This problem is intended to show the merits of a partially distributed inspection systems in which inspections are placed after processing steps that generate a high fraction defect rate. The processing sequence consists of eight operations with fraction defect rates for each operation as follows:

Three alternatives are to be compared: (1) fully distributed inspection, with an inspection after every operation; (2) partially distributed inspection, with inspections following operations 4 and 8 only; and (3) one final inspection station after operation 8. All inspections include sortations. In alternative (2), the inspection procedures are each designed to detect all of the defects for the preceding four operations. The cost of processing is Cpr = $1.00 for each of operations 1 through 8. Inspection/sortation costs for each alternative are given in the table below. Compare total processing and inspection costs for the three cases.

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Operation Defect rat0.01 0.01 0.01 0.1 0.01 0.01 0.01 0.11 Altemative Inspection and sortation cost C-= $0.10 per unit for each of the eight inspection stations C S0.40 per unit for each of the two inspection stations = $0.80 per unit for the one final inspection station