Bilateral phase-type distributions

In this article we define a class of distributions called bilateral phase type (BPH), and study its closure and computational properties. The class of BPH distributions is closed under convolution, negative convolution, and mixtures. The one-sided version of BPH, called generalized phase type (GPH), is also defined. The class of GPH distributions is strictly larger than the class of phase-type distributions introduced by Neuts, and is closed under convolution, negative convolution with nonnegativity condition, mixtures, and formation of coherent systems. We give computational schemes to compute the resulting distributions from the above operations and extend them to analyze queueing processes. In particular, we present efficient algorithms to compute the steady-state and transient waiting times in GPH/GPH/1 queues and a simple algorithm to compute the steady-state waiting time in M/GPH/1 queues.     

Timing replacement decisions under discontinuous technological change

We consider the problem of deciding whether to keep a piece of equipment or replace it with a more advanced technology in an environment of technological change. Our model assumes that the costs associated with the presently available technology and future technologies are known, but that the appearance times of future technologies are uncertain. We develop a procedure for computing the optimal keep-or-replace decision that iteratively incorporates a technological forecast. For a certain class of situations, we show that our approach requires the minimum possible amount of forecasted data.     

Establishing Reliability Goals for Naval Major-Caliber Ammunition

We describe a decision process for establishing the threshold reliabilities for components of naval major-caliber ammunition. We present a measure of reliability performance, called ef*, which relates directly to the weapons system's performance in a naval gunfire support environment. We use a simulation model to establish this relationship, a regression metamodel to estimate its parameters, and a simple decision process to specify component reliability thresholds which ensure that the ammunition is mission effective. We present this article as an example of the integration of discrete event dynamic system analysis within a decision process. © 1992 John Wiley & Sons, Inc.