Other Univariate Statistical Process Monitoring and Control Techniques

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Chapter 9

• Other Univariate Statistical Process Monitoring
  and Control Techniques

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9-2. Modified and Acceptance Control Charts

• When a high level of process capability has been
  achieved, it may be useful to relax the level of
  surveillance provided by standard control charts.
• Modified control limits for charts or
  acceptance control charts can be employed for
  this situation.

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9-2. Modified and Acceptance Control Charts

• 9-2.1 Modified Control Limits for the Chart
• Modified control limits are only used in the case
  where Cp or Cpk gt 1.
• The modified control chart is concerned only
  with detecting whether the true process mean ? is
  located such that the process is producing a
  fraction nonconforming in excess of some
  specified value, ?.
• ? can vary over the range ?L ? ? ? ?U

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9-2. Modified and Acceptance Control Charts

• 9-2.1 Modified Control Limits for the Chart
• The upper and lower control limits for the
  modified control chart are

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Example

• The amount of cement placed in a bag is specified
  as 50 .25 lb.
• 20 random samples of five bags each are taken
• Xbar and R values are shown on the next slide
• Coded by subtracting 50 lbs.

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Example, cont.

• Construct a modified 3s limit control chart
• If the true process fraction nonconforming is as
  large as 1, the process is nonconforming

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Example, cont.

• First, determine if the process variability is in
  control
• Rbar 1.5604/20 .07802
• D4 2.114, D3 0
• UCLR .07802(2.114) .16493
• CLR .07802
• LCLR .07802(0) 0
• Thus, process is in control for variability

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Example, cont.

• For n 5, d2 2.326 and Zd Z.01 2.33
• UCL .252.333/SQRT(5)(.07802/2.326)
• .2168 lb.
• LCL -.252.333/SQRT(5)(.07802/2.326)
• -.2168 lb.
• The process is well within control
• The closest value to the control limits is 12

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9-2. Modified and Acceptance Control Charts

• 9-2.2 Acceptance Control Charts
• Acceptance control charts take into account both
  the ?-risk and the ?-risk.
• Two approaches to designing the acceptance
  control chart
• Design the chart based on a specified n and
  process nonconforming ? that we would like to
  reject with probability 1 - ?.
• Choose a sample size for an acceptance control
  chart so that specified values of ?, ?, ?, and ?
  are obtained.

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9-2. Modified and Acceptance Control Charts

• 9-2.2 Acceptance Control Charts
• Approach 1 The control limits are

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Example

• Consider the data in the last example
• Suppose that if the true process fraction
  nonconforming is as large as 5, it is important
  to detect this out-of-control condition with a
  probability of 0.90

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Example, cont.

• Zg Z.05 1.645
• Zb Z.10 1.28
• Rbar .07802
• d2 2.326

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Example, cont.

• UCL .251.6451.28/SQRT(5)(.07802/2.326)
  .1756
• LCL -.251.6451.28/SQRT(5)(.07802/2.326)
• -.1756
• An examination of the observations indicates
  that the process is within these limits

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9-2. Modified and Acceptance Control Charts

• 9-2.2 Acceptance Control Charts
• Approach 2 A sample size of
• will yield the required values of ?, ?, ?, and
  ?.

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Example

• From the first example, a .0027, d .01
• Za/2 3 and Zg 2.33
• From the last example, b .10 and g .05
• Zb Z.10 1.28, Zg Z.05 1.645
• n (31.28)/(2.33 1.645)2 39

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Assignment

• Exercise 9-9

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End