2020 Fiscal Year Research-status Report
Non-parametric Bayesian approach to modelling system reliability
Project/Area Number |
18K04621
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Research Institution | Waseda University |
Principal Investigator |
早川 有 早稲田大学, 国際学術院, 教授 (80398916)
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Project Period (FY) |
2018-04-01 – 2022-03-31
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Keywords | System reliability / Non-parametric Bayesian / Hazard rate function / Gamma process / Warranty analysis / Geometric-like processes / Mean value function |
Outline of Annual Research Achievements |
Richard Arnold, Stefanka Chukova and Yu Hayakawa have carried out collaborative work on modelling system reliability using a non-parametric Bayesian approach. We and our colleague Sarah Marshall (from Auckland University of Technology) also worked on 2 other projects: 1) Mean and variance of an alternating geometric process; and 2) The alternating alpha-series process. These projects are complementary to our original goals. We are taking a non-parametric Bayesian approach to analyse hazard rate functions. Based on our results from the previous academic year, we have unified our approach to construct various failure hazard function models via gamma process-based priors. Richard Arnold will give a presentation in an invited session of 2021 World Meeting of the International Society for Bayesian Analysis in June 2021 and at the joint Australia-New Zealand Statistics Conference in July 2021. We wrote a paper on the alternating alpha-series process and submitted it for consideration to be included in the monograph entitled “Reliability and Maintenance Modeling with Optimization: Advances and Applications”. Yu Hayakawa will present this paper in an invited session of the Reliability and Maintenance Engineering Summit 2021 in September 2021. Richard Arnold and Sarah Marshall presented a paper on nonparametric Bayesian analysis of hazard rate functions and that on mean and variance on an alternating geometric process at 2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM), respectively.
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Current Status of Research Progress |
Current Status of Research Progress
4: Progress in research has been delayed.
Reason
As mentioned above, we are taking a non-parametric Bayesian approach to system reliability modelling. We have spent majority of our time unifying our approach to construct various failure hazard function models via gamma process-based priors.
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Strategy for Future Research Activity |
As mentioned above, we have made a major progress on unifying our approach to construct various hazard rate functions via gamma process-based priors. We are using the fact that the gamma process can be constructed from a Dirichlet process that is scaled by an independent gamma random variable. Based on these results, we plan to work on the following projects: 1) U shaped hazard rate functions are bathtub hazard rate functions which have no interval with a constant hazard rate. We consider two types of U-shaped hazard rate functions. One is based on a system specific view and the other a population level view. We plan to work on non-parametric Bayesian estimation of such hazard rate functions. 2) Log-convex hazard functions offer a flexible family of hazard rate functions, which include IFR, DFR and bathtub hazard rate functions. We plan to apply the translated gamma process to log-convex hazard rate functions as a prior to conduct hypothesis testing of bathtub hazard rate vs IFR.
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Causes of Carryover |
Reason: The travel cost to attend an international conference (APARM2020) was not incurred since it was held as an online conference.
Usage Plan: Computer(s), conference fees and membership fees of professional organisations
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Research Products
(8 results)