Optimal Accelerated Life Testing Sampling Plan Design with Piecewise Linear Function based Modeling of Lifetime Characteristics

TL;DR

This paper develops an optimal accelerated life testing sampling plan using a piecewise linear model to better capture nonlinear relationships between lifetime and stress factors, improving upon traditional linear models.

Contribution

It introduces a novel piecewise linear modeling approach within a Weibull distribution framework for accelerated life testing, accounting for unknown nonlinear stress-lifetime relationships.

Findings

Piecewise linear model outperforms linear models in simulations.

Optimal plan minimizes cost and variance effectively.

Fisher information matrix is detailed for acceptability criteria.

Abstract

Researchers have widely used accelerated life tests to determine an optimal inspection plan for lot acceptance. All such plans are proposed by assuming a known relationship between the lifetime characteristic(s) and the accelerating stress factor(s) under a parametric framework of the product lifetime distribution. As the true relationship is rarely known in practical scenarios, the assumption itself may produce biased estimates that may lead to an inefficient sampling plan. To this endeavor, an optimal accelerating life test plan is designed under a Type-I censoring scheme with a generalized link structure similar to a spline regression, to capture the nonlinear relationship between the lifetime characteristics and the stress levels. Product lifetime is assumed to follow Weibull distribution with non-identical scale and shape parameters linked with the stress factor through a piecewise linear function. The elements of the Fisher information matrix are computed in detail to formulate the acceptability criterion for the conforming lots. The decision variables of the sampling plan including sample size, stress factors, and others are determined using a constrained aggregated cost minimization approach and variance minimization approach. A simulated case study demonstrates that the nonlinear link-based piecewise linear approximation model outperforms the linear link-based model.