The quality control department at Malcomb Products must either inspect each part in a lot or not inspect any of the parts. That is, there are two decision alternatives: inspect all the parts or inspect none of the parts. The proportion of parts defectivse in the lot, Si, is known from historical data to assume the following probability distribution.
State of Nature,Sf Probability,P(Sf)
.02 .70
.04 .20
.06 .10
For the decision not to inspect any parts, the cost of quality is C = NS, K. For inspecting all the items in the lot, it is C. Nk, where:
N = 20 (lot size)
K = $18.00 (the cost of finding a defect)
k= $0.50 (the cost of sampling one item)
a. Develop a payoff table.
b. What decision should be made if the expected value criterion is used?
c. What is the expected value of perfect information?