The purpose of this paper is to extend the PI model proposed by Anily and Grosfeld  to consider the process when there is an arbitrary discrete shift distribution instead of a constant hazard rate.
As in Anily and Grosfeld , the principle that the first produced product is first inspected (FPFI) is adopted.
If one decides to terminate the inspection procedure even if there are uninspected products left, then the remaining unmet demand (RUD) will incur a unit shortage cost, s ($/product), where [gamma] < s (see Anily and Grosfeld ).
One can use the following property provided by Anily and Grosfeld  to reduce the computations: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for 0 [less than or equal to] K < d.
This study extends Anily and Grosfeld's  production and inspection (PI) model with one with nonrigid demand to one that considers an arbitrary discrete probability distribution instead of being limited to the case where the process possesses a constant hazard rate.