表題番号:2013B-246 日付:2014/04/11
研究課題Warranty Cost Analysis with Non-zero Repair Times: Models and Inference
研究者所属(当時) 資格 氏名
(代表者) 国際学術院 教授 早川 有
研究成果概要
A summary of research outcomes:

Research team of Waseda University Grant for Special Research Projects (2013B-246) consisted of the following members:

Principal researcher: Dr Yu Hayakawa, Waseda University
Research collaborator: Dr Stefanka Chukova, Victoria University of Wellington
Research collaborator: Yimo Xu, Waseda University (undergraduate student)
Research assistant: Yan Liu, Waseda University (PhD student)

In our research plan submitted for this grant, we stated that the main focus is on the modeling of the warranty claims and evaluation of the warranty servicing costs under non-renewing free replacement warranty policy. Our model is based the generalised alternating renewal process and we derive new results on this stochastic process with a finite time horizon. We also employ simulation methods to obtain numerical results.

We report that we have made good progress on this project and on some related projects as well.

Dr Stefanka Chukova visited the School of International Liberal Studies (SILS), Waseda University, during 12-19 December 2013. Dr Richard Arnold, her colleague from Victoria University of Wellington, was also visiting SILS on sabbatical from November 2013 to February 2014. Throughout the period of this grant, we worked together on the project described above and a few other related topics described below.

1) We model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free replacement warranties. We use an increasing geometric process to model the consecutive repair times. This model is based on the generalised alternating renewal process (GAR) and we derive new results on GAR process with a finite time horizon. This work is in the manuscript [1] whose details are given in the next section. This manuscript will be presented at the 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014, August 2014, Sapporo, Japan).

Yan Liu conducted a simulation study on the above model under non-renewing replacement warranty and obtained numerical results. Yimo Xu wrote a set of notes on the relevant technical details and proofs of the theorems. We are working on an extended version of the manuscript [1] by incorporating the simulation results under both non-renewing and renewing warranty replacement policies (the manuscript [5]).

2) We have constructed a model for correlated failures in multicomponent systems where failed components are repaired. Due to these repairs multiple failures of each component are observable. We assume that repair is instantaneous, but imperfect. Correlation amongst failures and the overall ageing of the system are modeled by treating each component failure as a shock which damages the other components in the system. Our results are in the manuscript [2]. This manuscript will be presented at the 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014).

3) Reliability data may incorporate a failure severity measure as well as the time of each failure. Such severities may however be qualitative ordinal data. We apply finite mixture methods to group units into fuzzy clusters, in order to model the joint distribution of failure times and severities. This work is in the manuscript [3]. This manuscript will be presented at the 6th Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2014).

4) We develop inference procedures for the shock models that we had previously published. We introduce a new type of grouping of subunits which allow for common cause failures, i.e., all the components within a subunit failure simultaneously. A paper on this project is in preparation.