capability
Process capability indices
Syntax
S = capability(data,specs)
Description
S = capability(data,specs) estimates capability
indices for measurements in data given the specifications
in specs. data can be either
a vector or a matrix of measurements. If data is
a matrix, indices are computed for the columns. specs can
be either a two-element vector of the form [L,U] containing
lower and upper specification limits, or (if data is
a matrix) a two-row matrix with the same number of columns as data.
If there is no lower bound, use -Inf as the first
element of specs. If there is no upper bound, use Inf as
the second element of specs.
The output S is a structure with the following
fields:
mu— Sample meansigma— Sample standard deviationP— Estimated probability of being within limitsPl— Estimated probability of being belowLPu— Estimated probability of being aboveUCp—(U-L)/(6*sigma)Cpl—(mu-L)./(3.*sigma)Cpu—(U-mu)./(3.*sigma)Cpk—min(Cpl,Cpu)
Indices are computed under the assumption that data values are independent samples from a normal population with constant mean and variance.
Indices divide a “specification width” (between specification limits) by a “process width” (between control limits). Higher ratios indicate a process with fewer measurements outside of specification.
Examples
Compute Capability Indices
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
References
[1] Montgomery, D. Introduction to Statistical Quality Control. Hoboken, NJ: John Wiley & Sons, 1991, pp. 369–374.