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SPEWMA procedure

Plots exponentially weighted moving-average control charts (A.F. Kane & R.W. Payne).


PRINT = string token What to print (warnings); default * i.e. nothing
TOLERANCEMULTIPLIER = scalar Multiplier to use to test whether to use mean sample size for control limits; default 1
WEIGHT = scalar Weight parameter used in the calculation of the exponentially weighted moving-average statistic; default 0.25
NSIGMA = scalar Number of multiples of sigma to use for control limits; default 3
WINDOW = scalar Which high-resolution graphics window to use; default 3
SCREEN = string token Whether or not to clear the graphics screen before plotting (clear, keep); default clea


DATA = variates or pointers Data measurements
SAMPLES = factors or scalars Factor identifying samples or scalar indicating the size of each sample
MEAN = scalars Sets or saves the sample mean value
SIGMA = scalars Sets or saves the sample standard deviation


SPEWMA plots exponentially weighted moving-average control charts for controlling the mean of a process. 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 chart plots a statistic w whose value for sample t is a weighted average of the mean of sample t, and the value of the statistic for sample t-1:

wt = rt × xbart + (1 – r) × wt1

where xbar is the variate of sample means, and r is the weighting parameter specified by the WEIGHT option of the procedure with default 0.25. (Notice that the statistic involves all the previous means, but with exponentially decreasing weights.)

The position of the central line for the chart is specified, in a scalar, by the MEAN parameter. If this is not set, or if it is set to a scalar containing a missing value, the overall mean of the samples is used. (So you can save the calculated mean by setting MEAN to a scalar containing a missing value.) There are also control lines –nsigma × var(w) and +nsigma × var(w), where nsigma is specified by the NSIGMA option (default 3) and var(w) is the variance of the statistic w. For sample t, this is

(3 × sigma / √(REPt)) × √( (r/(2 – r)) × (1 – (1 – r)2t) )

where REP is a variate containing the number of observations in each sample, and sigma is the standard deviation of a single observation. The SIGMA parameter can be used to supply a value for sigma. It this is not set or if it is set to a missing value, sigma is calculated using the within-sample replication as the average of the standard deviations of the samples, divided by a bias correction constant c4:

c4 = √(2/n) × GAMMA(n/2) / GAMMA((n-1)/2)

The TOLERANCE option determines whether an average replication is used if the replication of the individual samples is no exactly equal: this will happen unless either



MEAN(rep) * TOLERANCE < MAX(rep)

You can set PRINT=warnings to list any batches that are outside the control limits; by default these are suppressed. As usual, the WINDOWS option specifies which high-resolution graphics window to use for the plot (default 3), and the SCREEN option controls whether or not to clear the graphics screen before plotting the charts.




Further details of the method, and advice on the setting of the weight parameter, can be found for example in Ryan (1989) Section 5.5.

Action with RESTRICT

Neither the DATA variates nor the SAMPLE factors may be restricted.


Ryan, T.P. (1989). Statistical Methods for Quality Improvement. Wiley, New York.

See also


Commands for: Six sigma.


CAPTION   'SPEWMA example',\
          !t('Data from Montgomery (1985), Introduction to',\
          'Statistical Process Control, page 303.'); STYLE=meta,plain
VARIATE   [VALUES=10.5,6.0,10.0,11.0,12.5,9.5,6.0,10.0,10.5,14.5,\
          9.0,13.0,11.0,9.0,10.0,15.0,12.0,8.0] xbar_t
SPEWMA    [WEIGHT=0.2] xbar_t; SAMPLES=1; MEAN=10; SIGMA=2
Updated on March 5, 2019

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