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

question 9

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 of 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 one unit,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.

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Definitions:

Metabolism

The chemical processes that occur within a living organism to maintain life, involving the conversion of food to energy and new materials.

Excretion

The process by which the body removes waste products of metabolism and other non-useful materials.

Urticaria

A skin condition commonly known as hives, characterized by red, itchy, raised welts on the skin's surface that may result from allergic reactions or other causes.

Phenytoin

An anticonvulsant medication used to control seizures by slowing down impulses in the brain that cause seizures.