capability

Process capability indices

Syntax

S = capability(X,specs)

Description

S = capability(X,specs) returns a structure containing capability indices for the values in X given the specifications in specs. Before you put a process into production, you might run a capability study to determine if the process will run within the specifications enough of the time. Use capability indices to estimate expected percentages of defective parts.

Examples

Compute Capability Indices

Simulate a sample of 100 measurements from a process with a mean of 3 and a standard deviation of 0.005.

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

Set a lower specification limit of 2.99 and an upper specification limit of 3.01 for the process, and then compute capability indices.

specs = [2.99 3.01];
S = capability(X,specs)

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

Input Arguments

X — Input data

numeric vector | numeric matrix

Input data, specified as a numeric vector or matrix. If X is a matrix, capability operates on each column of X.

Data Types: single | double

specs — Specification limits

numeric vector | numeric matrix

Specification limits, specified as a numeric vector or matrix. If X is a vector, specs is a two-element vector that contains the lower and upper specification limits. If X is a matrix, specs is a two-row matrix with the same number of columns as X. The first row contains the lower specification limits, and the second row contains the upper specification limits.

If there is no lower specification bound, specify the first element of specs as –Inf. If there is no upper specification bound, specify the second element of specs as Inf.

Example: [0 4]

Data Types: single | double

Output Arguments

S — Capability indices

structure

Capability indices, returned as a structure with the following fields.

Field	Description
mu	Sample mean
sigma	Sample standard deviation
P	Estimated probability of being within the specification limits
Pl	Estimated probability of being below the lower specification limit L
Pu	Estimated probability of being above the upper specification limit U
Cp	(U-L)/(6*sigma)
Cpl	(mu-L)./(3.*sigma)
Cpu	(U-mu)./(3.*sigma)
Cpk	min(Cpl,Cpu)

When the capability function computes the indices, it assumes that the values in X are independent samples from a normal population with a fixed mean and variance.

Each C index is the ratio of a specification width (between specification limits) and a process width (between control limits). A higher index value indicates a process with fewer measurements outside of the specification limits.

References

[1] Montgomery, Douglas C. Statistical Quality Control. 7th ed. Nashville, TN: John Wiley & Sons, 2012.

Version History

Introduced in R2006b