More Variable Control Charts
A. A. Elimam
What about the Short Run?
X-bar and R charts track process with long production runs or repeated services
No. of sample measurements : Insufficient to create either chart
Would SPC ideas apply to new processes or short runs?
What happens when only one sample is taken from a process?
Situations when the traditional X-bar, R and S charts cannot be used.
Individual & Moving Range Charts
When ? data is collected once per period single value measurement few units of each product individual Values Chart• Plot Individual measurements, XPlot Individual measurements, Xii
• X-bar is the average of all XX-bar is the average of all Xii
Individual & Moving Range Charts
Moving Range Chart• Value-to-value difference of Value-to-value difference of
individual data, Rindividual data, Rii
• R-bar is the average of all RR-bar is the average of all Rii
• (m-1) ranges(m-1) ranges
• Plot Individual measurements, RPlot Individual measurements, Ri i
starting on the second observationstarting on the second observation
Individual & Moving Range Charts Control Limits
Individual Charts
UCL x x = X + = X + 2.66 R R
LCL x x = X - = X - 2.66 R R
Moving Range Charts
UCL R R = = 3.27 R R
LCL R R = = 0
At least 80 samples Interpret similar to traditional charts
Moving-Average & Moving-Range Charts
Combine n individual values to form a group
Create average & range per group Moving: new value in- oldest one out Find UCL, LCL & Process
Capability using the same methods for traditional control charts (TCC)
Moving-Average Charts
Moving Average smoothes out short term variation
User Concentrate on trends Mostly used for seasonal products Always lag behind changes in
process Best when process changes slowly
A Chart Plotting Individual Values
Explains concept of variation
compared to the average
Picture worth 1000 words
Useful in training staff on
interpreting R or S charts
Median and Range Charts
Study process variation 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
Median and Range Charts
Median Charts:
UCL Md Md = = XMdMd + + A6 6 RMdMd
LCL Md Md = = XMdMd - - A6 6 RMdMd
Range Charts
UCL R R = = D4 4 RMdMd
LCL R R = = D3 3 RMdMd
Record Median & Range on chart Interpret Charts similar to TCC
Run Charts Monitor changes in a particular
characteristic over time Can be used for Variable or Attribute Data: measurements, counts,
subgroup averages Easily spot trends, runs and other
patterns
Run Charts: Steps Identify time increments to study process Scale the Y axis to reflect values Collect data Record data on chart Interpret the chart (limited to looking for
data patterns) No out of control points
Variable Subgroup Size Charts
Subgroup size, n, Varies
Re-compute Control Limits (CL) for
each n
As n increases - CLs closer to center
Too many calculations
Limit the useful of this chart
Precontrol Charts Compare product made against tolerance
limits
Assumes process is capable of meeting
specifications
Uses specifications for limits
More false alarms or missed signals
Simple to setup
Precontrol Charts Useful for setup operations or short
production runs
Less powerful than TCC
Provide little about actual process
performance
Cannot be used in problem solving or
calculating process capability
Precontrol Charts
Use Portion of Tolerance Spread (PTS) to account for difference in spread for individuals and averages
Desired Process Capability (PC) dictates this portion:
PC index PTS
1.2 (100/1.2) = 83 %
1.1 (100/1.1) = 90 %
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)
Precontrol Charts: Steps Take measurements & apply setup rules Record and plot measurement 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
If 2 successive pieces fall outside green zone, one high and the other low, reduce variability
Whenever process is reset, need 5 successive pieces inside the green zone before sampling
Precontrol Charts: Steps Apply the precontrol sampling plan If 5 pieces in a row fall in the the green zonegreen zone--
begin running the jobbegin running the job Use the run rules, randomly sampling 2 Use the run rules, randomly sampling 2
pieces at intervals to monitor processpieces at intervals to monitor process For example: Sampling Two PARTS every For example: Sampling Two PARTS every
15 minutes.15 minutes. Suggest Sampling >= 25 pairs after setupsSuggest Sampling >= 25 pairs after setups Repeat whenever the process is resetRepeat whenever the process is reset
Short-Run Charts
TCC : effective in long continuous operations
Real life: need to switch products (FMS) Use Short-Run charts 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)
Nominal X-bar and R Charts
Uses coded measurements based on nominal dimension. For example “Print Dimension” of 3.75 (+ or -) 0.005 = 3.75
Shows process centering and spread Assumes similar variations for each of
the part numbers If variation of a part > 1.3 R-bar, then it
must be plotted on a separate graph
Nominal X-bar and R ChartsSteps
Identify parts monitored using same chart (same operator, machine , material, ...)
Find nominal spec. for each part Collect data using same subgroup size for
all parts
Coded Xi= measured value-nominal value
Calculate X-bar for each subgroup
Nominal X-bar and R ChartsSteps
Plot all X-bars on the chart Continue the above for the entire run of
this particular part number Repeat the above for another part
number If the number of subgroups (from any
combination of parts) >= 20, calculate the control limits
Nominal X-bar and R ChartsSteps
Centerline = Average of all coded X-bars Control limits: Nominal X-bar Chart
UCL x x = = Centerline + + A2 2 R
LCL x x = = Centerline - - A2 2 R Control limits: Nominal range Charts
UCL R R = = D4 4 R
LCL R R = = D3 3 R Draw center and CL on the chart Interpret the chart
Nominal X-bar and R Charts Most useful when FOR ALL PARTS• Subgroup size, n, is the same• Nominal is the most appropriate target value
Control charts should be selected based on:
• What aspect of process need to be monitored.• Identifying the chart that best meet such
need.