Reliability growth via testing

Abstract

Observed data values are typically assumed to come from an infinite population of items in reliability and survival analysis applications. The case of a finite population of items with exponentially distributed lifetimes is considered here. The data set consists of the lifetimes of a large number of items that are known to have exponentially distributed failure times with a failure rate that is known with high precision. Failure of the items is not self-announcing, as is the case with a smoke detector. A significant fraction of the items are sampled periodically, and the items that have failed are repaired to a like-new condition with respect to their survival distribution. The goal is to assess the impact of this periodic sampling and repair on the overall finite population reliability over time.

Keywords:

• Exponential distribution
• finite population
• reliability estimation
• survivor function

Acknowledegment

The author gratefully acknowledges the helpful comments provided by the three referees.