On Some Ageing Relations and Stochastic Orderings in Dynamic Models and Marshall-Olkin Family of Distributions

Das, Suchismita (2012) On Some Ageing Relations and Stochastic Orderings in Dynamic Models and Marshall-Olkin Family of Distributions. PhD thesis, Indian Institute of Science Education and Research Kolkata.

PDF (PhD thesis of Suchismita Das) Suchismita_-Das-PhD-thesis.pdf - Submitted Version Restricted to Repository staff only Download (8MB)

Abstract

Reliability theory is a general theory about system failure. It allows researchers to predict the age-related failure kinetics for a system of given architecture (reliability structure) and given reliability of its components. The concept of ageing is one of the most challenging issues in reliability theory. In maintenance problem, the consequences derived from an increasing failure rate have caused many researchers to address their efforts to study this condition. In reliability problems stochastic orders play an important role to assess how a system improves/deteriorates with age. Stochastic orders turn out to be a valuable tool in applied probability, with important applications in engineering, economics, biological sciences etc. Here, we discuss the properties of some ageing classes and different stochastic orders under some proposed models.

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