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.
Highlights
A repairable system is a system that can undergo reparation by mending or replacing some system components rather than re-establishing the entire system after failing
The developed model is known as the Army Materiel Systems Analysis Activity (AMSAA)
We considered the celebrated power law intensity adopted in AMSAA model, that is, λ(t) = γαtα−1
Summary
Citation: Tian, X.-Y. ; Shi, X.; Peng C.; Yi, X.-J. A Reliability Growth Process School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China
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