Accession Number : AD0611544

Title :   MARKOVIAN SEQUENTIAL REPLACEMENT PROCESSES,

Corporate Author : STANFORD UNIV CALIF

Personal Author(s) : Taylor,Howard M.

Report Date : 03 FEB 1965

Pagination or Media Count : 42

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)

Descriptors :   (*REPLACEMENT THEORY, OPERATIONS RESEARCH), (*DYNAMIC PROGRAMMING, REPLACEMENT THEORY), (*STATISTICAL PROCESSES, CONTROL), SEQUENTIAL ANALYSIS, DECISION THEORY, COSTS, MANAGEMENT PLANNING AND CONTROL

Distribution Statement : APPROVED FOR PUBLIC RELEASE