Variance of time to recruitment for a single grade manpower system with different epochs for exits and two types of decisions with correlated wastages having two thresholds involving two components

In this paper, the problem of time to recruitment is studied using a univariate policy of recruitment involving optional and mandatory thresholds for a single grade manpower system where wastages (loss in manpower) occur due to attrition generated by its policy decisions and frequent breaks taken by the personnel working in the system. Assuming that (i) the policy decisions and exits occur at different epochs (ii) the number of exits form a homogeneous Poisson process (iii) both the optional and mandatory thresholds for the cumulative loss of manpower have independently a normal component due to attrition and a second component due to frequent breaks (iv) wastage due to attrition and frequent breaks form separately a sequence of exchangeable and constantly correlated exponentially distributed random variables and (v) inter-policy decision times are of two types, one with high rate of attrition and the other having low rate of attrition, a stochastic model is constructed and variance of time to recruitment is obtained when the inter-policy decision times form (i) a geometric process and (ii) an order statistics.