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Statistical Inference for Burr Type X Distribution using Geometric Process in Accelerated Life Testing Design for Time censored data

Author(s)
Ahmadur Rahman Department of Statistics and O.R., Aligarh Muslim University, Aligarh-202002, India
Tabassum Naz Sindhu Department of Statistics, Quad-i-Azam University 45320, Islamabad 44000, Pakistan; Department of Sciences and Humanities, FAST - National University, Islamabad, Pakistan
Showkat Ahmad Lone Department of Statistics and O.R., Aligarh Muslim University, Aligarh-202002, India
Mustafa Kamal College of Science and Theoretical Studies, Saudi Electronics University, Dammam, Saudi Arabia
Abstract
In accelerated life testing researcher generally use a life stress relationship between life characteristic and stress to estimate the parameters of failure time distributions at use condition which is just a re-parameterization of original parameters but from statistical point of view it is easy and reasonable to deal with original parameters of the distribution directly instead of developing inference for the parameters of the life stress relationship. So, an attempt is made here to estimate the parameters of Burr Type X life distribution directly in accelerated life testing by assuming that the lifetimes at increasing stress levels forms a geometric process. A mathematical model for the analysis of constant stress accelerated life testing for type-I censored data is developed and the estimates of parameters are obtained by using the maximum likelihood method. Also a Fisher information matrix is constructed in order to get the asymptotic variance and interval estimates of the parameters. Lastly, a simulation study is performed to illustrate the statistical properties of the parameters and the confidence intervals.
Publication Details
Page(s) 577-586
DOI 10.18187/pjsor.v16i3.2252
Published Journal: Pakistan Journal of Statistics and Operation Research, Volume: 16, Issue: 3, Year: 2020

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Keywords
maximum likelihood estimation, Reliability function, Simulation Study, Fisher information matrix, Type-I censored sample, Confidence Intervals
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