Journal of Applied Mathematics and Decision Sciences
Volume 2 (1998), Issue 2, Pages 133-145

On selecting the most reliable components

Dylan Shi

Department of Mathematics, Indiana University Southeast, New Albany 47150, IN, USA

Copyright © 1998 Dylan Shi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 that all the life lengths of the components are independent and exponentially distributed and that the replacement policies depend only on the present state of the system at each failure, the system may be represented by a birth and death process. The existence of the optimum replacement policies are discussed and the ε-optimal policies axe derived. If the past experience of the system can also be utilized, the process is not a Markov process. The optimum Bayesian policies are derived and the properties of the resulting process axe studied. Also, the stochastic processes are simulated and the probability of absorption, the mean time to absorption and the average proportion of the retrograde motion are approximated.