Question

In a production operation of an electronics firm, a company manufactures I/O circuit chips that is used in a final assembly process. The chips, manufactured in batches sizes are either good (G) or defective (B). Historical data indicates that P(G) = .8 and P(B)=.2.

The company has the following options:

Send the batch, “as is,” onto the final production assembly. It costs $1,000 to send good parts onto production and $4,000 to send bad parts to final production (due to rework).

Rework all chips (once reworked, all chips are good). It cost $2,000 to rework chips

There is also a survey option that can be employed: An inspection on a single chip in the batch to determine if it is defective or not defective. It cost $100 to test a chip. The following relates to the test results Out come of the test is either defective chip (D) or not defective chip (ND) :P(D/G) = .1    therefore. P(ND/G) = .9, P(D/B) = .5     therefore, P(ND/B) = .5

Using decision theory and precision theory, determine the company’s best decision strategy based on probability assessment and costs. Also Calculate EVSI, EVPI and Efficiency.

Answer 1

Calculation Decision 0.8 0.8 1000- 800 Good 1600 Bad 0.2 4000 0.2 4000- 800 Sen 2000 1- 2000 Rework 0.1 0.1 0.8 100- Inspection 0.9 0.9*0.8 100 72 Bad 8+72+10+10 100 0.5 0.2 0.5 100- 0.2 0.2 0.5 100 0.5 10 2000-800- 1200 EVPI-SUM Pi(MiRij) 3700 1600+2000+100- Efficiency (1600/1200) * 100% =43% Decision We recommend Inspection since it has a lower cost.