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

question 50

Multiple Choice

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 not defective.Based on this additional information,what is the revised (posterior) probability for the accept state?

• A)24
• B)52
• C)18
• D)39
• E)78

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Definitions:

Performance Meets Objectives

A situation where the actual outcomes align with the targeted goals set by an organization or individual.

Controlling

The process of measuring performance and taking action to ensure desired results.

Plans Fulfilled

The successful execution or completion of predetermined strategies or objectives.

Take Corrective Action

The process of identifying, rectifying, and eliminating the root causes of problems or deviations to prevent recurrence and ensure performance standards are met.