Partial Expectation

Abstract

This chapter concerns a particular value of the standard normal, k, called the left-location parameter, and the average of the difference of all standard normal z values larger than k. This is called the partial expectation of z greater than k, and is denoted as E(z > k). A table of E(z > k) for k = −3.0 to +3.0 is listed. Another partial described in this chapter is when the location parameter is on the right-hand side, and of interest is the average of the difference of all standard normal z values smaller than k. This is called the partial expectation of z less than k, and is denoted as E(z < k). A table of E(z < k) for k = −3.0 to +3.0 is listed. These measures are of particular interest in inventory management when determining when to order new stock for an item and how much. The partial expectation is used to compute the minimum amount of safety stock for an item to control the percent fill. The percent fill is the portion of total demand that is immediately filled from stock available. Another use in inventory management is an adjustment to the forecast of an item when advance demand becomes available. Advance demand occurs when a customer orders stock that is not to be delivered until a future date. Several examples are presented to guide the user on the use of the partial expectation.