Process Capability
• The natural behavior of a process, when it is in
statistical control, is called its process capability.
• Process capability analysis compares the output of a
process (called “Voice of the Process”) with the
customer’s specification limits for the outputs (called
“Voice of the customer”).
Process Capability
• Formula: The most widely adopted formula for process
capability (natural behavior ) is
Process Capability = ± 3σ
where σ = the standard deviation of the process under a
state of statistical control.
Process Capability
•
If the process is centered at the nominal specification and
follows a normal distribution, 99.73% of the production
will fall within ± 3σ of the nominal specification.
• Statistically, this is a very predicable behavior.
Process Capability
• A major reason for process capability analysis is to be able to predict the ability
of the process to hold product specifications.
• We should try to select a process with the 6σ
process capability
well within the specification width.
Process Capability
•A common measure of this relationship is the
capability ratio:
Specification Range
USL - LSL
Cp=Capability ratio= ---------------- = -----------Process capability
where USL = upper specification limit
LSL = lower specification limit
and 6s is used as an estimate of 6σ.
6s
Process Capability
• The figure below shows four of many possible relations
between process capability and the specification limits and
the likely courses of action for each.
• It assumes that the process average is midway between
the specification limits.
Process Capability
Process Capability
•Table 18.5 shows selected capability ratios and
the corresponding level of defects (assuming
that the process average is midway between the specification limits).
• We can see that a defect rate of one part per million (1 ppm) requires a
capability ratio of about 1.63. That is,
Cp = 1.63 , if defect rate = 1 ppm
Process Capability
Table 18.5 here.
Process Capability
• The reality that the process average will not remain at the
midpoint of the specification range suggests that Cp should be at
least 1.33.
Cp ≥ 1.33
• Note that Cp index measures whether the process variability can fit within
the specification range. It does not indicate whether the process is
actually running within the specification.
Process Capability
•There are other capability indices commonly in use.
See the Table below.
Table 18.6 here.
Process Capability
•The Cp index is the simplest one, but it does not
include the process average (and thus it is only a
potential ability, rather than the actual ability that
the process will be running within the specification
range.
•The other indices Cpk and Cpm consider the process
average.
•Generally, the higher the value of a capability index,
the lower the amount of product that is outside the
specification limit.
Process Capability
• Next figure shows two processes, which have the same capability Cp because
6σ is the same for each process.
• Nevertheless, the process with µ2 is producing much more defectives because
its average is off the center of the specification limits.
• Thus, Cp measures only the potential capability.
• Because the process average is often not the specification midpoint, it is more
useful to have a capability index that reflects both the variation and the
location of the process average relative to the specification midpoint.
• The Cpk and Cpm indices are designed for such purpose.
Process Capability
Figure 18.15 here.
Process Capability
• Cpk is defined as:
• It reflects the current process mean’s proximity to either the USL or LSL,
and is estimated by
Process Capability
• Example (Kane, 1986):
• The standard capability ratio Cp is estimated as
USL – LSL
20 - 8
---------------- = ------------ = 1.0
6σ
12
which implies that if the process were centered between the specification
limits (at 14), then only a small proportion (about 0.27 percent) of
product would be defective.
Process Capability
• However, when we calculate Cpk , we obtain
16-8
20-16
Cpk = min { --------, --------- } =0.67
6
6
•This is because the process average is nearer the
USL.
•We have to reduce the standard deviation of the
process and/or center its average.
Process Capability
• Note that, if the actual process average is equal to the
midpoint of the specification range, then Cpk = Cp .
• Clearly, the higher the value of Cpk , the lower the
amount of product outside specification limits.
• Some organizations use Cpk as one of the major criteria
to certify their suppliers.
• A capability index can also be calculated around a target
value rather than the actual average. This is the index
Cpm , or the Taguchi index.
• Cpm focuses on reduction of variation from a target value
rather than reduction of variability to meet
specifications.