第三回研究会(通算第二十一回)

国際会議(MMR2017)におけるシステム信頼性研究部会によるスペシャルセッション

日時(会期):2017年7月3日~6日
場所:INP-ENSE^3, GreEn-ER, 21 Avenue des martyrs, 38000 Grenoble, France
Web site: http://mmr2017.imag.fr/

本年開催のMMR (Mathematical Methods in Reliability) にSpecial Sessionを3件設定させて頂き,それぞれ3件ずつ,日本からの参加予定者の方々にご講演・討論をお願いしております.ご興味のお有りの方は是非この機会にグルノーブルへお出かけください.現地にてお待ちしております.

Advanced Mathematical Methods in System Reliability and Maintenance – Special session organized by the Operations Research Society of Japan (ORSJ) – 1

Presenter 1: Taishin Nakamura (Tokyo Metropolitan University)
Title: Necessary Conditions for Optimal Arrangement of Connected-(r,s)-out-of-(m,n):F Lattice System with Minimal Cuts Overlapping
Authors: Taishin Nakamura, Hisashi Yamamoto, Xiao Xiao, Natsumi Takahashi and Tomoaki Akiba
Abstract: A connected-(r,s)-out-of-(m,n):F lattice system consists of m×n components arranged as an (m,n) matrix, and fails if and only if the system has an (r,s) sub-matrix where all components fail. One of the most significant problems in reliability theory is the component arrangement problem (CAP) on the assumption that component reliabilities are given and components are interchangeable. The CAP is to find optimal arrangements of components to maximize the system reliability. By taking optimal arrangements into account, we can make the best use of limited resources and maximize the performance of the system.
In this study, we provide necessary conditions for the optimal arrangement of the connected-(r,s)-out-of-(m,n):F lattice system with its minimal cuts overlapping, that is, m<2r or n<2s. Since we calculate the reliability of only the systems corresponding to the arrangements satisfying the conditions, we can considerably reduce the search space for the CAP. We evaluate the performance of the proposed algorithm by performing numerical experiments.

Presenter 2: Lu Jin (The University of Electro-Communications)
Title: Operation and Maintenance Policy with Flexible Load Sharing
Authors: Lu Jin, Tomofumi Uwano, and Kazuyuki Suzuki
Abstract: An integrated operation and maintenance policy with flexible load sharing is proposed for multiple-component deteriorating systems under a constant total workload. The underlying deterioration process of the system, which depends on the workload allocation, is described by a discrete-time Markov chain. The decision-making problem is formulated as a Markov decision process that minimizes the total expected cost (both operation and maintenance costs) on an infinite horizon. The properties of the resulting optimal decision policies are investigated, and a set of sufficient conditions for a monotone policy to be optimal are provided. The efficiency of the proposed integrated operation and maintenance policy with flexible load sharing is demonstrated through a numerical example.

Presenter 3: Hiroyuki Okamura (Hiroshima University)
Title: A note on computation of quasi-stationary distribution in continuous-time Markov chains
Authors: Hiroyuki Okamura and Tadashi Dohi
Abstract: This paper discusses the computation of quasi-stationary distribution for continuous-time Markov chain (CTMC). The quasi-stationary distribution is defined as a left eigenvector of an infinitesimal generator of the CTMC with absorbing states. Compared to the computation of steady-state probability vector of CTMC, the computation cost of quasi-stationary distribution is much higher. In the paper, we introduce an iterative approach to obtain the quasi-stationary distribution, which is similar to Gauss-Seidel algorithm for the computation of steady-state probability vector.

