9Component Reliability Estimation Through Competing Risk Analysis of Fuzzy Lifetime Data
Rashmi Bundel1, M. S. Panwar2* and Sanjeev K. Tomer2
1Department of Statistics, University of Rajasthan, JLN Marg, Jaipur, Rajasthan, India
2Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, U.P., India
Abstract
The competing risk analysis of lifetime data from multi-component series systems is often carried out to assess the reliability measures of systems’ components. In many cases, systems’ lifetimes are not observed precisely, or they are reported in a “vague” form. This imprecision or vagueness in data can be dealt with higher accuracy by incorporating fuzzy concepts. In the present chapter, we perform a competing risk analysis of lifetime data by considering lifetimes as fuzzy numbers. Using different membership functions, we provide procedures for maximum likelihood and Bayesian estimation of component reliability. We also evaluate bootstrap confidence intervals and the highest posterior density intervals. To observe the impact of various membership functions on the considered estimators, a comprehensive simulation study has been carried out. Finally, a real data set of small electric appliance has been analyzed.
Keywords: Series system, Bayesian inference, trapezoidal membership function, floored observation, small electric appliance data
9.1 Introduction
Estimation of the reliability function of a particular component in a series system by using ...
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