By Michael Mcafee
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Additional resources for Billy Yank - The Uniform of the Union Army 1861-1865
In actual fact promotion to a rank involves passage of a certain positive amount of time based on either or both of the following requirements: 1) time to learn to perform the duties of a given rank; 2) time needed for an evaluation of a person's qualifications for the next rank and of his/her competitive standing among other candidates in the same rank. The first time is required to absorb needed information and the second time to yield essential information. of 1) and The maximum 2) determines the minimum times Tr for possible promo- tion to r.
P T-l > Pt r + ptr+l + ••• + p T-l ~~~~--~~~~~-- T ~ r since 1+ P + t p r + > T-t + pT-l T Using the approximation e: = y - I P r(Y) or (33) T P r - e: for p close to one 1 - ie: (32) with p = 1 ... - one finds by a straightforward calculation Pr Prey) - Pr Pr N r T if=t . r N y-l 2 tr r=.!. 2 tr . e change in promotion probability due to growth is then approximately proportional to the length of time tr during which growth has effectively operated and to one half the growth rate. A process of decline similarly decreases the chances of promotion by one half the rate of decline times the effective time of operation.
And constant T yields Thus'a career profile of constant p 48 Nr+1 T - rT -N-- • T - (r+1) T r p Nr+1 -N-= P r Nr 1 --= p Nr+1 sr+1 For constant p T- rT when T - (r+1) T T . T-T-(r+1) rT T - rT T - (r+1) T or . the span of control reaches its minimum value is minimal, that is for r = 0 1 T P . T-T· Table 2 shows spans of control s as a function of various promotion probabilities and intervals. Table 2 Spans of Control at Lowest Level Consistent with Various Initial Promotion Probabilities and Promotion Times.
Billy Yank - The Uniform of the Union Army 1861-1865 by Michael Mcafee