Prediction in trend-renewal processes for repairable systems
نویسندگان
چکیده
منابع مشابه
Prediction in trend-renewal processes for repairable systems
Some problems of point and interval prediction in a trend-renewal process (TRP) are considered. TRP’s, whose realizations depend on a renewal distribution as well as on a trend function, comprise the non-homogeneous Poisson and renewal processes and serve as useful reliability models for repairable systems. For these processes, some possible ideas and methods for constructing the predicted next...
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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 paper studies a more general model for recurrent events, called the Trend-Renewal Process (TRP). This is a time transformed renewal process, having both the ordinary renewal process and ...
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Methods of estimating unknown parameters of a trend function for trend-renewal processes are investigated in the case when the renewal distribution function is unknown. If the renewal distribution is unknown, then the likelihood function of the trend-renewal process is unknown and consequently the maximum likelihood method cannot be used. In such a situation we propose three other methods of es...
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The trend-renewal-process (TRP) is defined to be a time-transformed renewal process, where the time transformation is given by a trend function λ(·) which is similar to the intensity of a nonhomogeneous Poisson process (NHPP). A nonparametric maximum likelihood estimator of the trend function of a TRP can be obtained much in the same manner as for the NHPP using kernel smoothing. But for a TRP ...
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We analyze the notion of ‘reliability prediction’ by studying in detail a key property that is tacitly assumed to make reliability prediction possible. The analysis leads in turn to a special type of point process for which the connection of future to past can be explicitly displayed. In this type of process, the semi-renewal process, all finitedimensional distributions are completely determine...
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ژورنال
عنوان ژورنال: Statistics and Computing
سال: 2013
ISSN: 0960-3174,1573-1375
DOI: 10.1007/s11222-013-9393-5