Analysis of Type-II progressively hybrid censored data

The mixture of Type-I and Type-II censoring schemes, called the hybrid censoring scheme, is quite common in life-testing or reliability experiments. Recently, Type-II progressive censoring scheme has become quite popular for analyzing highly reliable data. One drawback of the Type-II progressive censoring scheme is that the length of the experiment can be quite large. In this paper, we introduce a Type-II progressively hybrid censoring scheme, where the experiment terminates at a pre-specified time. For this censoring scheme, we analyze the data under the assumptions that the lifetimes of the different items are independent and exponentially distributed random variables with parameter @l. We obtain the maximum-likelihood estimator of the unknown parameter in an exact form. Asymptotic confidence intervals based on @l@^, ln@l@^, confidence interval based on likelihood ratio test and two bootstrap confidence intervals are also proposed. Bayes estimate and credible interval of the unknown parameter are obtained under the assumption of gamma prior of the unknown parameter. Different methods have been compared using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.

[1]  Bong-Jin Yum,et al.  Development of r,T hybrid sampling plans for exponential lifetime distributions , 1996 .

[2]  A. Cohen,et al.  Query 18: Life Testing and Early Failure , 1966 .

[3]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[4]  Peter Congdon.  Bayesian statistical modelling , 2002 .

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

[6]  Irwin Guttman,et al.  Bayesian analysis of hybrid life tests with exponential failure times , 1987 .

[7]  Norman L. Johnson,et al.  Life Testing and Early Failure , 1966 .

[8]  P. Hall.  Theoretical Comparison of Bootstrap Confidence Intervals , 1988 .

[9]  N. Balakrishnan,et al.  Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution , 2003 .

[10]  R. Dykstra,et al.  A Confidence Interval for an Exponential Parameter from a Hybrid Life Test , 1982 .

[11]  E. Cramer.  Balakrishnan, Narayanaswamy ; Aggarwala, Rita: Progressive censoring : theory, methods, and applications / N. Balakrishnan ; Rita Aggarwala. - Boston ; Basel ; Berlin, 2000 , 2000 .

[12]  A. Cohen,et al.  Progressively Censored Samples in Life Testing , 1963 .

[13]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data. , 1983 .

[14]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[15]  B. Efron.  The jackknife, the bootstrap, and other resampling plans , 1987 .

[16]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[17]  Benjamin Epstein.  Estimation from Life Test Data , 1960 .

[18]  Narayanaswamy Balakrishnan,et al.  Analysis of Progressively Censored Competing Risks Data , 2003, Advances in Survival Analysis.

[19]  G. K. Bhattacharyya,et al.  Exact confidence bounds for an exponential parameter under hybrid censoring , 1987 .

[20]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[21]  Debasis Kundu,et al.  Hybrid censoring schemes with exponential failure distribution , 1998 .

[22]  B. Epstein.  Truncated Life Tests in the Exponential Case , 1954 .