Applied Modeling Techniques and Data Analysis 1

9 Maximization Problem Subject to Constraint of Availability in Semi-Markov Model of Operation

The semi-Markov (SM) decision processes theory delivers the methods that allow us to control the operation processes of systems. The infinite duration SM decision processes are presented in this chapter. We discuss the gain maximization problem subject to an availability constraint for the infinite duration of the SM model of the operation in the reliability aspect. The problem is transformed into a linear programming maximization problem.

9.1. Introduction

In many articles and books, we can find applications of semi-Markov (SM) processes in reliability theory. We consider the most interesting and important books on these issues to be Gertsbakh (1969), Mine and Osaki (1970), Howard (1971), Silvestrov (1980) and Grabski (2015). The SM decision processes theory was developed by Howard (1969, 2015, 2018), Main and Osaki (1971), Gercbakh (2001) and Jewell (2018). These processes are also discussed in Feinberg (1994) and Boussemart and Limnios (2004), as well as by Beutler and Ross (1986), Boussemart et al. (2001) and Boussemart and Limnios (2004). Feinberg (1994) presented the Markov decision processes with a constraint on the average asymptotic failure rate. We should mention that the extended abstract of the discussed problem has been published in the AIP Conference Proceedings (1969).

The gain maximization problem subject to an availability constraint for the SM model of the operation ...