Calculating Prediction and Tolerance Intervals

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In this video, you learn how to construct prediction intervals and tolerance intervals in JMP using the file Diameter 04.jmp. This data set contains diameter measurements for 100 parts, collected in rational subgroups.

First, we create a distribution analysis for Diameter. To do this, we use the Distribution platform from the Analyze menu. We select Diameter for Y, Column and click OK.

A 95% confidence interval is provided, by default, in the Summary Statistics table. This is reported as Upper 95% Mean and Lower 95% Mean. Based on these data, we are 95% confident that the true mean diameter is between 16.13 and 16.15 mm.

To generate a prediction interval, we select the Prediction Interval from the red triangle for Diameter.

In the resulting dialog box, you can specify the confidence level and the number of future samples to include in the interval.

By default, JMP produces a two-sided prediction interval. Options for one-sided intervals are also available.

We’ll accept the default values and specify a two-sided 95% prediction interval for the next observation.

The prediction interval is 16.02 to 16.25 mm. Assuming that the process does not change, you can be 95% confident that the diameter for the next part will fall within this interval.

Now, we construct a tolerance interval for these same data. To do this, we select Tolerance Interval from the red triangle for Diameter.

In the dialog box, you can specify the confidence level and the proportion of future values to be covered by the tolerance interval.

By default, JMP produces a two-sided tolerance interval, but you can select a one-sided interval instead. JMP also produces a tolerance interval assuming the normal distribution. If the underlying distribution is not normal, you can select a nonparametric tolerance interval instead.

We’ll construct a 95% confidence interval to cover 95% of future observations, using the other default settings.

From this interval, we can be 95% confident that at least 95% of future diameter values will fall between 16.01 and 16.27.

[PatrickGiuliano]

Hello @Mia , 

To your knowledge, has anyone developed an algorithm or add-in in JMP to calculate distribution free prediction intervals? I'm looking for this same "nonparametric" option for the calculation of prediction intervals as what is available for tolerance intervals.  I will put in the request to the development team but for now I'm looking for a stopgap solution to calculate this manually in JMP using simple column formulas, more complex JSL or an add-in if available.

I have a good textbook reference but I am having trouble deciphering it: 

Gerald Hahn and William Meeker, Statistical Intervals: A Guide for Practitioners 1991, Wiley & Sons

Thanks, @PatrickGiuliano 

[Jeff_Perkinson]

Hello @Mia , 

To your knowledge, has anyone developed an algorithm or add-in in JMP to calculate distribution free prediction intervals? I'm looking for this same "nonparametric" option for the calculation of prediction intervals as what is available for tolerance intervals.  I will put in the request to the development team but for now I'm look for a stopgap solution to calculate this manually in JMP using simple column formulas, more complex JSL or an add-in if available.

I have a good textbook reference but I am having trouble deciphering it: 

Gerald Hahn and William Meeker, Statistical Intervals: A Guide for Practitioners 1991, Wiley & Sons

Hi @PatrickGiuliano, I suspect you were looking for @mia_stephens with your comment above. 

[PatrickGiuliano]

Thank you @Jeff_Perkinson   Yes.   my mistake.

[mia_stephens]

Hi @PatrickGiuliano, I'm not aware of anything. I thought I had some materials on this, but am not finding and can't seem to locate my copy of Hahn/Meeker - I'm fairly certain it's covered there, perhaps with lookup tables as they have for nonparametric tolerance intervals. Might be good to post this on the community discussion forum - perhaps another JMP power user has created a script or add-in. Sorry to not be of more help!

[PatrickGiuliano]

Thanks @mia_stephens.  Thank you to @Kristen Bradford @ JMP Technical Support (SAS 7613401446) for confirming that this feature does not exist currently in JMP.  I searched the community and didn't find anything either.  I will put in a request through EA17 Beta and through the "JMP Wish List."  Cheers  @PatrickGiuliano 

[hogi]

wish: second part of Additional Nonparametric Statistics Options in Distribution Platform (Nonpar Equivalence and Nonpar ...