XSCHART Statement: SHEWHART Procedure

Example 18.41 Specifying Probability Limits

Note: See X-Bar and s Charts with Probability Limits in the SAS/QC Sample Library.

This 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 18.41.1: 

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 18.41.2.

Output 18.41.1: Probability Limits on $\bar{X}$ and s Charts

Probability Limits on X and Charts


Output 18.41.2: 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. 
            

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