Accelerated Life Tests for Weibull Series Systems With Masked Data

This article introduces a p-stage step-stress accelerated life test on n system products, where each system contains ms-independent non-identical components connected in series, and it fails if any component has broken down. Due to cost considerations or environmental restrictions, masked causes of system failures and type-I censored observations might occur in the collected data. The time to failure under a pre-specified stress environment is described by a Weibull-distributed cumulative exposure model. A computationally feasible procedure based on the hybrid EM-NR algorithm is developed for maximum likelihood estimation of the model. Further, the reliability of the system and components are estimated at a specified time under usual operating conditions. The proposed method is illustrated through a numerical example and a simulation study under various masking levels.

[1]  I. Meilijson.  A fast improvement to the EM algorithm on its own terms , 1989 .

[2]  E. Elsayed,et al.  A general accelerated life model for step-stress testing , 2005 .

[3]  Thorn J. Hodgson,et al.  Maximum likelihood analysis of component reliability using masked system life-test data , 1988 .

[4]  Chiranjit Mukhopadhyay,et al.  Maximum likelihood analysis of masked series system lifetime data , 2006 .

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

[6]  Ananda Sen,et al.  A Bayesian approach to competing risks analysis with masked cause of death , 2010, Statistics in medicine.

[7]  Frank M. Guess,et al.  Estimating system and component reliabilities under partial information on cause of failure , 1991 .

[8]  Do Sun Bai,et al.  Optimum simple step-stress accelerated life tests with censoring , 1989 .

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

[10]  L. Kuo,et al.  Bayesian reliability modeling for masked system lifetime data , 2000 .

[11]  Adamantios Mettas,et al.  Modeling and analysis for multiple stress-type accelerated life data , 2000, Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (Cat. No.00CH37055).

[12]  Loon Ching Tang,et al.  Planning step-stress life-test with a target acceleration-factor , 1999 .

[13]  Necip Doganaksoy,et al.  Interval estimation from censored and masked system-failure data , 1991 .

[14]  I. H. Khamis,et al.  Optimum M-step, step-stress design with K stress variables , 1997 .

[15]  T. Mazzuchi,et al.  A general Bayes exponential inference model for accelerated life testing , 2004 .

[16]  W. Nelson,et al.  Optimum Simple Step-Stress Plans for Accelerated Life Testing , 1983, IEEE Transactions on Reliability.

[17]  Asit P. Basu,et al.  Bayesian analysis of incomplete time and cause of failure data , 1997 .

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

[19]  Ewan Macarthur,et al.  Accelerated Testing: Statistical Models, Test Plans, and Data Analysis , 1990 .

[20]  Sanjib Basu,et al.  Bayesian analysis of competing risks with partially masked cause of failure , 2003 .

[21]  J. S. Usher.  Weibull component reliability-prediction in the presence of masked data , 1996, IEEE Trans. Reliab..

[22]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[23]  Frank M. Guess,et al.  Bayes estimation of component-reliability from masked system-life data , 1996, IEEE Trans. Reliab..

[24]  Masami Miyakawa,et al.  Analysis of Incomplete Data in Competing Risks Model , 1984, IEEE Transactions on Reliability.

[25]  Ammar M. Sarhan.  Reliability estimations of components from masked system life data , 2001, Reliab. Eng. Syst. Saf..

[26]  Emmanuel Yashchin,et al.  Parametric Modeling for Survival with Competing Risks and Masked Failure Causes , 2002, Lifetime data analysis.

[27]  Chenhua Li,et al.  Optimum Bivariate Step-Stress Accelerated Life Test for Censored Data , 2007, IEEE Transactions on Reliability.

[28]  M. Nikulin,et al.  Accelerated Life Models: Modeling and Statistical Analysis , 2001 .

[29]  Emmanuel Yashchin,et al.  Survival with competing risks and masked causes of failures , 1998 .

[30]  F. Guess,et al.  Exact maximum likelihood estimation using masked system data , 1993 .

[31]  J. J. Higgins,et al.  A new model for step-stress testing , 1998 .

[32]  I Guttman,et al.  Dependent masking and system life data analysis: Bayesian inference for two-component systems , 1995, Lifetime data analysis.

[33]  Ammar M. Sarhan.  Estimation of system components reliabilities using masked data , 2003, Appl. Math. Comput..

[34]  W. Nelson.  Accelerated Life Testing - Step-Stress Models and Data Analyses , 1980, IEEE Transactions on Reliability.

[35]  Frank M. Guess,et al.  System life data analysis with dependent partial knowledge on the exact cause of system failure , 1994 .

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

[37]  J. René van Dorp,et al.  A Bayes approach to step-stress accelerated life testing , 1996, IEEE Trans. Reliab..

[38]  Frank M. Guess,et al.  Bayesian inference for masked system lifetime data , 1995 .