
Accession Number : AD0701687
Title : A NOTE ON MATRIX RENEWAL FUNCTION.
Descriptive Note : Technical rept.,
Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
Personal Author(s) : Kshirsager,A. M. ; Gupta,Y. P.
Report Date : 23 JAN 1970
Pagination or Media Count : 12
Abstract : The LaplaceSteiltjes Transform of the matrix renewal function M(t) of a Markov Renewal process is expanded in powers of the argument s, in this paper, by using a generalized inverse of the matrix IP sub 0, where P sub 0 is the transition probability matrix of the imbedded Markov chain. This helps in obtaining the values of moments of any order of the number of renewals and also of the moments of the first passage times, for large values of t, the time. All the results of renewal theory are hidden under the Laplacian curtain and this expansion helps to lift this curtain at least for large values of t and is thus useful in applications of Markov Renewal processes to inventory control of repairable items, and to counter theory. (Author)
Descriptors : (*STOCHASTIC PROCESSES, STATISTICAL FUNCTIONS), INVENTORY CONTROL, INTEGRAL TRANSFORMS, MATRICES(MATHEMATICS), MAINTENANCE
Subject Categories : Statistics and Probability
Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE