Process Capability

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Process Capability

• Process capability provides an indication of
  whether or not a process is capable of producing
  good units.
• Process capability ratio (Cp) -- compares the
  distance between design specifications to the
  capability of the process
• Process capability index (Cpk) -- compares the
  distance between the process mean and the
  tightest design spec to the capability of the
  process

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Process Capability

• To determine the process capability, we must know
  the the standard deviation of the process.
• In constructing control charts, we were using the
  standard deviation of the samples.
• The standard deviation of the process can be
  estimated from the standard deviation of the
  samples.

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Calculations

• Control chart limits are 3sm limits where sm is
  the standard deviation of the process means. That
  is,
• For process capability, we assume the process
  itself follows a normal distribution with
  standard deviation s.
• From basic statistics we know s is related to sm
  by
• Therefore, an estimate for the process s is

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Process capability ratio
Process capability index
Process mean is 8.53 Process standard deviation
is 0.172
Design specs are 8.50 /- .40
Process capability ratio 0.78
Process capability index 0.72 (UTL)
Process is not capable since index
Note that simply comparing data points to design
specifications is not a valid indicator of
capability
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Process Capability

• For a process to be capable, both the ratio and
  the index must be 1.
• Some references use a value of 1.3.
• Note ratio index

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Cost of variation

• The unit meets design specs. Why isnt that
  enough?
• 3s quality implies that 99.7 of units meet
  design specs
• Why did Motorola implement their six-sigma
  (99.9999998) program?
• What is the advantage of achieving high process
  capability ratios?

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Motorolas 6s program

• Motorola discovered that the processes they were
  using could easily have a shift in the mean of up
  to 1.5s.
• This generally occurred without a change in the
  standard deviation of the process.
• The process capability ratio remains unchanged.
• The process capability index is reduced.

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SPC synergies

• Over time, a process has been improved and it now
  has a high process capability ratio.
• This process is being monitored with a control
  chart.
• At some point in time, the process begins to
  change.
• This change is identified on the control chart
  and the process is brought back in-control.
• With a high process capability, the process has
  been corrected before defects occur.