Here's my question. I'm reading an old work document written back in the 80s. The purpose is to calculate a 95/95 one-sided

**tolerance**interval for a parameter of interest. To do this, they use the following equation:

x + 1.645*S

where

S = sqrt( (dF/dx * zx * sx)^2 + (dF/dy * zy * sy)^2 + ... )

It is assumed that each parameter, i.e., x, y, ..., follows a normal distribution.

Note that each term has a corresponding z applied to it for a 95% confidence interval. The entire thing is then multiplied again outside the square root by 1.645. Does this give a 95/95 one-sided tolerance interval, or is this closer to a confidence interval?

I've seen a variety of explanations online that explain calculating the tolerance interval as x+KS where S is only based on one parameter, and hence one sample size (n). The k-factor is then looked up based on n. However, in the above scenario, each component of S has a different n. I can't find anything that addresses this scenario.

I'm an engineer that hasn't had to use statistics in almost 20 years, please be gentle with the response. And please let me know if this question is better suited for a different forum.