Statistics Toolbox™

Capability Studies

Before going into production, many manufacturers run a capability study to determine if their process will run within specifications enough of the time. Capability indices produced by such a study are used to estimate expected percentages of defective parts.

Capability studies are conducted with the capability function. The following capability indices are produced:

• mu — Sample mean

• sigma — Sample standard deviation

• P — Estimated probability of being within the lower (L) and upper (U) specification limits

• Pl — Estimated probability of being below L

• Pu — Estimated probability of being above U

• Cp — (U-L)/(6*sigma)

• Cpl — (mu-L)./(3.*sigma)

• Cpu — (U-mu)./(3.*sigma)

• Cpk — min(Cpl,Cpu)

As an example, simulate a sample from a process with a mean of 3 and a standard deviation of 0.005:

data = normrnd(3,0.005,100,1);

Compute capability indices if the process has an upper specification limit of 3.01 and a lower specification limit of 2.99:

S = capability(data,[2.99 3.01])
S = 
       mu: 3.0006
    sigma: 0.0047
        P: 0.9669
       Pl: 0.0116
       Pu: 0.0215
       Cp: 0.7156
      Cpl: 0.7567
      Cpu: 0.6744
      Cpk: 0.6744

Visualize the specification and process widths:

capaplot(data,[2.99 3.01]);
grid on

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Function Reference