The Trend-Renewal Process for Statistical Analysis of Repairable Systems
Authors: Lindqvist, B.H.1; Elvebakk, G.1; Heggland, K.2
Source: Technometrics, Volume 45, Number 1, 1 February 2003 , pp. 31-44(14)
Publisher: American Statistical Association
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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.Keywords: HETEROGENEITY; LIKELIHOOD INFERENCE; POISSON PROCESS; RECURRENT EVENT; RENEWAL PROCESS; RESIDUAL PROCESS
Document Type: Research article
DOI: 10.1198/004017002188618671
Affiliations: 1: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway 2: Norwegian Computing Centre, N-0314 Oslo, Norway
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