A semi-Markov model for the duration of stay in a non-homogenous academic manpower system

A.U Udom

doi:10.4314/gjmas.v8i1.50813

Abstract

The semi-Markov approach to a non-homogenous manpower system is considered. The mean duration of stay in a grade and the total duration of stay in the system are obtained. A renewal type equation is developed and used in deriving the limiting distribution of the semi – Markov process. Empirical estimators of the semi-Markov parameters which are uniformly consistent and asymptotically normally distributed are used to obtain the average length of stay for the academic manpower of the University of Nigeria.

Highlights

The problem of disaggregating heterogeneity in manpower systems has been discussed by a number of authors
This disaggregation of a manpower system normally correspond to some classification of the manpower system into homogenous subgroups as for example, in the institution with grades of staff discussed by Young and Almond (1961), the classification of manpower system by age as in Uche and Udom (2006) and the classification of a system by degrees of commitment to the system, for example Bartholomew (1971) and McClean (1976)
The simple Markov model assumes that transition from one grade to another or leaving occurs at a constant rate, the completed length of service (CLS) in grade i prior to leaving has a degenerate geometric distribution

Summary

INTRODUCTION

The problem of disaggregating heterogeneity in manpower systems has been discussed by a number of authors. Transition models based on the Markov theory and renewal theory have been used in the description of these heterogeneous populations; see for example Bartholomew (1982) Most of these models are transition models and are concerned with the effect of constant transition probabilities on changing class structure. The simple Markov model assumes that transition from one grade to another or leaving occurs at a constant rate, the completed length of service (CLS) in grade i prior to leaving has a degenerate geometric distribution. This assumption inherent in the simple Markov model does not apply to many situations. The model to obtain the average duration of stay in the various academic grades, and total duration of stay in the system for the University of Nigeria Academic Manpower system

THE SEMI-MARKOV MODEL

AVERAGE LENGTH OF STAY IN GRADE J

APPLICATION

CONCLUSION

48 REFERENCES