Adaptive Design and Inference for Step-Stress Accelerated Life Tests with Lifetimes from Exponential and Log-Location-Scale Families of Distributions

Date

2024

Authors

Ismail-Aldayeh, Haifa

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Abstract

This dissertation focuses on the development of an adaptive design for step-stress accelerated life testing (ALT) to address the challenges posed by extended lifetimes of consumer products. The advancement in manufacturing has led to longer operational life spans, making it difficult to perform product life testing at normal operating conditions. Accelerated life testing mitigates this issue by subjecting units to higher stress levels to acquire lifetime information more quickly, which can then be used to estimate the product's lifetime under normal operation through extrapolation using a regression model.

However, testing units at higher stress levels presents technical difficulties. To overcome this challenge, an adaptive design of step-stress ALT is proposed in this work. The stress levels are determined sequentially based on information obtained from preceding steps. After each stress level, the model parameters are updated, and decisions regarding the next stress level are made using D-, C-, A-, E-, and M-optimality design criteria. The adaptive design and inference are illustrated using exponential lifetimes with progressive Type-I censoring for D- and C-optimality criteria, assuming a log-linear relationship between the mean lifetime and stress levels.

A comparative study is conducted between the adaptive step-stress ALT (ada-ssALT) and the simple step-stress ALT (ssALT) models. Numerical tuning of parameters is performed to reduce estimation bias and improve precision, along with determining confidence intervals using approximate and empirical approaches. Multiple design criteria, including D-, C-, A-, E-, and M- optimality criteria, are considered. Computational results demonstrate the superiority of ada-ssALT over ssALT. A real case study shows that the proposed algorithm outperforms ssALT in the presence of a shock effect.

Furthermore, the dissertation extends the adaptive step-stress ALT framework to incorporate a broader range of lifetime distributions. While the exponential distribution assumes a constant hazard function, a log-location-scale family enables the analysis of data with a shape parameter, providing flexibility. The generalized form of ada-ssALT is developed for lifetime distributions following a log-location-scale family at each stress level. This includes model formulation, maximum likelihood estimation, and derivation of the information matrix, assuming a linear relationship between the standardized stress level and the location parameter. A simulation study is conducted to compare the results of ada-ssALT with ssALT under various design criteria, including D, C, A, M, and E.

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Management Science and Statistics