schart (Statistics Toolbox)

Chart of standard deviation for Statistical Process Control

Syntax

schart(DATA,conf)
schart(DATA,conf,specs)
schart(DATA,conf,specs)
[outliers,h] = schart(DATA,conf,specs)

Description

schart(data) displays an S chart of the grouped responses in DATA. The rows of DATA contain replicate observations taken at a given time. The rows must be in time order. The graph contains the sample standard deviation s for each group, a center line at the average s value, and upper and lower control limits. The limits are placed at a three-sigma distance on either side of the center line, where sigma is an estimate of the standard deviation of s. If the process is in control, fewer than 3 out of 1000 observations would be expected to fall outside the control limits by random chance. So, if you observe points outside the limits, you can take this as evidence that the process is not in control.

schart(DATA,conf) allows control of the confidence level of the upper and lower plotted control limits. The default conf = 0.9973 produces three-sigma limits.

norminv(1 - (1-.9973)/2)
ans =
            3

To get k-sigma limits, use the expression 1-2*(1-normcdf(k)). For example, the correct conf value for 2-sigma limits is 0.9545, as shown below.

k = 2;
1-2*(1-normcdf(k))
ans =
       0.9545

schart(DATA,conf,specs) plots the specification limits in the two element vector specs.

[outliers,h] = schart(data,conf,specs) returns outliers, a vector of indices to the rows where the mean of DATA is out of control, and h, a vector of handles to the plotted lines.

Example

This example plots an S chart of measurements on newly machined parts, taken at one hour intervals for 36 hours. Each row of the runout matrix contains the measurements for 4 parts chosen at random. The values indicate, in thousandths of an inch, the amount the part radius differs from the target radius.

```
load parts
schart(runout)
```

All points are within the control limits, so the variability within subgroups is consistent with what would be expected by random chance. There is no evidence that the process is out of control.

Reference

[1] Montgomery, D., Introduction to Statistical Quality Control, John Wiley and Sons 1991. p. 235.

See Also
capaplot, ewmaplot, histfit, xbarplot

rstool signrank