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Reliability Analysis of a System with Multiple-Stage Policy Considering Type I and II Errors

Mitsuhiro Imaizumi

School of Contemporary Management, Aichi Gakusen University, 1 Shirotori, Oike-cho, Toyota 471-8532, Japan

E-mail Address: imaizumi@gakusen.ac.jp

Corresponding author.

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Mitsutaka Kimura

Department of Cross Cultural Studies, Gifu City Women’s College, 7-1 Hitoichibakita-machi, Gifu 501-0192, Japan

E-mail Address: kimura@gifu-cwc.ac.jp

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https://doi.org/10.1142/S0218539319500281Cited by:1 (Source: Crossref)

Abstract

This paper formulates a stochastic model for a system with illegal access. The server has the function of IDS, and illegal access is checked in multiple stages which consist of simple check and detailed check. In this model, we consider type I and II errors of simple check and a type I error of detailed check. There are two cases where IDS judges the occurrence of illegal access erroneously. One is when illegal access does not occur, and the other is when illegal access occurs. We apply the theory of Markov renewal processes to a system with illegal access, and derive the mean time and the expected checking number until a server system becomes faulty. Further, an optimal policy which minimizes the expected cost is discussed. Finally, numerical examples are given.

Keywords:

References

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