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