1. More Variable Control Charts A. A. Elimam

2. What about the Short Run? n n X-bar and R charts track process with long production runs or repeated services n n No. of sample measurements : Insufficient to create either chart n n Would SPC ideas apply to new processes or short runs? n n What happens when only one sample is taken from a process? n n Situations when the traditional X-bar, R and S charts cannot be used.

3. Individual & Moving Range Charts When ? n n data is collected once per period n n single value measurement n n few units of each product n n individual Values Chart Plot Individual measurements, X iPlot Individual measurements, X i X-bar is the average of all X iX-bar is the average of all X i

4. Individual & Moving Range Charts n n Moving Range Chart Value-to-value difference of individual data, R iValue-to-value difference of individual data, R i R-bar is the average of all R iR-bar is the average of all R i (m-1) ranges(m-1) ranges Plot Individual measurements, R i starting on the second observationPlot Individual measurements, R i starting on the second observation

5. Individual & Moving Range Charts Control Limits n n Individual Charts x = X + R UCL x = X + 2.66 R x = X - R LCL x = X - 2.66 R n n Moving Range Charts R = R UCL R = 3.27 R R = LCL R = 0 n n At least 80 samples n n Interpret similar to traditional charts

6. Moving-Average & Moving-Range Charts n n Combine n individual values to form a group n n Create average & range per group n n Moving: new value in- oldest one out n n Find UCL, LCL & Process Capability using the same methods for traditional control charts (TCC)

7. Moving-Average Charts n n Moving Average smoothes out short term variation n n User Concentrate on trends n n Mostly used for seasonal products n n Always lag behind changes in process n n Best when process changes slowly

8. A Chart Plotting Individual Values n n Explains concept of variation compared to the average n n Picture worth 1000 words n n Useful in training staff on interpreting R or S charts

9. Median and Range Charts n n Study process variation n n Steps: record subgroup measurements rank in decreasing order find median & range in each subgroup Median Chart Center = all medians AVG Range Chart Center = all ranges AVG Determine UCL & LCL for the Median & Range Charts

10. Median and Range Charts n n Median Charts: Md = Md + 6 Md UCL Md = X Md + A 6 R Md Md = Md - 6 Md LCL Md = X Md - A 6 R Md n n Range Charts R = 4 Md UCL R = D 4 R Md R = 3 Md LCL R = D 3 R Md n n Record Median & Range on chart n n Interpret Charts similar to TCC

11. Run Charts n n Monitor changes in a particular characteristic over time n n Can be used for Variable or Attribute n n Data: measurements, counts, subgroup averages n n Easily spot trends, runs and other patterns

12. Run Charts: Steps n n Identify time increments to study process n n Scale the Y axis to reflect values n n Collect data n n Record data on chart n n Interpret the chart (limited to looking for data patterns) n n No out of control points

13. Variable Subgroup Size Charts n n Subgroup size, n, Varies n n Re-compute Control Limits (CL) for each n n n As n increases - CLs closer to center n n Too many calculations n n Limit the useful of this chart

14. Precontrol Charts n n Compare product made against tolerance limits n n Assumes process is capable of meeting specifications n n Uses specifications for limits n n More false alarms or missed signals n n Simple to setup

15. Precontrol Charts n n Useful for setup operations or short production runs n n Less powerful than TCC n n Provide little about actual process performance n n Cannot be used in problem solving or calculating process capability

16. Precontrol Charts n n Use Portion of Tolerance Spread (PTS) to account for difference in spread for individuals and averages n n Desired Process Capability (PC) dictates this portion: PC index PTS 1.2(100/1.2) = 83 % 1.1(100/1.1) = 90 %

17. Precontrol Charts: Steps Create the zones for the used PTS Place USL, LSL and center (SC) on chart Divide (USL-SC) in 2 equal zones: green- yellow Divide (SC-LSL) in 2 equal zones: green- yellow Green zones (GO SECTION) are next to center Yellow zones (CAUTION) are next to the limits Zones above or below yellow area are colored in RED (UNDESIRABLE)

18. Precontrol Charts: Steps Take measurements & apply setup rules n n Record and plot measurement n n If measured piece is in green zone-continue running inside limits but outside green zone-check next piece second piece is also outside green zone-reset process in red zone, stop, make corrections & reset process n n If 2 successive pieces fall outside green zone, one high and the other low, reduce variability n n Whenever process is reset, need 5 successive pieces inside the green zone before sampling

19. Precontrol Charts: Steps Apply the precontrol sampling plan n the green zone- begin running the job n If 5 pieces in a row fall in the green zone- begin running the job n Use the run rules, randomly sampling 2 pieces at intervals to monitor process n For example: Sampling Two PARTS every 15 minutes. n Suggest Sampling >= 25 pairs after setups n Repeat whenever the process is reset

20. Short-Run Charts n n TCC : effective in long continuous operations n n Real life: need to switch products (FMS) n n Use Short-Run charts n n Different Methods: First and last pieces 100 % inspection (costly, maybe inaccurate) TCC for each part # & each different run of each part # (many charts- little information)

21. Nominal X-bar and R Charts n n Uses coded measurements based on nominal dimension. For example “Print Dimension” of 3.75 (+ or -) 0.005 = 3.75 n n Shows process centering and spread n n Assumes similar variations for each of the part numbers n n If variation of a part > 1.3 R-bar, then it must be plotted on a separate graph

22. Nominal X-bar and R Charts Steps n n Identify parts monitored using same chart (same operator, machine, material,...) n n Find nominal spec. for each part n n Collect data using same subgroup size for all parts n n Coded X i = measured value-nominal value n n Calculate X-bar for each subgroup

23. Nominal X-bar and R Charts Steps n n Plot all X-bars on the chart n n Continue the above for the entire run of this particular part number n n Repeat the above for another part number n n If the number of subgroups (from any combination of parts) >= 20, calculate the control limits

24. Nominal X-bar and R Charts Steps n n Centerline = Average of all coded X-bars n n Control limits: Nominal X-bar Chart x = + 2 UCL x = Centerline + A 2 R x = - 2 LCL x = Centerline - A 2 R n n Control limits: Nominal range Charts R = 4 UCL R = D 4 R R = 3 LCL R = D 3 R n n Draw center and CL on the chart n n Interpret the chart

25. Nominal X-bar and R Charts n n Most useful when FOR ALL PARTS Subgroup size, n, is the same Nominal is the most appropriate target value n n Control charts should be selected based on: What aspect of process need to be monitored. Identifying the chart that best meet such need.