On some predictors of times to failure of censored items in progressively censored samples

In this article, we consider the problem of predicting times to failure of units censored in multiple stages in a progressively censored sample from an absolutely continuous population. The best linear unbiased predictors (BLUP), the maximum-likelihood predictors (MLP), and the conditional median predictors (CMP) are considered. The properties of MLP such as unbiasedness, consistency and efficiency are examined. The MLP or modified MLP (MMLP) are derived for exponential and extreme value populations. In addition, for these populations, the conditional distributions are used to derive the CMP. Comparison of different predictors are made with respect to mean squared prediction error (MSPE). Finally, some numerical examples are presented to illustrate all the prediction methods discussed here. Using simulation studies, prediction intervals are also generated for these examples.

[1]  Narayanaswamy Balakrishnan,et al.  A Useful Property of Best Linear Unbiased Predictors with Applications to Life-Testing , 1997 .

[2]  Y. Takada.  Relation of the Best Invariant Predictor and the Best Unbiased Predictor in Location and Scale Families , 1981 .

[3]  Paul I. Nelson,et al.  Best Linear Unbiased Prediction of Order Statistics in Location and Scale Families , 1975 .

[4]  Calyampudi R. Rao,et al.  Large-sample approximations to the best linear unbiased estimation and best linear unbiased prediction based on progressively censored samples and some applications , 1997 .

[5]  Narayanaswamy Balakrishnan,et al.  Advances in Statistical Decision Theory and Applications , 1998 .

[6]  P. Sen,et al.  Order statistics and inference : estimation methods , 1992 .

[7]  Narayanaswamy Balakrishnan,et al.  Interval Estimation of Parameters of Life From Progressively Censored Data , 1994 .

[8]  Narayanaswamy Balakrishnan,et al.  Order statistics from extreme value distribution, i: tables of means, variances and covariances , 1992 .

[9]  Paul I. Nelson,et al.  15 Prediction of order statistics , 1998 .

[10]  Mohammad Ahsanullah,et al.  ON CHARACTERIZING DISTRIBUTIONS VIA LINEARITY OF REGRESSION FOR ORDER STATISTICS , 1997 .

[11]  A. Goldberger.  Best Linear Unbiased Prediction in the Generalized Linear Regression Model , 1962 .

[12]  Kenneth S. Kaminsky,et al.  Maximum likelihood prediction , 1985 .

[13]  J. F. Lawless,et al.  A Prediction Problem Concerning Samples From the Exponential Distribution, With Application in Life Testing , 1971 .

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

[15]  Wayne Nelson,et al.  Applied life data analysis , 1983 .

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

[17]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[18]  B. Arnold,et al.  A first course in order statistics , 2008 .

[19]  Y. Takada,et al.  Median unbiasedness in an invariant prediction problem , 1991 .

[20]  Narayanaswamy Balakrishnan,et al.  An efficient computational method for moments of order statistics under progressive censoring , 2002 .

[21]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[22]  DavidR . Thomas,et al.  Linear Order Statistic Estimation for the Two-Parameter Weibull and Extreme-Value Distributions from Type II Progressively Censored Samples , 1972 .

[23]  B. Arnold,et al.  A first course in order statistics , 1994 .