A production line has three machines A, B, and C, with reliabilities of 90, 95, and 94, respectively. The machines are arranged so thatif one breaks down, the others must shut down. Engineers are weighing two alternative designs for increasing the line's reliability. Plan1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. In either case, three machines (A.B. and C) would be used with reliabilities equal to the original three.a. Compute overall system reliability under Plan 1. (Round your intermediate calculations and final answer to 4 decimal places.)Answer is complete but not entirely correct.Reliability0.9859b. Compute overall system reliability under Plan 2 (Round your intermediate calculations and final answer to 4 decimal places.)

The capacity of a system or component to consistently carry out its intended function over a…

Answered: A production line has three machines A,…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section4.8: Data Envelopment Analysis (dea)

Problem 42P

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A production line has three machines A, B, and C, with reliabilities of .99, .96, and .93, respectively. The machines are arranged so that if one breaks down, the others must shut down. Engineersare weighing two alternative designs for increasing the line’s reliability. Plan 1 involves addingan identical backup line, and plan 2 involves providing a backup for each machine. In either case,three machines (A, B, and C) would be used with reliabilities equal to the original three.a. Which plan will provide the higher reliability?
50-Step Assembly Line Consider an assembly line with 50 steps that are carried out sequentially. Each of the 50 steps has a defect probability of 1%. The final product produced on the assembly line is defective if any one of the 50 steps made a defect. At the end of the assembly line there are two operators independently inspecting the product. Each of them is recognizing a defective product with a 90% probability. Assuming that the product is not defective, it is moved to the shipping department. Otherwise, the product is scrapped. Probability that a defective product is produced (independent of the defect being found or not) (in decimal form): What is the probability that a defective product is moved to the shipping department?
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The president of AS Electronics, Inc., has two design options for his new line of cathode ray tubes (CRTs). The forecast for the CRTs is 100,000 units annually. The company will make 100,000 units using one of the two designs at a cost of $75 each. Good CRTs can be sold, but bad CRTs are destroyed and have no salvage value. (Ignore any disposal cost issues for the moment.) The company can sell good CRTs for $150. Design option A has a .90 probability of yielding 59 good CRTs per 100 and a .10 probability of yielding 64 good CRTs per 100. The design will cost $1,000,000. Design option B has a .80 probability of yielding 64 good CRTs per 100 and a .20 probability of yielding 59 good CRTs per 100. The design will cost $1,350,000. Draw and label the decision tree (for two design options with two possible yields each). Calculate the first-year payoff for each option. [Payoff = Annual Revenues – annual manufacturing costs – design costs] Calculate the expected payoff for each of the…
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