CONSTANT STRESS ACCELERATED LIFE TESTING DESIGNWITH TYPE-II CENSORING SCHEME FOR PARETO DISTRIBUTION USING GEOMETRIC PROCESS
Subject Areas : International Journal of Mathematical Modelling & Computations
Mustafa
Kamal
1
(Aligarh Muslim University
India
Mr. Mustafa Kamal received his B.Sc., M.Sc. and M.Phil. in Statistics from Aligarh Muslim University India, respectively in 2006, 2009 and 2011. Currently he is working as a Project Fellow in a project given by UGC to the Department of Statistics and Operations Research, Aligarh Muslim University, India under DRS-I (SAP) (Code: 1206). He is an active member of The Gnedenko e-Forum established by the International Group on Reliability (I.G.O.R.). His current research interests include Reliability Theory, Accelerated Life Testing, Statistical Inference and Quality Control.)
Keywords: Maximum Likelihood Estimation, Reliability Function, Fisher Information Matrix, Asymptotic Confidence Interval, Simulation study,
Abstract :
In many of the studies concerning Accelerated life testing (ALT), the log linear function between life and stress which is just a simple re-parameterization of the original parameter of the life distribution is used to obtain the estimates of original parameters but from the statistical point of view, it is preferable to work with the original parameters instead of developing inferences for the parameters of the log-linear link function. In this paper the geometric process is used to estimate the parameters of Pareto Distribution with type-II censored data in constant stress accelerated life testing. Assuming that the lifetimes under increasing stress levels form a geometric process, estimates of the parameters are obtained by using the maximum likelihood method. In addition, asymptotic confidence interval estimates of the parameters using Fisher information matrix are also obtained. The statistical properties of estimates of the parameters and the confidence intervals are illustrated by a Simulation study.