SPEWMA procedure

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

Options

Parameters

Description

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:

w_t = r_t × xbar_t + (1 – r) × w_t–₁

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 / √(REP_t)) × √( (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

MIN(REP) * TOLERANCE < MEAN(rep)

or

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.

Options: PRINT, TOLERANCEMULTIPLIER, WEIGHT, NSIGMA, WINDOW, SCREEN.

Parameters: DATA, SAMPLES, MEAN, SIGMA.

Method

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.

Reference

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

See also

Procedures: SPCAPABILITY, SPCCHART, SPCUSUM, SPPCHART, SPSHEWHART.

Commands for: Six sigma.

Example

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,\
          9.5,12.0,12.5,10.5,8.0,9.5,7.0,10.0,13.0,9.0,\
          12.0,6.0,12.0,15.0,11.0,7.0,9.5,10.0,12.0,8.0,\
          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