Exact Semiparametric Inference and Model Selection for Load-Sharing Systems

Abstract

As a specific proportional hazard rates model, sequential order statistics can be used to describe the lifetimes of load-sharing systems. Inference for these systems needs to account for small sample sizes, which are prevalent in reliability applications. By exploiting the probabilistic structure of sequential order statistics, we derive exact finite sample inference procedures to test for the load-sharing parameters and for the nonparametrically specified baseline distribution, treating the respective other part as a nuisance quantity. This improves upon previous approaches for the model, which either assume a fully parametric specification or rely on asymptotic results. Simulations show that the tests derived are able to detect deviations from the null hypothesis at small sample sizes. Critical values for a prominent case are tabulated.

Confidence bands for exponential distribution functions under progressive type-II censoring

“…More results on inference with SOSs can be found, for instance, in [29] and [30]. For recent works, see, e.g., [31] and [32]. Finally, notice that SOSs with proportional hazard rates are closely related to generalized order statistics; see [26,27,33].…”

Link functions for parameters of sequential order statistics and curved exponential families

“…, which describe successive changes in the system due to component failures, and the baseline distribution function F will usually be unknown and will have to be estimated based on the available data. In a non-parametric approach such as in [9], [10], and [23], the distribution function F can be estimated. However, in lifetime experiments, the number of observations is commonly fairly small.…”