Technometrics, Inc., a large producer of electronic components, is having some problems with the manufacturing process for a particular component. The profit contribution of this component is $40 per unit. Under the contract the company has with its customers, Technometrics' warranty requires them to pay a shipping charge of $20 per defective part which they repair for $30 each and ships for another $20. Further they pay a compensation for delay in the customer's business which works out to about $80 for each component that the customer finds to be defective. However, before shipping the components to customers, Technometrics could choose to spend an additional $30 per component to rework any components thought to be defective (regardless of whether the part is really defective). The reworked components can be sold at the regular price and will definitely not be defective in the customers' applications. Unfortunately, Technometrics cannot tell ahead of time, which components will fail to work in their customers' applications. The following payoff table shows Technometrics' net cash flow per component.

Figure 1Payoff Table

ComponentTechnometrics' Choice

ConditionShip as isRework first

Good+$40+$10

Defective-$20+$10

Required:

1.Is Technometric correct in summarizing their information?

2.If Technomterics believes that their process is likely to generate good parts with a probability of 90% what should they do? Ship as is or rework?

3.How much should Technometrics be willing to pay for a test that could evaluate the condition of the component before making the decision to ship as is or rework first? After passing this test, the component will not fail at the customers.

4.Mr Shaw, an engineer in Technometrics has limited faith in the tests and believes that the probability of detecting the defect correctly is only 80% from the test, and there is a 20% chance of misclassification of defective part as correct part. He does not to buy such an incorrect test. What will you advice? How much will you play for it, if any?