Journal of Applied Mathematics and Decision Sciences
Volume 2 (1998), Issue 2, Pages 133-145
On selecting the most reliable components
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 -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.