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 1 Payoff Table

Component Technometrics' Choice

Condition Ship as is Rework first

Good +$40 +$10

Defective -$20 +$10

Required:

1. 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?

2. 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.

3. Mr Shaw, an engineer in echnometrics believes that the probability of producing a defect is around 20%? What will be Mr Shaw's recommendation for Technometrics?

4. If Mr. Shaw has to make the decision of paying for the test report, how much will he be willing to pay?

5. Is Mr. Shaw willing to pay more than Technometrics? Why? Please explain.