On selecting the most reliable components

[摘要] Consider a series system consisting of n components of k types. Whenever a unit fails,it is replaced immediately by a new one to keep the system working. Under the assumption thatall the life lengths of the components are independent and exponentially distributed and that thereplacement policies depend only on the present state of the system at each failure, the systemmay be represented by a birth and death process. The existence of the optimum replacementpolicies are discussed and theε-optimal policies axe derived. If the past experience of the systemcan also be utilized, the process is not a Markov process. The optimum Bayesian policies arederived and the properties of the resulting process axe studied. Also, the stochastic processesare simulated and the probability of absorption, the mean time to absorption and the averageproportion of the retrograde motion are approximated.

[学科分类] 自然科学（综合）