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Capability Studies

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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:

rng default; % For reproducibility
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 = struct with fields:
       mu: 3.0006
    sigma: 0.0058
        P: 0.9129
       Pl: 0.0339
       Pu: 0.0532
       Cp: 0.5735
      Cpl: 0.6088
      Cpu: 0.5382
      Cpk: 0.5382

Visualize the specification and process widths:

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

Figure contains an axes object. The axes object with title Probability Between Limits = 0.91292 contains 5 objects of type line, patch.

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