Inference for a progressive stress model from Weibull distribution under progressive type-II censoring

Abstract Based on progressively type-II censored samples, this paper considers progressive stress accelerated life tests when the lifetime of an item under use condition follows the Weibull distribution with a scale parameter satisfying the inverse power law. It is assumed that the progressive stress is directly proportional to time and the cumulative exposure model for the effect of changing stress holds. Point estimation of the model parameters is obtained graphically by using Weibull probability paper plot that serves as a tool for model identification and also by using the maximum likelihood method. Interval estimation is performed by finding approximate confidence intervals (CIs) for the parameters as well as the studentized-t and percentile bootstrap CIs. Monte Carlo simulation study is carried out to investigate the precision of the estimates and compare the performance of CIs obtained. Finally, two examples are presented to illustrate our results.

[1]  D. Bai,et al.  Optimum simple ramp-tests for the Weibull distribution and type-I censoring , 1992 .

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

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

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

[5]  Narayanaswamy Balakrishnan,et al.  A Simple Simulational Algorithm for Generating Progressive Type-II Censored Samples , 1995 .

[6]  Do Sun Bai,et al.  Optimum simple step-stress accelerated life-tests with competing causes of failure , 1991 .

[7]  D. N. Prabhakar Murthy,et al.  A modified Weibull distribution , 2003, IEEE Trans. Reliab..

[8]  Narayanaswamy Balakrishnan,et al.  Progressive censoring methodology: an appraisal , 2007 .

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

[10]  C. Chan,et al.  A proportional hazards approach to correlate SiO/sub 2/-breakdown voltage and time distributions , 1990 .

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

[12]  Feiheliang,et al.  STATISTICAL INFERENCE OF WEIBULL DISTRIBUTION FOR TAMPERED FAILURE RATE MODEL IN PROGRESSIVE STRESS ACCELERATED LIFE TESTING , 2004 .

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

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

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

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

[17]  N. Balakrishnan,et al.  Optimal step-stress test under progressive type-I censoring , 2004, IEEE Transactions on Reliability.

[18]  William Q. Meeker,et al.  Planning accelerated life tests with two or more experimental factors , 1995 .

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

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

[21]  Xiang-kang Yin,et al.  Some Aspects of Accelerated Life Testing by Progressive Stress , 1987, IEEE Transactions on Reliability.

[22]  S. Okabe,et al.  Estimation for the parameters in the step-up voltage test under the weibull power law model , 2009, IEEE Transactions on Dielectrics and Electrical Insulation.

[23]  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..

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

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

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

[27]  N. Balakrishnan,et al.  Point and interval estimation for Gaussian distribution, based on progressively Type-II censored samples , 2003, IEEE Trans. Reliab..

[28]  N. Balakrishnan,et al.  Inference for the extreme value distribution under progressive Type-II censoring , 2004 .

[29]  W. T. Starr,et al.  Progressive Stress-A New Accelerated Approach to Voltage Endurance , 1961, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

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

[31]  Siu-Keung Tse,et al.  Parameters estimation for weibull distributed lifetimes under progressive censoring with random removals , 1996 .

[32]  Shuo-Jye Wu,et al.  Estimation for the two-parameter pareto distribution under progressive censoring with uniform removals , 2003 .

[33]  N. Klein,et al.  A statistical model for step and ramp voltage breakdown tests in thin insulators , 1976 .