Improved techniques for parametric and nonparametric evaluations of the first‐passage time for degradation processes
For degradation data in reliability analysis, estimation of the first‐passage time (FPT) distribution to a threshold provides valuable information on reliability characteristics. Recently, Balakrishnan and Qin (2019; Applied Stochastic Models in Business and Industry, 35:571–590) studied a nonparame...
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| Published in | Applied stochastic models in business and industry Vol. 36; no. 4; pp. 730 - 753 |
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| Abstract | For degradation data in reliability analysis, estimation of the first‐passage time (FPT) distribution to a threshold provides valuable information on reliability characteristics. Recently, Balakrishnan and Qin (2019; Applied Stochastic Models in Business and Industry, 35:571–590) studied a nonparametric method to approximate the FPT distribution of such degradation processes if the underlying process type is unknown. In this article, we propose some improved techniques based on saddlepoint approximation, which enhance those existing methods. Numerical examples and Monte Carlo simulation studies are used to illustrate the advantages of the proposed techniques. Limitations of the improved techniques are discussed and some possible solutions to such are proposed. Some concluding remarks and practical recommendations are provided based on the results. |
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| AbstractList | For degradation data in reliability analysis, estimation of the first‐passage time (FPT) distribution to a threshold provides valuable information on reliability characteristics. Recently, Balakrishnan and Qin (2019; Applied Stochastic Models in Business and Industry, 35:571–590) studied a nonparametric method to approximate the FPT distribution of such degradation processes if the underlying process type is unknown. In this article, we propose some improved techniques based on saddlepoint approximation, which enhance those existing methods. Numerical examples and Monte Carlo simulation studies are used to illustrate the advantages of the proposed techniques. Limitations of the improved techniques are discussed and some possible solutions to such are proposed. Some concluding remarks and practical recommendations are provided based on the results. Abstract For degradation data in reliability analysis, estimation of the first‐passage time (FPT) distribution to a threshold provides valuable information on reliability characteristics. Recently, Balakrishnan and Qin (2019; Applied Stochastic Models in Business and Industry , 35:571–590) studied a nonparametric method to approximate the FPT distribution of such degradation processes if the underlying process type is unknown. In this article, we propose some improved techniques based on saddlepoint approximation, which enhance those existing methods. Numerical examples and Monte Carlo simulation studies are used to illustrate the advantages of the proposed techniques. Limitations of the improved techniques are discussed and some possible solutions to such are proposed. Some concluding remarks and practical recommendations are provided based on the results. |
| Author | Butler, Ronald W. Palayangoda, Lochana K. Ng, Hon Keung Tony |
| Author_xml | – sequence: 1 givenname: Lochana K. surname: Palayangoda fullname: Palayangoda, Lochana K. organization: Southern Methodist University – sequence: 2 givenname: Hon Keung Tony orcidid: 0000-0003-4685-2199 surname: Ng fullname: Ng, Hon Keung Tony email: ngh@mail.smu.edu organization: Southern Methodist University – sequence: 3 givenname: Ronald W. surname: Butler fullname: Butler, Ronald W. organization: Southern Methodist University |
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| Snippet | For degradation data in reliability analysis, estimation of the first‐passage time (FPT) distribution to a threshold provides valuable information on... Abstract For degradation data in reliability analysis, estimation of the first‐passage time (FPT) distribution to a threshold provides valuable information on... |
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| SubjectTerms | Approximation Computer simulation Degradation first‐passage time distribution gamma process inverse‐Gaussian process Lévy process Monte Carlo simulation Nonparametric statistics Numerical methods Reliability analysis saddlepoint approximation Stochastic models Wiener process |
| Title | Improved techniques for parametric and nonparametric evaluations of the first‐passage time for degradation processes |
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