Example 41.1: Specifying Probability Limits

XSCHART Statement

Example 41.1: Specifying Probability Limits

See SHWXS2 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 41.1.1:

   title 'Mean and Standard Deviation Charts With Probability Limits';
   symbol v=dot c=salmon;
   proc shewhart data=turbine;
      xschart kwatts*day  / alpha     = 0.01
                            outlimits = oillim
                            cframe    = lib
                            cinfill   = bwh
                            cconnect  = salmon;
   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 (OILSUM) that saves the probability limits. The data set OILLIM is shown in Output 41.1.2.

Output 41.1.1: Probability Limits on $\bar{X}$ and s Charts

Output 41.1.2: 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.

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