Interval-Valued Parametric Distribution Functions: Methodologies and Applications

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 param- eters 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 diculty for han- dling 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 more realistic results. In this regard, the present paper will discuss the system reliability for coherent system based on a new notion of random variable with interval-valued parameters. The concepts of probability density function and cumula- tive distribution function of the random variable with interval-valued parameters will be stated in this paper. Using the same techniques in classical 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, several numerical examples are provided in reliability systems and queueing theory to clarify our discussions.