Statistics – Process Capability (Cp) & Process Performance
(Pp)
Process Capability
Process capability can be defined as a measurable property of a
process relative to its specification. It is expressed as a
process capability index ${C_p}$. The process capability index is
used to check the variability of the output generated by the
process and to compare the variablity with the product tolerance.
${C_p}$ is governed by following formula:
Formula
${ C_p = min[frac{USL – mu}{3 times sigma}, frac{mu –
LSL}{3 times sigma}] }$
Where −

${USL}$ = Upper Specification Limit.

${LSL}$ = Lower Specification Limit.

${mu}$ = estimated mean of the process.

${sigma}$ = estimated variability of the process, standard
deviation.
Higher the value of process capability index ${C_p}$, better is
the process.
Example
Consider the case of a car and its parking garage. garage size
states the specification limits and car defines the process
output. Here process capability will tell the relatonship between
car size, garage size and how far from middle of the garage you
can parked the car. If car size is litter smaller than garage
size then you can easily fit your car into it. If car size is
very small compared to garage size then it can fit from any
distance from center. In term of process of control, such process
with little variation, allows to park car easily in garage and
meets the customer’s requirement. Let’s see the above stated
example in terms of process capability index ${C_p}$.

${C_p = frac{1}{2}}$ – garage size is smaller than car and
can not accomodate your car. 
${C_p = 1}$ – garage size is just sufficient for car and can
accomodate your car only. 
${C_p = 2}$ – garage size is two times than your car and can
accomodate two cars at a time. 
${C_p = 3}$ – garage size is three times than your car and
can accomodate three cars at a time.
Process Performance
Process performance works to check the conformance of the sample
generated using the process. It is expressed as a process
performance index ${P_p}$. It checks whether it is meeting
customer requirement or not. It varies from Process Capability in
the fact that Process Performance is applicable to a particular
batch of material. Sampling method may need to be quite
substancial to support of the variation in the batch. Process
Performance is only to be used when a process control cannot be
evaluated. ${P_p}$ is governed by following formula:
Formula
${ P_p = frac{USL – LSL}{6 times sigma} }$
Where −

${USL}$ = Upper Specification Limit.

${LSL}$ = Lower Specification Limit.

${sigma}$ = estimated variability of the process, standard
deviation.
Higher the value of process performance index ${P_p}$, better is
the process.
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