2019 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 – 2021-03-31
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Keywords | System reliability / Non-parametric Bayesian / Hazard rate function / Warranty analysis / Geometric-like processes / Mean value funciton / Capture-recapture / Biclustering |
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 Sarah Marshall also worked on 3 other projects: 1) Construction of models with nonzero repair times dependent on hazard rate; 2) A review paper on Geometric-like processes with their applications; and 3) The mean value function of an alternating geometric process. These projects are complementary to our original goals. We are taking a non-parametric Bayesian approach to analyse hazard rate functions. We have made a major progress on simulation and inference for a non-parametric hazard rate function drawn from a gamma process prior. A short paper has been submitted for inclusion in the 2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modelling (APARM 2020). We are also working on biclustering in capture-recapture experiments from a non-parametric Bayesian perspective. This work is applicable to the estimation of the number of undetected faults after a panel of independent reviewers has tested a piece of software. We wrote a paper on nonzero repair times dependent on hazard rate. This paper was published in April 2020 in the journal Quality and Reliability Engineering International. We also completed a review paper on Geometric-like processes with their applications. This paper will be published this year in the journal Reliability and Engineering System Safety. A paper on mean value function of an alternating geometric process was presented at 2 conferences in New Zealand.
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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 to work on the fundamentals for the framework of non-parametric Bayesian analysis of hazard rate functions using the gamma process prior. We have written a short paper on our results (submitted to APARM 2020).
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Strategy for Future Research Activity |
As mentioned above, we have made a major progress on simulation and inference for hazard rate function via gamma process prior. We used 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 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 as a prior of the hazard rate function to conduct hypothesis testing of bathtub hazard rate vs IFR. We also plan to work on non-parametric Bayesian procedure to obtain posterior expectation of the hazard rate function under IFR via Monte Carlo simulation of weighted Chinese restaurant process. Our plan also includes working on a non-parametric Bayesian hypothesis testing of IFR vs DFR.
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Research Products
(6 results)