Exact Semiparametric Inference and Model Selection for Load-Sharing Systems

TL;DR

This paper develops exact finite sample inference methods for load-sharing systems modeled by sequential order statistics, addressing small sample challenges in reliability analysis.

Contribution

It introduces novel exact inference procedures for load-sharing parameters and baseline distribution, improving upon parametric and asymptotic methods.

Findings

Tests effectively detect deviations at small sample sizes

Exact inference procedures outperform asymptotic approaches

Critical values are tabulated for practical use

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.