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Cp or Cpk is known as Process capability index for the variability in the process of manufacturing and is calculated only when the process is in statistically control, means there is only variation due to chance and no special/assignable cause present.
Process variability is defined by their three properties i.e.
Shape
Spread
Location (centring)
As far as the shape is concerned it is governed by the normal distribution as the indices are calculated when process is statically under control and the sample size n is most of the time >30,hence a normal distribution curve( bell shape) is obtained.
Due to the common cause or variation due to chance, if the spread of the variability is more than the VOC(voice of customer) or design specification then the Cp index <1 as Cp= tol./6* sigma. Hence there is positive indication that non-conforming product would be produced by the process.
Similarly, Cpk is the measure of centring of the process with respect to mid of the design Tolerance (VOC) and is defined by
Min. of
(UCL- mean of the process)/3*sigma
(LCL-mean of the process)/3*sigma
Where UCL= upper control limit of design tol
LCL= Lower control limit of design tol
Now lower the value of Cpk & having <1 would lead to the centre of the process away from the centre of VOC or the tol. Resulting the production of non-conforming product.
If one could visualise the bell graphs superimposed on the extreme tolerances (VOC) limits along with centre line,the phenomena of production of nonconforming products could be easily perceived.
As a thumb rule, we recommend that the Cp & Cpk values should be1.66 and1.33 respectively.
