# Accession Number:

## AD0611544

# Title:

## MARKOVIAN SEQUENTIAL REPLACEMENT PROCESSES,

# Descriptive Note:

# Corporate Author:

## STANFORD UNIV CALIF

# Personal Author(s):

# Report Date:

## 1965-02-03

# Pagination or Media Count:

## 42.0

# Abstract:

A sequential control process is a dynamic system which is observed periodically and classified into one of a number of possible states. After each observation one of a finite number of possible decisions is made. These decisions are the control they determine the chance laws of the system. A replacement process is a control process with an additional special action, called replacement, which instantaneously returns the system to some initial state. This report discusses replacement processes whose state space is a subset of a finite dimensional Euclidean space. The rule which minimizes the Total Expected Discounted Cost is known and is used to show the existence of a non-randomized stationary decision rule which minimizes the Average Cost per Unit Time. A relationship between the optimal rules under both criteria is given wherein the optimal average cost rule is the limit, in some sense, of a sequence of discounted cost rules which yields a functional equation characterizing the optimal average cost rule. Finally, some examples employing the theory are given. Author