Estimation of stress–strength reliability for Maxwell distribution under progressive type-II censoring scheme

This paper deals with the estimation of stress–strength reliability $$P=P[Y<X]$$P=P[Y<X], when the strength X and stress Y both follow Maxwell distribution with different parameters. We obtain maximum likelihood and Bayes estimates of P using progressive type-II censored samples. We also provide procedures to evaluate asymptotic and bootstrap confidential intervals, as well as, Bayesian credible and highest posterior density intervals for P. We present simulation study and analyze a real data set for numerical illustrations.

[1]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[2]  Debasis Kundu,et al.  Estimation of P[Y, 2006, IEEE Transactions on Reliability.

[3]  Sanjeev K. Tomer,et al.  UMVU estimation of the reliability function of the generalized life distributions , 2003 .

[4]  Hare Krishna,et al.  Reliability estimation in Maxwell distribution with Type‐II censored data , 2009 .

[5]  Hare Krishna,et al.  Estimation of P(Y < X) in Lindley distribution using progressively first failure censoring , 2015, Int. J. Syst. Assur. Eng. Manag..

[6]  N. Balakrishnan,et al.  Progressive Censoring: Theory, Methods, and Applications , 2000 .

[7]  河田 幸三,et al.  Progress in science and engineering of composites : proceedings of the Fourth International Conference on Composite Materials, ICCM-IV Oct 25-28 1982 Tokyo Japan , 1982 .

[8]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[9]  Debasis Kundu,et al.  Estimation of for Weibull Distributions , 2006 .

[10]  Esmaile Khorram,et al.  Inference of stress-strength for the Type-II generalized logistic distribution under progressively Type-II censored samples , 2018, Commun. Stat. Simul. Comput..

[11]  J. Lawless.  Statistical Models and Methods for Lifetime Data , 2002 .

[12]  D. Kundu,et al.  Estimation of P(Y < X) for the Three-Parameter Generalized Exponential Distribution , 2008 .

[13]  Sanjeev K. Tomer,et al.  Estimation procedures for Maxwell distribution under type-I progressive hybrid censoring scheme , 2015 .

[14]  Ming-Hui Chen,et al.  Monte Carlo Estimation of Bayesian Credible and HPD Intervals , 1999 .

[15]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[16]  Hare Krishna,et al.  Reliability estimation in Maxwell distribution with progressively Type-II censored data , 2012 .

[17]  Richard A. Johnson,et al.  3 Stress-strength models for reliability , 1988 .

[18]  Ali I. Genç.  Estimation of P(X>Y) with Topp–Leone distribution , 2011 .

[19]  Debasis Kundu,et al.  On estimation of R=P(Y, 2012 .

[20]  A. Bekker,et al.  Reliability Characteristics of the Maxwell Distribution: A Bayes Estimation Study , 2005 .

[21]  N. Metropolis,et al.  The Monte Carlo method. , 1949 .

[22]  G. Herd.  Estimation of the parameters of a population from a multi-censored sample , 1956 .

[23]  Narayanaswamy Balakrishnan,et al.  The Art of Progressive Censoring , 2014 .

[24]  S. Kotz,et al.  The stress-strength model and its generalizations : theory and applications , 2003 .