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Parameter estimation in a condition-based maintenance model. (English) Zbl 1195.62157

Summary: A parameter estimation problem for a condition-based maintenance model is considered. We model a failing system that can be in a healthy or unhealthy operational state, or in a failure state. System deterioration is assumed to follow a hidden, three-state continuous time Markov process. Vector autoregressive data are obtained through condition monitoring at discrete time points, which gives partial information about the unobservable system state.
Two kinds of data histories are considered: histories that end with observable system failure and histories that end when the system is suspended from operation but has not failed. Maximum likelihood estimates of the model parameters are obtained using the EM algorithm and a closed form expression for the pseudo-likelihood function is derived. Numerical results are provided which illustrate the estimation procedure.

MSC:

62N05 Reliability and life testing
62N02 Estimation in survival analysis and censored data
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60J27 Continuous-time Markov processes on discrete state spaces
62G05 Nonparametric estimation
65C60 Computational problems in statistics (MSC2010)
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References:

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