Statistics Toolbox

Capability Studies

Before going into full-scale production, many manufacturers run a pilot study to determine whether their process can actually build parts to the specifications demanded by the engineering drawing.

Using the data from these capability studies with a statistical model allows us to get a preliminary estimate of the percentage of parts that will fall outside the specifications.

• [p,Cp,Cpk] = capable(mean(runout),spec)
  p =
     1.3940e-09
  Cp =
      2.3950
  Cpk =
      1.9812
  

The result above shows that the probability (p = 1.3940e-09) of observing an unacceptable runout is extremely low. Cp and Cpk are two popular capability indices.

C_p is the ratio of the range of the specifications to six times the estimate of the process standard deviation.

For a process that has its average value on target, a C_p of 1 translates to a little more than one defect per thousand. Recently many industries have set a quality goal of one part per million. This would correspond to a C_p = 1.6. The higher the value of C_p, the more capable the process.

C_pk is the ratio of difference between the process mean and the closer specification limit to three times the estimate of the process standard deviation.

where the process mean is µ. For processes that do not maintain their average on target, C_pk, is a more descriptive index of process capability.

EWMA Charts

Design of Experiments