Minimal repair under a step-stress test

In the one- and multi-sample cases, in the context of life-testing reliability experiments, we introduce minimal repair processes under a simple step-stress test, based on exponential distributions and an associated cumulative exposure model, and then develop likelihood inference for such a model.

[1]  Harold E. Ascher.  Repairable Systems Reliability , 2008 .

[2]  Udo Kamps,et al.  A concept of generalized order statistics , 1995 .

[3]  Bo Henry Lindqvist,et al.  Statistical Modeling and Analysis of Repairable Systems , 2006, 0708.0362.

[5]  Laurence A. Baxter.  Reliability applications of the relevation transform , 1982 .

[6]  Helge Langseth,et al.  Competing risks for repairable systems : A data study , 2006 .

[7]  Hoang Pham,et al.  Availability and maintenance of series systems subject to imperfect repair and correlated failure and repair , 2006, Eur. J. Oper. Res..

[8]  H. Ascher.  Evaluation of Repairable System Reliability Using the ``Bad-As-Old'' Concept , 1968 .

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

[10]  Majid Asadi,et al.  On the mean residual life of records , 2008 .

[11]  Martin Krakowski.  The relevation transform and a generalization of the gamma distribution function , 1973 .

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

[13]  Narayanaswamy Balakrishnan,et al.  Prediction intervals for future records , 2008 .

[14]  Ramesh C. Gupta,et al.  Some results on randomly stopped minimal repair processes , 1995 .

[15]  Félix Belzunce,et al.  Multivariate aging properties of epoch times of nonhomogeneous processes , 2003 .

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

[17]  R. Barlow,et al.  Optimum Preventive Maintenance Policies , 1960 .

[18]  Baha-Eldin Khaledi,et al.  On stochastic orderings between residual record values , 2007 .

[19]  C. E. Love,et al.  Application of Weibull proportional hazards modelling to bad-as-old failure data , 1991 .

[20]  Nozer D. Singpurwalla,et al.  Stochastic Properties of a Sequence of Interfailure Times under Minimal Repair and under Revival , 1984 .

[21]  M. Finkelstein,et al.  Minimal repair in heterogeneous populations , 2004, Journal of Applied Probability.

[22]  K. Lau,et al.  Characterization of the exponential distribution by the relevation transform , 1990, Journal of Applied Probability.

[23]  Dragan Banjevic,et al.  System repairs: When to perform and what to do? , 2008, Reliab. Eng. Syst. Saf..

[24]  Ramesh C. Gupta,et al.  Closure and Monotonicity Properties of Nonhomogeneous Poisson Processes and Record Values , 1988 .

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

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

[27]  Moshe Shaked,et al.  Stochastic comparisons of mixtures of convexly ordered distributions with applications in reliability theory , 2001 .

[28]  Narayanaswamy Balakrishnan,et al.  A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests , 2009 .

[29]  Udo Kamps,et al.  Marginal distributions of sequential and generalized order statistics , 2003 .