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# Minimize total expected cost

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An item is subjected to a series of n tests (example: hardness, weight, length, etc.). Two known constants are associated with carrying out the ith test in the series. The constants are Ki (the cost per item of carrying out the ith test) and Ri (the probability of rejecting the item based on the ith test). The tests are independent in the sense that they may be run in any order, and the constants (Ki and Ri) are independent of the test order. For a given sequence of tests, an item is subjected to each test in the sequence in turn as long as the test does not reject the item (if an item is rejected by any test, no further tests are performed).

Determine the test sequence that minimizes the total expected cost of testing an item. Prove that your proposed sequence is optimal in minimizing the total expected cost of testing an item.

##### Solution Summary

This shows how to determine the test sequence that minimizes the total expected cost of testing an item.

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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