SPCCHART procedure

Plots c or u charts representing numbers of 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 (c, u); default c

METHOD = string
Method to use to obtain the control limits (given, loglinear, 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 c and u charts are used in statistical process control to evaluate testing schemes in which numbers of defects are measured in successive batches of items. The number of defects per 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 c chart plots number of defects per batch, while the u chart plots the number of defects per item.

   The charts contain not only the observed numbers of defects 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 in a u chart will depend on the batch sizes. The TOLERANCE option determines whether an average sample size is used if the individual sizes 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.

    untransformed
this is the default setting, and requests the method conventionally used in SPC. For a c chart, the centre line is at

c = (total number defects) / (number of batches)

and the limits are at c + 3 × √(c). For a u chart, the centre line is at

u = (total number defects) / (total number of items)

and the limits are at u + 3 × √(u/n).

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

    loglinear
obtains the values by fitting a generalized linear model with Poisson distribution and log link.

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.