Premium
Reliability modelling incorporating load share and frailty
Author(s) -
Asha G.,
Raja A. Vincent,
Ravishanker Nalini
Publication year - 2017
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2294
Subject(s) - weibull distribution , covariate , bivariate analysis , reliability (semiconductor) , computer science , econometrics , component (thermodynamics) , stochastic modelling , reliability engineering , statistics , mathematics , engineering , machine learning , power (physics) , physics , quantum mechanics , thermodynamics
The stochastic behaviour of lifetimes of a two component system is often primarily influenced by the system structure and by the covariates shared by the components. Any meaningful attempt to model the lifetimes must take into consideration the factors affecting their stochastic behaviour. In particular, for a load share system, we describe a reliability model incorporating both the load share dependence and the effect of observed and unobserved covariates. The model includes a bivariate Weibull to characterize load share, a positive stable distribution to describe frailty, and also incorporates effects of observed covariates. We investigate various interesting reliability properties of this model using cross ratio functions and conditional survivor functions. We implement maximum likelihood estimation of the model parameters and discuss model adequacy and selection. We illustrate our approach using a simulation study. For a real data situation, we demonstrate the superiority of the proposed model that incorporates both load share and frailty effects over competing models that incorporate just one of these effects. An attractive and computationally simple cross‐validation technique is introduced to reconfirm the claim. We conclude with a summary and discussion.