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The reliability demonstration depends on the assumed failure time distribution with scale parameter σ. The reliability standard, or probability of survival at time t and location μ is stated as follows:
where μ is solved for using the following:
where p* is the standard probability of survival at time t*.
Since the test is of n independent units, the number of failures has a binomial (n, p) distribution where p is the probability of a unit failing before time t. Therefore, we can express α as a function of t and n:
where μ* and σ* are from the assumed reliability standard.
For n, Brent’s method is used to find the root of:
and Φ() is the cumulative distribution function of the assumed failure time distribution.

Help created on 3/19/2020