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

2026-02-05

AI Summary

This study addresses the limitations of traditional accelerated life testing, which relies on pre-specified parametric stress–life relationships and is prone to estimation bias and efficiency loss due to model misspecification. Under Type-I censoring, the authors propose a generalized Weibull model employing a piecewise linear link function that avoids assuming a global parametric form, thereby flexibly capturing nonlinear stress–life dependencies. By integrating the Fisher information matrix, an optimal sampling plan is developed through the joint minimization of experimental cost and parameter estimation variance. Simulation results demonstrate that the proposed approach significantly outperforms conventional linear models in both estimation accuracy and sampling efficiency, enhancing the robustness and adaptability of accelerated life test design.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Active Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• accelerated life testing
• sampling plan
• lifetime characteristics
• stress factors
• nonlinear relationship

Innovation

• piecewise linear function
• accelerated life testing
• nonlinear link function
• Weibull distribution
• optimal sampling plan