Abstract

Constant-stress procedures based on parametric lifetime distributions and models are often used for accelerated life testing in product reliability experiments. Maximum likelihood estimation (MLE) is the typical statistical inference method. This paper presents a new inference method, named the random variable transformation (RVT) method, for Weibull constant-stress accelerated life tests with progressively Type-II right censoring (including ordinary Type-II right censoring). A two-parameter Weibull life distribution with a scale parameter that is a log-linear function of stress is used. RVT inference life distribution parameters and the log-linear function coefficients are provided. Exact confidence intervals for these parameters are also explored. Numerical comparisons of RVT-based estimates to MLE show that the proposed RVT inference is promising, in particular for small sample sizes.

Highlights

  • I N many industrial fields, it is required for lots of products to operate for a long period of time

  • We study the performance of coverage probabilities of these

  • Simulation for parameter estimation of the Weibull distribution shows that, in terms of estimation bias and MSE, the performance of the proposed random variable transformation (RVT) method is significantly better than that of the Maximum likelihood estimation (MLE) method

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Summary

INTRODUCTION

I N many industrial fields, it is required for lots of products to operate for a long period of time. It provides higher flexibility to the experimenter in the design stage by allowing the removal of test units at non-terminal time points, and it proves to be highly efficient and effective in utilizing the available resources (Montanari and Cacciari [30], Balakrishnan and Aggarwala [31]) Another advantage of progressive censoring is that the degeneration-related information of the test units is obtained from those removed units (Balasooriya et al [32]). Wang [37] derived interval estimation for exponential progressive Type-II censored step-stress ALT. We consider CSALT with progressive Type-II censoring, and provide RVT inference for parameter estimation and CIs. The Weibull CSALT model considered is under the following two assumptions. The observed Fisher-information matrix for is given by

RVT INFERENCE
INTERVAL ESTIMATION OF UNKNOWN PARAMETERS
Exact CI for the Shape Parameter
Generalized CIs for Other Parameters
SIMULATION STUDY
A REAL EXAMPLE AND ITS ANALYSIS
Findings
CONCLUSION
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