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More Variable Control Charts A. A. Elimam

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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.

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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

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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

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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

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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)

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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 %

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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)

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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

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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

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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)

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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

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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

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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

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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

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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.

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