Example 17.41 Specifying Probability Limits :: SAS/QC(R) 12.1 User's Guide

Example 17.41 Specifying Probability Limits

See SHWXS2 in the SAS/QC Sample LibraryThis example illustrates how to create $\bar{X}$ and s charts with probability limits. The following statements read the kilowatt power output measurements from the data set Turbine (see Creating Charts for Means and Standard Deviations from Raw Data) and create the $\bar{X}$ and s charts shown in Output 17.41.1:

ods graphics off;
symbol v=dot h=.8;
title 'Mean and Standard Deviation Charts With Probability Limits';
proc shewhart data=Turbine;
   xschart KWatts*Day  / alpha     = 0.01
                         outlimits = Oillim;
run;

The ALPHA= option specifies the probability ( $\alpha$ ) that a subgroup summary statistic is outside the limits. Here, the limits are computed so that the probability that a subgroup mean or standard deviation is less than its lower limit is $\alpha /2=0.005$ , and the probability that a subgroup mean or standard deviation is greater than its upper limit is $\alpha /2=0.005$ . This assumes that the measurements are normally distributed.

The OUTLIMITS= option names an output data set (Oillim) that saves the probability limits. The data set Oillim is shown in Output 17.41.2.

Output 17.41.1: Probability Limits on $\bar{X}$ and s Charts

Output 17.41.2: Probability Limit Information

Mean and Standard Deviation Charts with Probability Limits

_VAR_	_SUBGRP_	_TYPE_	_LIMITN_	_ALPHA_	_SIGMAS_	_LCLX_	_MEAN_	_UCLX_	_LCLS_	_S_	_UCLS_	_STDDEV_
KWatts	Day	ESTIMATE	20	0.01	2.57583	3370.79	3485.41	3600.03	119.432	196.396	283.570	198.996

The variable _ALPHA_ saves the value of $\alpha$ . The value of the variable _SIGMAS_ is computed as $k=\Phi ^{-1}(1-\alpha /2)$ , where $\Phi ^{-1}$ is the inverse standard normal distribution function. Note that, in this case, the probability limits for the mean are equivalent to $2.58\sigma$ limits.

Since all the points fall within the probability limits, it can be concluded that the process is in statistical control.

XSCHART Statement: SHEWHART Procedure

Example 17.41 Specifying Probability Limits