Calculates capability statistics (R.W. Payne).
Option
PRINT = string tokens |
Controls output (cpk, ppk, histogram); default cpk, ppk |
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Parameters
DATA = variates or pointers |
Data measurements |
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SAMPLES = factors or scalars |
Factor identifying samples or scalar indicating the size of each sample |
LOWERLIMIT = scalars |
Specifies the lower specification limit for each set of data |
UPPERLIMIT = scalars |
Specifies the upper specification limit for each set of data |
CPK = scalars |
Saves the index Cpk |
PPK = scalars |
Saves the index Ppk |
Description
SPCAPABILITY calculates capability statistics. These are used to assess the extent to which the output of a process lies within its specification limits. The data values consist of samples of measurements made on successive occasions, which are specified by the DATA and SAMPLES parameters. DATA can be set to a variate containing the measurement and SAMPLES to a factor identifying the samples. Alternatively, if the samples are all of the same size and occur in the DATA variate one sample at a time, you can set SAMPLES to a scalar indicating the size of each sample. Finally, if the samples are in separate variates, you can set DATA to a pointer containing the variates (SAMPLES is then unset). The LOWERLIMIT parameter supplies the lower specification limit of the process, and the UPPERLIMIT parameter supplies the upper limit.
There are two indexes that can be calculated. The index Cpk is the minimum of the two quantities Cpl and Cpu. These are defined as
Cpl = (LOWERLIMIT – mean) / (3 × sigma)
Cpu = (UPPERLIMIT – mean) / (3 × sigma)
where sigma is the within-sample standard deviation (see for example Ryan 1989, Chapter 7). The alternative index, Ppk, is the minimum of the two quantities Ppl and Ppu. These have similar definitions to Cpl and Cpu, except that sigma now also includes the between-sample variation.
The PRINT option controls which of these are printed, with settings cpk and ppk. There is also a setting histogram, which plots a histogram of the data together with vertical lines indicating the lower and upper limits. By default PRINT=cpk,ppk. Alternatively, the indexes can be saved, in scalars, using the parameters CPK and PPK.
Option: PRINT.
Parameters: DATA, SAMPLES, LOWERLIMIT, UPPERLIMIT, CPK, PPK.
Method
SPCAPABILITY estimates the within-sample standard deviation (for Cpk) by the average of the standard deviations of the samples, each divided by a bias correction constant c4:
c4 = √(2/n) × GAMMA(n/2) / GAMMA((n-1)/2)
where n is the sample size. Similarly the standard deviation for Ppk is the bias-corrected standard deviation of the samples, all pooled together.
Action with RESTRICT
Neither the DATA variates nor the SAMPLE factors may be restricted.
Reference
Ryan, T.P. (1989). Statistical Methods for Quality Improvement. Wiley, New York.
See also
Procedures: SPCCHART, SPCUSUM, SPEWMA, SPPCHART, SPSHEWHART.
Commands for: Six sigma.
Example
CAPTION 'SPCAPABILITY example',\
!t('Data from Montgomery (1985), Introduction',\
'to Statistical Process Control, page 207.'); STYLE=meta,plain
VARIATE Diameter
READ Diameter
74.030 74.002 74.019 73.992 74.008
73.995 73.992 74.001 74.011 74.004
73.988 74.024 74.021 74.005 74.002
74.002 73.996 73.993 74.015 74.009
73.992 74.007 74.015 73.989 74.014
74.009 73.994 73.997 73.985 73.993
73.995 74.006 73.994 74.000 74.005
73.985 74.003 73.993 74.015 73.988
74.008 73.995 74.009 74.005 74.004
73.998 74.000 73.990 74.007 73.995
73.994 73.998 73.994 73.995 73.990
74.004 74.000 74.007 74.000 73.996
73.983 74.002 73.998 73.997 74.012
74.006 73.967 73.994 74.000 73.984
74.012 74.014 73.998 73.999 74.007
74.000 73.984 74.005 73.998 73.996
73.994 74.012 73.986 74.005 74.007
74.006 74.010 74.018 74.003 74.000
73.984 74.002 74.003 74.005 73.997
74.000 74.010 74.013 74.020 74.003
73.988 74.001 74.009 74.005 73.996
74.004 73.999 73.990 74.006 74.009
74.010 73.989 73.990 74.009 74.014
74.015 74.008 73.993 74.000 74.010
73.982 73.984 73.995 74.017 74.013 :
SPCAPABILITY Diameter; SAMPLES=5; LOWERLIMIT=73.95; UPPERLIMIT=74.05