On inference in a class of exponential distribution under imperfect maintenance

Hoda Kamranfar (1) , Kambiz Ahmadi (2) , Mitra Fouladirad (3)

1 University of Birjand [Iran]
2 Shahrekord University
3 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres

This paper deals with statistical inference for lifetime data in presence of imperfect maintenance. For the maintenance model, the Sheu and Griffith model is considered. The lifetime distribution belongs to exponential distribution class. The maximum likelihood estimation procedure of the model parameters is discussed, and confidence intervals are provided using the asymptotic likelihood theory and bootstrap approach. Based on conjugate and discrete priors, Bayesian estimators of the model parameters are developed under symmetric and asymmetric loss functions. The proposed methodologies are applied to simulated data and sensitivity analysis to different parameters and data characteristics is carried out. The effect of model misspecification is also assessed within this class of distributions through a Monte Carlo simulation study. Finally, two datasets are analyzed for demonstrative aims.

Mots clés: Bayesian inference; Confidence interval; Exponential-based class; Imperfect repair; Maximum likelihood estimation; Model misspecification

Domaines: Mathématiques [math]

Hoda Kamranfar, Kambiz Ahmadi, Mitra Fouladirad. On inference in a class of exponential distribution under imperfect maintenance. Communications in Statistics - Simulation and Computation, 2022, pp.1-27. ⟨10.1080/03610918.2022.2103567⟩. ⟨hal-04064552⟩