Calcite | Level 5

## Control limits in proc rareevents

In proc rareevents the control limits by default are alpha=0.005, whereas in Shewhart charts by default they are 3 sigma limits. I know the limits in Shewhart procedure can be set up either by alpha or sigma for any chart, but  since we tend to use default values, I wonder why proc rareevents default limits are set differently from Shewhart charts?  Is it because rareevents procedure is based on two skewed distributions (geometric or exponential) and alpha=0.005 limits can be wider than 3 sigma? Can anyone here help me out? Thanks in advance!

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SAS Employee

## Re: Control limits in proc rareevents

In the RAREEVENTS procedure you can specify alpha values for the lower and upper probability limits independently.  Each defaults to 0.005, for a total probability of 0.01 that a measurement from the (estimated or specified) distribution will fall outside the limits, i.e. the probability of a type I error is 0.01.  That is higher than with a standard 3-sigma limits Shewhart chart, so the default RAREEVENTS limits are more sensitive (narrower).

There is nothing magical about the default alpha=0.005 values.  Using 0.005 instead of 0.00135 (for example) produces a more sensitive chart at the expense of more false positives.

Calcite | Level 5

## Re: Control limits in proc rareevents

Thanks for your response. The follow-up question is that why proc rareevents  doesn't use 3 sigma limits just as proc shewhart charts?

Calcite | Level 5

## Re: Control limits in proc rareevents

I get the answer to my own question by reading some SPC books. What proc rareevents does is not providing actual special cause tests like in proc shewhart. It only offers probability - based tests to aid in interpreting run chart, so proc rarevents actualy provides run charts, which is why its limits are probability based, not in 3 sigma. Thanks.

Calcite | Level 5

## Re: Control limits in proc rareevents

Need to double check the answer with SAS support though.

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