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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Bibliographic Details
Published inApplied stochastic models in business and industry Vol. 36; no. 4; pp. 730 - 753
Main Authors Palayangoda, Lochana K., Ng, Hon Keung Tony, Butler, Ronald W.
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 01.07.2020
Subjects
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
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Summary: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.
ISSN:1524-1904
1526-4025
DOI:10.1002/asmb.2528