# Reliability assessment model for multiple stress factors accelerated degradation test using a Wiener process with random effects

## TL;DR

This paper introduces a new model for testing product reliability under multiple stress factors using a Wiener process, which accounts for random effects and measurement errors.

## Contribution

The novelty lies in extending the Wiener process model to handle multiple stress factors and random effects simultaneously in accelerated degradation testing.

## Key findings

- The model provides an explicit expression for the lifetime distribution under normal operating conditions.
- Maximum likelihood estimates for model parameters and reliability metrics are derived using the profile likelihood approach.
- Simulation studies and a numerical example confirm the effectiveness of the proposed method.

## Abstract

In practical applications, products are usually exposed to multiple stress factors (including environmental stresses and operating stresses) simultaneously. However, existing work on accelerated degradation test mainly focuses on the case of a single stress factor. This motivates the need to develop a reliability assessment model for accelerated degradation test involving multiple stress factors. Therefore, this paper proposes a Wiener process-based accelerated degradation test model that simultaneously considers multiple stress factors, random effects and measurement errors. Then the explicit expression for the lifetime distribution under normal operating conditions of the proposed Wiener accelerated degradation test model is obtained, along with its approximate mean lifetime. In addition, the maximum likelihood estimates of model parameters are derived using the profile likelihood approach, and maximum likelihood estimates for some reliability metrics under normal operating conditions are also obtained. Besides, we construct confidence intervals for model parameters and some reliability metrics using the bias-corrected and accelerated percentile bootstrap method. Finally, the performance of the proposed method is demonstrated by extensive simulation studies, and a numerical example.