The rate of occurrence of failures for semi-Markov processes and estimation

被引：30

作者：

Ouhbi, B

Limnios, N

机构：

[1] Ecole Natl Super Arts & Metiers, Meknes, Morocco

[2] Univ Technol Compiegne, Equipe Math Appl, F-60205 Compiegne, France

来源：

STATISTICS & PROBABILITY LETTERS | 2002年 / 59卷 / 03期

关键词：

rate of occurrence of failures; semi-Markov process; non-parametric estimator; asymptotic properties;

D O I：

10.1016/S0167-7152(02)00139-6

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper investigates the rate of occurrence of failures (ROCOF) of finite state semi-Markov systems. Firstly, a formula for evaluating the ROCOF for semi-Markov systems is derived. As a consequence of this result, we derive the ROCOF of Markov systems as well as the ROCOF of the alternating renewal processes and we give their asymptotic values. From the semi-Markov ROCOF formula, we propose a statistical estimator of this function. Finally, the uniform strong consistency and the asymptotic normality of this estimator are obtained. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：245 / 255

页数：11

共 15 条

[1] Ascher H., 1984, REPAIRABLE SYSTEMS R
[2] BILLINGSLEY P, 1968, PROBABILITY MEASURES
[3] COX DR, 1966, STAT ANAL SERIES EVE, V23, P5
[4] Feller W., 1966, INTRO PROBABILITY TH, V2
[5] Gut, 1988, STOPPED RANDOM WALKS
[6] LAM Y, 1997, J APPL PROBAB, V34, P234
[7] ANALYSIS OF A COUNTING PROCESS ASSOCIATED WITH A SEMI-MARKOV PROCESS - NUMBER OF ENTRIES INTO A SUBSET OF STATE-SPACE
MASUDA, Y
SUMITA, U
[J]. ADVANCES IN APPLIED PROBABILITY, 1987, 19 (04) : 767 - 783
[8] OPRISAN G, 1999, STAT PROBABILISTIC M
[9] Asymptotic behavior of the sample Markov renewal matrix
Ouhbi, B
Limnios, N
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 325 (08): : 921 - 924
[10] OUHBI B, 1999, SEMI MARKOV MODELS A

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