2021 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 – 2023-03-31
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Keywords | System reliability / Non-parametric Bayesian / Hazard rate function / Gamma process / Warranty analysis / Geometric-like processes / Alpha-Serice process |
Outline of Annual Research Achievements |
Richard Arnold, Stefanka Chukova (both from Victoria University of Wellington) and Yu Hayakawa have carried out collaborative work on modelling system reliability using a non-parametric Bayesian approach. In particular, we have studied representations of commonly used hazard rate functions in reliability theory from a non-parametric Bayesian perspective, e.g., U-shaped, bathtub (superposition and mixture) and log-convex hazard rate functions. We and our colleague Sarah Marshall (from Auckland University of Technology) also continued to work on other project on the alternating alpha-series process. This project is complementary to our original goals. Richard Arnold presented a paper on non-parametric estimation of bathtub hazard rate functions and that on gamma process priors for hazard rate functions at 2021 World Meeting of the International Society for Bayesian Analysis (ISBA 2021) and the Australian and New Zealand Statistical Conference 2021 (ANZSC 2021), respectively. A paper on the alternating alpha series process was presented by Sarah Marshall at the 31st European Conference on Operational Research (EURO 2021) and a related paper was presented by Yu Hayakawa at Reliability and Maintenance Engineering Summit 2021 (RMES 2021).
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Current Status of Research Progress |
Current Status of Research Progress
4: Progress in research has been delayed.
Reason
Due to Covid and the fact that we were not able to travel to meet each other in 2021, our projects were delayed.
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Strategy for Future Research Activity |
We plan to construct samplers for various types of hazard rate functions commonly used in reliability theory 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. The following projects are to be worked on: 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 function. The first type (superposition bathtub) is a superposition of decreasing and increasing failure rate functions (IFR and DFR). The second one (mixture bathtub) is a mixture of distributions with decreasing and increasing failure rate functions. We plan to work on non-parametric Bayesian estimation of these hazard rate functions. 2) Log-convex hazard rate functions include typical hazard rate functions such as IFR, DFR and bathtub hazard rate functions as special cases. The translated gamma process is to be used to log-convex hazard rate functions as a prior to conduct hypothesis testing of bathtub hazard rate functions vs IFR functions. We will develop software for simulating from these models, and for estimating them using the MCMC samplers. We plan to have software suitable for sharing with others, as well as a journal article describing our methodology.
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Causes of Carryover |
Reason: The travel cost to attend an international conference (RMES 2021) was not incurred since it was held as an online conference.
Usage Plan: A lap top computer or (if travel becomes possible again during the year) a research visit to Tokyo
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Research Products
(7 results)