Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring

Based on progressively type-II censored samples, constant-partially accelerated life tests (PALTs) when the lifetime of items under use condition follow the two-parameter Burr type-XII (Burr(c,k)) distribution are considered. The likelihood equations of the involved parameters are derived and then reduced to a single nonlinear equation to be solved numerically to obtain the maximum likelihood estimates (MLEs) of the parameters. The observed Fisher information matrix, as well as the asymptotic variance-covariance matrix of the MLEs are derived. Approximate confidence intervals (CIs) for the parameters, based on normal approximation to the asymptotic distribution of MLEs, studentized-t and percentile bootstrap CIs are derived. A Monte Carlo simulation study is carried out to investigate the precision of the MLEs and to compare the performance of the CIs considered. Finally, two examples presented to illustrate our results are followed by conclusions.

[1]  E. K. Al-Hussaini,et al.  Accelerated life tests under finite mixture models , 2006 .

[2]  Do Sun Bai,et al.  Optimal design of partially accelerated life tests for the exponential distribution under type-I censoring , 1992 .

[3]  W. Meeker.  Accelerated Testing: Statistical Models, Test Plans, and Data Analyses , 1991 .

[4]  A. A. Soliman,et al.  Estimation of parameters of life from progressively censored data using Burr-XII model , 2005, IEEE Transactions on Reliability.

[5]  Alaa H. Abdel-Hamid,et al.  Progressive stress accelerated life tests under finite mixture models , 2007 .

[6]  T. Apostol.  Mathematical Analysis , 1957 .

[7]  Cm Kim,et al.  ANALYSES OF ACCELERATED LIFE TEST DATA UNDER TWO FAILURE MODES , 2002 .

[8]  Udo Kamps,et al.  On optimal schemes in progressive censoring , 2006 .

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

[10]  Z. F. Jaheen,et al.  Bayesian prediction for progressively censored data from the Burr model , 2002 .

[11]  N. Balakrishnan,et al.  Exponential progressive step-stress life-testing with link function based on Box–Cox transformation , 2008 .

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

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

[14]  N. Balakrishnan,et al.  Point and Interval Estimation for a Simple Step-Stress Model with Type-II Censoring , 2007 .

[15]  A. M. Nigm,et al.  Prediction bounds for the burr model , 1988 .

[16]  Z. F. Jaheen,et al.  Bayesian estimation of the parameters,reliability and failure rate functions of the burr type xii failure model , 1992 .

[17]  W. B. Nelson,et al.  Residuals and Their Analyses for Accelerated Life Tests With Step and Varying Stress , 2008, IEEE Transactions on Reliability.

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

[19]  Shuo-Jye Wu,et al.  Optimal step-stress test under type I progressive group-censoring with random removals , 2008 .

[20]  A. H. Abdel-Hamid,et al.  Bayesian Estimation of the Parameters, Reliability and Hazard Rate Functions of Mixtures Under Accelerated Life Tests , 2004 .

[21]  Alan Watkins,et al.  On constant stress accelerated life tests terminated by Type II censoring at one of the stress levels , 2008 .

[22]  F. Pascual,et al.  Accelerated Life Test Planning With Independent Weibull Competing Risks , 2008, IEEE Transactions on Reliability.

[23]  E. K. Al-Hussaini,et al.  Step partially accelerated life tests under finite mixture models , 2008 .

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

[25]  G. K. Bhattacharyya,et al.  A tampered failure rate model for step-stress accelerated life test , 1989 .

[26]  Z. F. Jaheen,et al.  Statistical inference for the Burr model based on progressively censored data , 2002 .

[27]  M. A. M. Ali Mousa.  Empirical bayes estimators for the burr type XII accelerated life testing model based on type-2 censored data , 1995 .

[28]  Essam Khalaf Al-Hussaini,et al.  Estimation in step-stress accelerated life tests for the exponentiated exponential distribution with type-I censoring , 2009, Comput. Stat. Data Anal..