Real Statistics Support for Tolerance Intervals

Worksheet Functions

Real Statistics Functions: The Real Statistics Resource Pack provides the following functions.

TOLERANCE_LOWER(R1, p, α, type) = lower limit of the 100p% tolerance interval based on the sample in R1, confidence level 1 – α.

If type ≥ 0 then it is assumed that the data in R1 is normally distributed and so the value m-k*s is returned where m = the mean of the data in R1, s = the standard deviation of R1, n = the number of elements in R1 and k = TOLERANCE_NORM(n, p, α, type).

If type = -1, then the lower limit of the one-sided non-parametric tolerance interval is returned, while if type = -2 then the lower limit of the two-sided non-parametric tolerance interval is returned.

TOLERANCE_UPPER(R1, p, α, type) = upper limit of the 100p% tolerance interval based on the sample in R1, confidence level 1 – α.

If type ≥ 0 then it is assumed that the data in R1 is normally distributed and so the value m+k*s is returned where m = the mean of the data in R1, s = the standard deviation of R1, n = the number of elements in R1 and k = TOLERANCE_NORM(n, p, α, type).

If type = -1, then the upper limit of the one-sided non-parametric tolerance interval is returned, while if type = -2 then the upper limit of the two-sided non-parametric tolerance interval is returned.

TOLERANCE_SIZE(p, α, tails) = the minimum sample size required for a tails-sided non-parametric 100p% tolerance interval with confidence level 1–α; tails = 1 or 2 (default)

The default for p is .90, the default for α is .05 and the default for type is 2. For the two-sided interval, TOLERANCE_SIZE is valid for values of p up to about 99.999%, much higher for the one-sided interval.

Observations

The values in Figure 2 of Non-parametric Tolerance Intervals can be computed using these worksheet functions. E.g. cell O13 can be computed by the worksheet formula =TOLERANCE_UPPER(B3:I17,O4,O5,1), while cell T18 can be computed by the formula =TOLERANCE_LOWER(B3:I17,T4,T5,-2).

The minimum sample size for the one-sided non-parametric tolerance interval with p = .90 and α = .01 is 44, as calculated by the formula =TOLERANCE_SIZE(.9, .01, 1). The minimum sample size for the two-sided interval is 64 as calculated by =TOLERANCE_SIZE(.9, .01, 2).

Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

Reference

JMP (2020) Tolerance intervals. SAS
https://www.jmp.com/support/help/en/15.1/index.shtml#page/jmp/tolerance-intervals-2.shtml#

7 thoughts on “Real Statistics Support for Tolerance Intervals”

    • Hello Stathis,
      I just checked and TOLERANCE_UPPER is returning a numeric value for the data shown on the webpage when type = -1 or -2.
      What do you see when you enter the formula =VER() in any cell?
      If you aren’t using the example data, can you email me an Excel file with your data so that I can try to figure out what is ging wrong?
      Charles

      Reply
      • Thank you Charles,

        I figured it out, it was a sample size problem, I was trying to perform =TOLERANCE_UPPER(A2:A61,0.99,0.05,-1) while the sample size was 60. When I make it =TOLERANCE_UPPER(A2:A61,0.95,0.05,-1), it gave me correct answer.

        Thanks again,
        Stathis

        Reply
  1. Great set of tools, Dr. Zaiontz! Would you happen to have a function for a tolerance interval for a rare event (perhaps a Poisson tolerance interval)? I currently use R and SAS but a non-stats colleague would like an Excel solution.
    Best,
    Jesse

    Reply
    • Jesse,
      Thank you for your kind words. I appreciate it.
      Real Statistics doesn’t support a Poisson tolerance interval. Do you have a reference for this capability that would be helpful for its implementation?
      Charles

      Reply
  2. Does real statistics have a function similar to TOLERANCE_SIZE, but for sample size for tolerance intervals on a normal distribution?

    Reply

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