For any fixed values of k, α, and p (see Tolerance Interval), you can estimate the sample size required to obtain the specified tolerance interval by using Excel’s Goal Seek capability.
Example
Example 1: What is the sample size necessary to achieve a 95% tolerance interval with 99% confidence for Example 1 of Tolerance Interval Example?
We fill in the Goal Seek dialog box as shown in Figure 1.
Figure 1 – Goal Seek to estimate sample size
After pressing the OK button, we obtain a sample size of 172.851, as shown in Figure 2.
Figure 2 – Goal Seek results
Actually, using a little trial and error, a value of n = 166 or 167 would give an even better estimate.
Links
Examples Workbook
Click here to download the Excel workbook with the examples described on this webpage.
References
NCSS (2019) Tolerance intervals for normal data
https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/PASS/Tolerance_Intervals_for_Normal_Data.pdf
NIST (2019) Tolerance intervals for a normal distribution
https://www.itl.nist.gov/div898/handbook/prc/section2/prc263.htm#cases