Non-parametric estimation for semi-Markov kernels with application to reliability analysis

Abstract

The authors consider an irreducible Markov renewal process (MRP) with a finite number of states. Their aim is to derive estimators of a censored MRP with a finite number of states either in a fixed time T or in the Nth jump. The estimators given here are seen to be of the Kaplan‐Meier type. The asymptotic properties these estimators are given. The reliability of a semi‐Markov system model is examined numerically by the estimators, and a comparison is made with estimators obtained by Lagakos et al. © 1996 John Wiley & Sons, Ltd.

Reliability and Inference for Multi State Systems: The Generalized Kumaraswamy Case

“…Furthermore, the availability A(t) and maintainability M(t) at time t for a semi-Markov system are defined respectively by the following (for details see [29,32]):…”

Estimation and Reliability for a Special Type of Semi-Markov Process

“…For a semi-Markov system, the estimator of the reliability at time t > 0 is given by (cf. Ouhbi and Limnios, 1996):…”

Maximum Likelihood Estimation in Alternating Renewal Processes Under Window Censoring

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