The Quality Control Manager for the NKA Inc Based on Historical Data,if the Lot Is Poor Quality,40% of to Accept

question 37

Essay

The quality control manager for the NKA Inc.must decide whether to accept (alternative 1),further analyze (alternative 2),or reject (alternative 3)the shipment (lot)of incoming material.The historical data indicates that there is 30% chance that the lot is poor quality (S₁),50% chance that the lot is fair quality (S₂),and 20% chance that the lot is good quality (S₃).Assume the following payoff table is available.The values in the payoff table are in thousands of dollars. $$\begin{array} { l c c c } & { \text { States of Nature } } \\\text { Decision } & \mathrm { S } _ { 1 } & \mathrm {~S} _ { 2 } & \mathrm {~S} _ { 3 } \\\text { Accept } & 20 & 30 & 90 \\\text { Further analyze } & 60 & 70 & 15 \\\text { Reject } & 80 & 50 & 30\end{array}$$ Based on historical data,if the lot is poor quality,40% of the items are defective.If the lot is fair quality,22% of the items are defective.If the lot is good quality,10 % of the items are defective.The quality control manager inspects one unit from a recent shipment.
-After inspecting it the manager determines that the unit is defective.Based on this additional information,determine the revised (posterior)probabilities for each of the three states of nature.

---

Definitions:

Geodemographic

Relating to the study of the population and the distribution patterns according to geographic locations and demographic factors.

Psychographic

Relating to the study of personality, values, opinions, attitudes, interests, and lifestyles.

Cognitive

Relating to the mental processes of perception, memory, judgment, and reasoning.

Channel Overload

The state that occurs when a communication channel is overwhelmed with too much information, leading to decreased effectiveness.