A Reliability Growth Process Model with Time-Varying Covariates and Its Application

Xin-Yu Tian, Xincheng Shi, Cheng Peng and Xiao-Jian Yi
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Xin-Yu Tian: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Xincheng Shi: Department of Psychology, University of California, Los Angeles, CA 90095, USA
Cheng Peng: Department of Statistics, University of Chicago, Chicago, IL 60637, USA
Xiao-Jian Yi: School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2021, vol. 9, issue 8, 1-15

Abstract: The nonhomogeneous Poisson process model with power law intensity, also known as the Army Materiel Systems Analysis Activity (AMSAA) model, is commonly used to model the reliability growth process of many repairable systems. In practice, it is necessary to test the reliability of the product under different operational environments. In this paper we introduce an AMSAA-based model considering the covariate effects to measure the influence of the time-varying environmental condition. The parameter estimation of the model is typically performed using maximum likelihood on the failure data. The statistical properties of the estimation in the model are comprehensively derived by the martingale theory. Further inferences including confidence interval estimation and hypothesis tests are designed for the model. The performance and properties of the method are verified in a simulation study, compared with the classical AMSAA model. A case study is used to illustrate the practical use of the model. The proposed approach can be adapted for a wide class of nonhomogeneous Poisson process based models.

Keywords: AMSAA model; reliability growth; covariate effects; maximum likelihood; statistical inference (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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