System Reliability and Maintenance Modeling – Special session organized by the Operations Research Society of Japan (ORSJ) – 2

Presenter 1: Shuhei Ota (Hosei University)
Title: A study on reliability deterioration and improvement of coherent
systems under dependent failure-occurrence environment
Authors: Shuhei Ota and Mitsuhiro Kimura
Abstract: In this study, we investigate the effect of dependent failure
occurrence on system reliability assessment. In general, it is known
that an n-component parallel system cannot deliver its designed
reliability if the lifetimes of the individual components have positive
dependence. On the other hand, an $n$-component series system can exceed
its designed reliability under such dependent failure-occurrence
environment. This research analyzes to what extent the dependence among
the components worsens/improves the reliability of n-component coherent
systems. The dependence among the components is modeled by FGM copula.
We obtain the results by using numerical examples. Moreover, in these
examples, we newly consider the allowable values of the parameters of
FGM copula although they have been simply assumed [0,1]^n in the
literature.

Presenter 2: Syouji Nakamura (Kinjo Gakuin University)
Title: Optimum Incremental Backup Policies with Failures at Random
Updating Times
Authors: Syouji Nakamura, Xufeng Zhao, and Toshio Nakagawa
Abstract: In order to ensure the data security, plans of incremental
backups are usually set up to save the costs which is suffered from full
backups. In this paper, we suppose that failures occur at data updating
times and incremental backups are implemented only at the end of data
updates and full backups are done at time $T$ and update $N$ to balance
the costs of data backup and failure recovery. Using the theory of
renewal process, we obtain the expected costs of backup and recovery and
the expected cost rates for full backups. Optimum solutions of $T$ and $
N$ to minimize the expected cost rates are discussed in analytical ways
and computed with numerical examples.

Presenter 3: Shinji Inoue (Kansai University)
Title: Markovian Imperfect Debugging Modeling for Software Reliability
Assessment with Change-Point
Authors: Shinji Inoue and Shigeru Yamada
Abstract: We discuss Markovian software reliability modeling with the
effects of change-point and imperfect debugging environment. Testing-
time when the characteristic of the software failure-occurrence or fault
-detection phenomenon changes notably is called {¥it change-point}.
Considering the effect at change-point on software reliability growth
process must be important to improve the accuracy of software
reliability assessment. And, assuming imperfect debugging activities in
software reliability modeling contributes to reflecting more actual
situation of debugging activities. We also show numerical illustration
of our model for software reliability analysis by using actual data.

Warranty and Maintenance Modeling with Applications – Special session organized by the Operations Research Society of Japan (ORSJ) – 3

Presenter 1: Tomohiro Kitagawa (National Defence Academy of Japan)
Title: Three repair options depending on failure time for a system equipped on ship
Authors: Tomohiro Kitagawa, Tetsushi Yuge, and Shigeru Yanagi
Abstract: A maintenance model for a system equipped on ship taking a voyage with a random duration is proposed. When a failure occurs, one action is chosen from three, return to the base, instantaneous repair on-site and to leave it alone and repair it after the end of the voyage. Our goal is to determine the optimal action depending on the occurrence time of failures, where the optimal policy minimizes the expected cost until the completion of one voyage, ensuring a certain mean availability.

Presenter 2: Nobuyuki Tamura (Hosei University)
Title: State-age-dependent replacement policy for a semi-Markovian deteriorating system with major and minor failures
Author: Nobuyuki Tamura
Abstract: We consider a multi-state system whose deterioration is modeled as a semi-Markov process with an absorbing state. The system can suffer major and minor failures. When the system reaches the absorbing state, a major failure occurs and the system is replaced. Meanwhile, minor failures can occur depending upon the state and the sojourn time. Upon the occurrence of a minor failure, the system is minimally repaired. For the system, we propose a state-age-dependent replacement policy which minimizes the expected long-run cost rate. Also, we investigate structural properties of the optimal replacement policy.

Presenter 3: Yu Hayakawa (Waseda University)
Title: Delayed reporting of faults in warranty claims
Authors: Richard Arnold, Stefanka Chukova, and Yu Hayakawa
Abstract: We present a model for the delayed reporting of faults: multiple non-fatal faults are accumulated and then simultaneously reported and repaired. The reporting process is modelled as a stochastic process dependent on the underlying stochastic process generating the faults. The joint distribution of the reporting times and numbers of reported faults is derived. We will also present a few extensions of the above model, which deal with multiple fault types, planned preventative maintenance and customer rush.

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