Sequential estimation of the guarantee times for systems of several exponential components

The minimum guaranteed lifetimes of series and parallel systems of components are the minimum and maximum of the individual guaranteed lifetimes, respectively. If the individual lifetimes independently follow two-parameter exponential distributions with a common scale parameter but possibly differing location parameters, then the minimum guaranteed lifetime of a series and parallel system of such components are the minimum and maximum of the location parameters, respectively. In this paper, we discuss sequential estimation of the minimum and maximum of several two-parameter exponential location parameters. Sequential stopping rules are developed under both the minimax risk and bounded maximum risk criteria. Asymptotic properties are provided for each stopping rule.