Optimizing Performance

  It may be possible to optimize the series of challenges that must be passed before an action is to be performed by taking into account the length of time, T, it takes to process a particular test and the relative frequency, p, of its occurrence. The time it would take to eliminate case i if tests are done serially would be something like,

Σⁱ_k=1 p_kT_k 

so one might try to do the more frequent and easier tests first. Operations research has produced procedures like PERT for planning projects.

  This might be a consideration for those interested in reducing government inefficiency. Laws could be designed by the Legislatures with consideration for the needs of the Executive and Judicial branches as well as the public in general by simplifying the decisions required. Executive orders could handle the way in which requests of the Executive branch are processed by separating rare difficult requests from the more common simple ones. The same may be true for the way in which the courts hear their petitions.

The actions of all branches of government should be subject to considerations of "good conduct."


Supplemental (Mar 1): The expected processing time for a series of tests that individually take time T_k would be,

T_avg=Σⁿ_k=1 p_kT'_k where T'_k= Σ^k_i=1 T_i  or equivalently,

T_avg=Σⁿ_k=1 μ_kT_k where μ_k= Σⁿ_i=k p_i.

Note that μ₁=1 so T_avg is always greater than the time it takes to do the first test and why we would prefer to do the shorter tests first.