may be skewed. (Check for normality: Histograms, normal probability plots, Chi-square goodness of fit. Alternatives: Transform data, use non-normal control chart methods). Always use the sample standard deviation (stdev.s), not the population standard deviation (stdev), unless your data is from the complete population. A minimum number (e.g. 20) of data points are needed for a meaningful estimate of the mean and standard deviation. The method or regulation may require that only the most recent n (e.g. 20 or 30) data points be used. The measurement being evaluated is not included in calculation of WLs and CLs. It is only included in the next iteration of the chart.

17 Data Set Size and Normal Distribution

18 Basic Steps for Constructing Your Control Chart Select the metric you will be evaluating. Determine basis and values of your control and/or warning limits (fixed, arithmetic, statistical). Determine appropriate time period or number of data points to incorporate into your chart. Determine a priori how you will evaluate data outside limits. Collect data and construct control chart. Evaluate data.

19 Now Let s Make a Control Chart!

20 Set up your spread sheet

21 Insert formula for average

22 Insert formula for sample standard deviation

23 Type in $K$1 which will transcribe the value from the formula cell

24 Drag cursor to autofill the mean value

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26 Insert formula for lower warning limit

27 Drag and fill cells

28 Insert formula for upper warning limit

29 Drag and fill

30 Insert formula for lower control limit

31 Drag and fill

32 Insert formula for upper control limit

33 Drag and fill

34 Use cursor to highlight date and measurement columns; include headers

35 Insert tab>line or Area Chart>Line

36 Still need to add mean and limits

37 Place cursor on chart and right-click mouse; select data

38 Click Add button

39 Series name box will be blank with blinking line. 1. Place cursor over Mean column label and left click to fill series name. 2. Back space over the ={1}

40 Highlight the values for the mean in C2:C34 to fill in series values and then click Ok

41 Click Add again to add the LWL

42 Continue as with the Mean values.

43 Until LWL, UWL, LCL and UCL are added to the chart.

44 Now we have a basic control chart. But it needs fixing up. First let s make it bigger by dragging a corner.

45 Add a legend.

46 Rather have data points than a line for values? Right-click the line>format Data Series.

47 Click paint bucket.

48 Under Line option select No line

49 Under Marker select automatic. Change color, size if desired.

50 Often we need to change the range of the y-axis for better presentation. Left click the y-axis to change range, units, etc.

51 The x-axis intersecting at y=20 looks better. Show cusum spread sheet formuals??

52 What do the units on the y-axis mean? We need axis titles.

53 Just type into the Axis Title boxes beside the y-axis and below the x-axis

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55 Let s add a title.

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58 Our new point 9/3/16 is compared with the mean and limits. Depending on the method/guidance: 1. Add the new data point and calculate new cumulative values. 2. Add the new data point and calculate new values but eliminating the nth previous point from analysis (e.g. only last 20 or 30)

59 CuSum Control Chart formulas individual mean value

60 CuSum Control Chart formulas individual LWL value

61 CuSum Control Chart formulas individual UWL value

62 CuSum Control Chart formulas next individual mean value Copy/Paste formulas from line above, range auto adjusts

63 CuSum Control Chart formulas next individual LWL value

64 CuSum Control Chart formulas next individual UWL value

65 Right click control chart to edit series values; change to include most recent n values

66 Charting Your Data is a Great Tool Other QC metrics (CV (%RSD), % valid measures, etc.) By Instrument By Technician By Day of the Week (Should you buy a car made on Monday or Friday?)

67 Standard Practice for Use of Control Charts in Statistical Process Control Resources APHA/AWWA/WEF Standard Methods for the Examination of Water and Wastewater. 22nd Edition. American Public Health Assoc., Washington, DC (Section 1020 B.13) ASTM Standard Practice for Use of Control Charts in Statistical Process Control, ASTM E , ASTM International, West Conshohocken, PA, 2016 USEPA Handbook for Analytical Quality Control in Water and Wastewater Laboratories, USEPA, EPA-600/

68 Questions or further information: Pete De Lisle Coastal Bioanalysts, Inc Enterprise Court Gloucester, VA (Fax) 68