Plots exponentially weighted moving-average control charts (A.F. Kane & R.W. Payne).
Options
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 |
Parameters
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 |
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:
wt = rt × xbart + (1 – r) × wt–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