Interval-Valued Parametric Distribution Functions: Application to System Reliability Analysis

Abstract

A lot of methods and models in classical reliability theory assume that all parameters of lifetime density function are precise.But in the real world applications imprecise information is often mixed up in the lifetimes and/or parameters of systems.However, the parameters sometimes cannot be recorded precisely due to machine errors, experiment, personal judgment, estimation or some other unexpected situations.When parameters in the lifetime distribution are interval-valued, the conventional reliability system may have difficulty for handling reliability function.Therefore, estimation methods for reliability characteristics have to be adapted to the situation of interval-valued parameters of life times in order to obtain realistic results.In this regard, the present paper will discuss  the system reliability for coherent system based on a new notion of random variable withinterval-valued parameters.The concepts of  probability density function and cumulative distribution function of the random variable with interval-valued parameters will be stated in this paper.Using the same techniques in probability theory, the probability measure of the random variable  can be constructed from the   probability density function and cumulative distribution function.In the proceeding discussion,  numerical  examples are provided in reliability systems to clarify our discussions.