2018 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 / failure models / warranty analysis / Geometric-like processes / capture-recapture / biclustering |
Outline of Annual Research Achievements |
In our research plan, the main focus is on non-parametric Bayesian approach to modelling system reliability. As planned Richard Arnold, Stefanka Chukova and Yu Hayakawa have worked on modelling system reliability using non-parametric Bayesian approach. We together with Sarah Marshall also worked on two other projects: 1) Construction of models related to delayed reporting of faults in warranty claims and nonzero repair times dependent on the failure hazard; 2) Writing a review paper and a book chapter on geometric and geometric-like processes and their applications. These projects are complementary to our original goals and are described below. We are taking a nonparametric Bayesian approach to hazard function modelling. We have created a draft technical report summarising our findings and have implanted simulation models for the Gamma Process methodology which we are using. We are also working on biclustering in capture-recapture experiments from a nonparametric Bayesian perspective. We wrote a paper on delayed reporting of faults in warranty claims, in which the reporting process is modelled as a stochastic process dependent on the underlying stochastic process generating the faults. This research inspired another project on nonzero repair times dependent on the failure hazard. We also worked on a review paper and a book chapter on geometric-like processes and their applications in warranty analysis. Conference presentations have been given on this topic and we also present our paper at MMR 2019. The book chapter has been accepted for publication.
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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, the main focus of our research is on non-parametric Bayesian approach to modelling system reliability. We are taking a nonparametric Bayesian approach to hazard function modelling. The high level of complexity of this approach has meant we spent a significant amount of time on review of the literature and on model formulation. We have created a draft technical report summarising our findings and have implanted simulation models for the Gamma Process methodology which we are using.
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Strategy for Future Research Activity |
We plan to work on a non-parametric Bayesian procedure to obtain the posterior expectation of the hazard rate function under IFR via Monte Carlo simulations of the weighted Chinese restaurant process. We will also construct a non-parametric Bayesian hypothesis test procedure for the case: IFR vs DFR. U-shaped hazard rate functions, which are bathtub-shaped hazard rate functions with no constant failure rate period, are used to model systems with an initial DFR period followed by an IFR period. We will work on non-parametric Bayesian estimation for this special class of hazard rate functions. Log-convex hazard rate functions offer a very flexible family of models including IFR, DFR and bathtub hazard rate functions. We plan to apply the translated weighted gamma process (i.e., some positive constant is added to this process) to log-convex hazard rate functions as priors and posterior quantities in the model will be obtained. A hypothesis test of a bathtub hazard rate vs IFR will be conducted by evaluating the posterior probability that the derivative of log hazard rate function evaluated at zero is negative.
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Causes of Carryover |
We received internal grants from Waseda University, which were used towards the travel expenses of Dr Richard Arnold and Dr Stefanka Chukova. Therefore, the total amount spent for the fiscal year 2018 is less than the budget. We plan to use the unused amount from the fiscal year 2018 for travel expenses to attend 11th International Conference on Mathematical Methods in Reliability.
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Research Products
(11 results)