interval-valued parametric distribution functions: methodologies and applications

A lot of methods and models in classical reliability theoryassume that all parameters of lifetime density function are precise. butin the real world applications imprecise information is often mixed upin 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 unexpectedsituations. 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 reliabilitycharacteristics have to be adapted to the situation of interval-valuedparameters of life times in order to obtain more realistic results. in thisregard, the present paper will discuss the system reliability for coherentsystem based on a new notion of random variable with interval-valuedparameters. the concepts of probability density function and cumula-tive distribution function of the random variable with interval-valuedparameters will be stated in this paper. using the same techniquesin classical probability theory, the probability measure of the randomvariable can be constructed from the probability density function andcumulative distribution function. in the proceeding discussion, severalnumerical examples are provided in reliability systems and queueingtheory to clarify our discussions.