Inference and optimal design on step-stress partially accelerated life test for hybrid system with masked data

Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations(MLEs)of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover,two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality criteria.Finally, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.

A Comprehensive Review of Accelerated Life Test

Accelerated life test (ALT) is an important branch of reliability test and is a focus of research both for statisticians and reliability engineers. The paper outlines the four topics of study embodied in ALT: statistical analysis of constant-stress test, step-stress test and progressive stress test, and optimal design of ALT. It gives a general review of engineering applications of ALT, and points out some possible directions in ALT, gives some suggestions for further study.

Step-stress accelerated degradation test planning based on Wiener processwith correlation

To assess the lifetime distribution of highly reliable or expensive product,one of the most commonly used strategies is to construct step-stress accelerated degradation test(SSADT)which can curtail the test duration and reduce the test cost.In reality,it is not unusual for a unit with a higher degradation rate which exhibits a more volatile degradation path.Recently,Ye,Chen,and Shen[(2015).A new class of Wiener process models for degradation analysis.Reliability Engineering and System Safety,139,58–67]proposed a Wiener process to capture the positive correlation between the drift rate and the volatility.In this paper,an optimal SSADT plan is developed under the assumption that the underlying degradation path follows the Wiener process with correlation.Firstly,the stochastic diffusion process is introduced to model a typical SSADT problem.Then the design variables,including the sample size,the measurement frequency and the numbers of measurements under each stress level,are optimised by minimising the asymptotic variance of the estimated p-percentile of the product’s lifetime distribution subject to the total experimental cost not exceeding a pre-specified budget.Finally,a numerical example is presented to illustrate the proposed method.

Statistical Inference for a Simple Step Stress Model with Competing Risks Based on Generalized Type-ⅠHybrid Censoring

This paper investigates a simple step-stress accelerated lifetime test(SSALT)model for the inferential analysis of exponential competing risks data.A generalized type-I hybrid censoring scheme is employed to improve the efficiency and controllability of the test.Firstly,the MLEs for parameters are established based on the cumulative exposure model(CEM).Then the conditional moment generating function(MGF)for unknown parameters is set up using conditional expectation and multiple integral techniques.Thirdly,confidence intervals(CIs)are constructed by the exact MGF-based method,the approximate normality-based method,and the bias-corrected and accelerated(BCa)percentile bootstrap method.Finally,we present simulation studies and an illustrative example to compare the performances of different methods.