scholarly journals Constant-stress partially accelerated life tests for inverted Weibull distribution with multiple censored data

Author(s):  
Amal S. Hassan ◽  
Salwa M. Assar ◽  
Ahmed N. Zaky

<p>Testing the lifetime of items under normal use condition often requires a long period of time, especially for products having high reliability. To minimize the costs involved in testing without reducing the quality of the data obtained, the items run at higher than usual level of stresses to induce early failures in a short time. This article concerns with constant–stress partially accelerated life test with multiple censored data. The life time of test item is assumed to follow inverted Weibull distribution. Maximum likelihood estimates are obtained for the model parameters and acceleration factor. In addition, asymptotic variance and covariance matrix of the estimators is given. The confidence intervals of the unknown parameters and acceleration factor are constructed for large sample sizes. Simulation studies are performed to investigate the performance of the estimators.</p>

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. M. Mohie EL-Din ◽  
S. E. Abu-Youssef ◽  
Nahed S. A. Ali ◽  
A. M. Abd El-Raheem

Based on progressive censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows power generalized Weibull distribution. The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) are obtained for the distribution parameters and the acceleration factor. In addition, the approximate and bootstrap confidence intervals (CIs) of the estimators are presented. Furthermore, the optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs and BEs for the parameters involved.


Author(s):  
M. Kumar ◽  
P. N. Bajeel ◽  
P. C. Ramyamol

In this paper, constant–stress partially accelerated life tests (PALT) are considered for a product with the assumption that the lifetime of the product follows Weibull distribution with known shape parameter and unknown scale parameter. Based on data obtained using Type-II censoring, the maximum likelihood estimates (MLEs) of the Weibull parameters and acceleration factor are obtained assuming linear and Arrhenius relationships with the lifetime characteristics and stress. Exact distributions of the MLEs of the parameters of Weibull distribution are also obtained. Optimal acceptance sampling plans are developed using both linear and Arrhenius relationships. Some numerical results are also presented to illustrate the resulted test plans.


Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1786 ◽  
Author(s):  
A. M. Abd El-Raheem ◽  
M. H. Abu-Moussa ◽  
Marwa M. Mohie El-Din ◽  
E. H. Hafez

In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.


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