SPPCHART procedure

Plots p or np charts for binomial testing for defective items (A.F. Kane & R.W. Payne).


Options

PRINT = string
What to print (warnings); default * i.e. nothing

PLOT = string
Type of chart to plot (p, np); default p

METHOD = string
Method to use to obtain the control limits (complementaryloglog, given, logit, probit, untransformed); default untr

TOLERANCEMULTIPLIER = scalar
Multiplier to use to test whether to use mean sample size for control limits; default 1

WINDOW = scalar
Which high-resolution graphics window to use; default 3

SCREEN = string
Whether or not to clear the graphics screen before plotting (clear, keep); default clea


Parameters

NDEFECTIVE = variates
Number of defective items

NTESTED = scalars or variates
Number of items tested

CENTRELINE = scalars
Sets or saves centre line

LOWERCONTROLLIMIT = scalars or variates
Sets or saves lower control limit

UPPERCONTROLLIMIT = scalars or variates
Sets or saves upper control limit


Description

The p and np charts are used in statistical process control to evaluate testing schemes in which successive batches of items are classified as either good or defective. The number of defective items in each batch is specified, in a variate, by the NDEFECTIVE parameter. The NTESTED parameter supplies the number of items in each batch - this can be a scalar if the batches are all of the same size, otherwise it is a variate.

   The PLOT option controls the type of chart: the p chart plots the proportion of defective items while the np chart (which is most useful each batch of items has the same total size) plots the number of defective items.

   The charts contain not only the observed numbers or proportions but also a centre line (indicating a target value) and lines showing upper and lower control limits (bounding the zone outside which the process is said to be out of control). The control limits relevant to each batch will depend on the batch sizes. The TOLERANCE option determines whether an average total size is used if the individual totals are not exactly equal: this will happen unless either

MIN(NTESTED) * TOLERANCE < MEAN(TESTED)

or

MEAN(TESTED) * TOLERANCE < MAX(NTESTED)

The METHOD option specifies how the various lines are to be defined, with the following settings. They are defined below for a p chart. For an np chart, the values are simple multiplied by the batch size(s).

    untransformed
this is the default setting, and requests the method conventionally used in SPC. The centre line is at

p = (total number defective) / (total number tested)

and the limits are at p + 3 × √(p / (1-p))

    given
specifies that the values are supplied by the CENTRELINE, LOWERCONTROLLIMIT and UPPERCONTROLLIMIT parameters.

    logit
obtains the values as the batch mean +/- three times its standard error as estimated on the logit scale of a generalized linear model (with binomial distribution).

    probit
obtains the values as the batch mean +/- three times its standard error as estimated on the probit scale of a generalized linear model

    complementaryloglog
obtains the values as the batch mean +/- three times its standard error as estimated on the complementary-log-log scale of a generalized linear model.

For settings of METHOD other than given, the CENTRELINE, LOWERCONTROLLIMIT and UPPERCONTROLLIMIT parameters can be used to save the centre line and limits.

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

 

Options: PRINT, PLOT, METHOD, TOLERANCEMULTIPLIER, WINDOW, SCREEN.

Parameters: NDEFECTIVE, NTESTED, CENTRELINE, LOWERCONTROLLIMIT, UPPERCONTROLLIMIT.


Method

For further information about the standard SPC methods see for example Chapter 5 of Montgomery (1985). Chapter 3 of the Guide to GenStat, Part 2 Statistics gives more details about generalized linear models.


Action with RESTRICT

Any restrictions are ignored.


Reference

Montgomery, D.C. (1985). Introduction to Statistical Process Control. Wiley, New York.