Journal ArticleDOI
The trend-renewal process for statistical analysis of repairable systems
TLDR
The trend-renewal process (TRP) is a time-transformed renewal process having both the ordinary renewal process and the nonhomogeneous Poisson process as special cases.Abstract:
The most commonly used models for the failure process of a repairable system are nonhomogeneous Poisson processes, corresponding to minimal repairs, and renewal processes, corresponding to perfect repairs. This article introduces and studies a more general model for recurrent events, the trend-renewal process (TRP). The TRP is a time-transformed renewal process having both the ordinary renewal process and the nonhomogeneous Poisson process as special cases. Parametric inference in the TRP model is studied, with emphasis on the case in which several systems are observed in the presence of a possible unobserved heterogeneity between systems.read more
Citations
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Book
The Statistical Analysis of Recurrent Events
TL;DR: Models and Frameworks for Analysis of Recurrent Events based on Counts and Rate Functions and Analysis of Gap Times are presented.
Journal ArticleDOI
Reliability Meets Big Data: Opportunities and Challenges
William Q. Meeker,Yili Hong +1 more
TL;DR: In this article, the authors review some applications where field reliability data are used and explore some of the opportunities to use modern reliability data to provide stronger statistical methods to operate and predict the performance of systems in the field.
Journal ArticleDOI
Statistical Analysis of Reliability Data
Journal Article
On the statistical modeling and analysis of repairable systems
TL;DR: In this article, the authors present a framework where the ob-served events are modeled as marked point processes, with marks labeling the types of events, and the emphasis is more on modeling than on statistical inference.
References
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A General Definition of Residuals
David Cox,E. J. Snell +1 more
TL;DR: In the context of normal-theory linear models, the n x 1 vector of random variables Y is assumed to have the form as mentioned in this paper, and residuals are used to assess the adequacy of linear models.
Journal ArticleDOI
On the Distribution of the Likelihood Ratio
TL;DR: In this paper, the asymptotic distribution of the likelihood ratio λ is examined when the value of the parameter is a boundary point of both the set of points corresponding to the hypothesis and the set corresponding to an alternative.