Question

Q7. A quality control procedure involves 100% inspection of parts received from a supplier. Historical records show the following defective rates have been observed.

                       

                        Percent Defective                   Probability

                                    0                                  0.15

                                    1                                  0.25

                                    2                                  0.40

                                    3                                  0.20

The cost for the quality control 100% inspection is $250 for each shipment of 500 parts. If the shipment is not 100% inspected, defective parts will cause rework problems later in the production process. The rework cost is $25 for each defective part.

1. Construct a payoff table for this problem.
2. The plant manager is considering eliminating the inspection process in order to save the $250 inspection cost per shipment. Do you support this action? Why?

Answer 1

If a decision of inspecting all parts i staken, the payoff in all cases will be ( 250)

If the parts are not inspected, the payoff with rework of defective items

With 0 defectives =0

With 1 defectives = 500x0.01 x 25 = 125

With 2 defectives = 500x0.02 x 25 =250

With 3 defectives =500x0.03 x 25 = 375

Option / State of nature	P(0)0.15	P(1) 0.25	p(2) 0.4	P(3) 0.2	NV
Inspect all	250	250	250	250	250
Don't inspect all	0	125	250	375	206.25

Since the values are negative ( cost), the lower value is more beneficial, which means that inspection of all items is not advisable.