Nonparametric estimation of time trend for repairable systems data. (English) Zbl 1407.62109
Rykov, Vladimir V. (ed.) et al., Mathematical and statistical models and methods in reliability. Applications to medicine, finance, and quality control. Invited papers based on the presentation at the 6th international conference (MMR 2009), Moscow, Russia, June 22–26, 2009. Boston, MA: Birkhäuser. Stat. Ind. Technol., 277-288 (2010).
Summary: The trend-renewal-process (TRP) is defined to be a time-transformed renewal process, where the time transformation is given by a trend function \(\lambda(\cdot)\) 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 in principle in a similar manner as for the NHPP using kernel smoothing. But for a TRP one must consider the simultaneous estimation of the renewal distribution, which is here assumed to belong to a parametric class such as the Weibull-distribution. A weighted kernel estimator for \(\lambda(\cdot)\) is suggested and studied. Other approaches are also briefly discussed.
For the entire collection see [Zbl 1203.60007].
For the entire collection see [Zbl 1203.60007].
Software:
SPLIDAReferences:
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