A Stochastic Model of Personnel Mobility: Application of Reliability Theory in Manpower System Analysis

Given the distribution of natural losses from any rank of a graded manpower system, and the rate of promotion to higher ranks, we define the mobility of rank members as a function of the cumulative lengths of service of all rank members and those members destined for promotion. We show that when the rank contains many individuals, and promotions are made without regard to seniority, mobility decreases with time in service if the natural loss function has an increasing failure rate, and increases with time in service if the loss function has a decreasing failure rate; mobility increases with time in service if promotions are awarded by seniority. We also derive bounds for the average time in service of rank members, based on the loss function and the promotion rate. In addition, we compare the average time to promotion, average time to resignation, and average time in service for the two promotion policies mentioned above. Our results show that promotion by seniority produces the longest possible average member service times if the loss function has an increasing failure rate, and the shortest average service times if the loss function has a decreasing failure rate. Using real data, we derive and categorize the theoretical natural loss distribution for a system of university faculty, the implied promotion policy governing the transition-to-tenure process, and the individual mobility function for nontenured members. This analysis does not require a large amount of data.