able without adjustment? (c) What is the cumulative probability distribution for

Question

able without adjustment? (c) What is the cumulative probability distribution for the number of sets which are tested and found to be acceptable without adjustment? corresponding graph. Sketch the loo Probabilities: 0.9 0.8 Output Input Probabilities 0.7 0.6 Figure 5.4: Series-Parallel System A system consists of two branches in parallel, each branch having two compo- nents. The probabilities of successful operation of components A, B, C, and D are 0.9, 0.8, 0.7, and 0.6, as shown above. If a component fails, the output from its branch is zero. If only one branch operates, the output is 50%. Of course, if both branches operate, the output is 100%. a) Find the probability of zero output. b) Find the expected percentage output. 10. For constant rate of input, the rate of output of a system is determined by

Explanation / Answer

#9.
a)
Zero output will occur is A or B fails in branch upper branch and C or D fails in lower branch

Required probabibility is given by
(AB' + A'B + A'B') (CD' + C'D + C'D')
= (0.9*0.2 + 0.1*0.8 + 0.1*0.2) (0.7*0.4 + 0.3*0.6 + 0.3*0.4)
= 0.1624

b)
Expected percentage output is given by
100*(ABCD) + 50*(ABCD' + ABC'D + ABC'D' + A'BCD + AB'CD + A'B'CD) + 0*(A'BC'D + A'B'C'D + A'B'CD' + A'B'C'D' + AB'C'D + AB'C'D')

= 100*(0.9*0.8*0.7*0.6) + 50*(0.9*0.8*0.7*0.4 + 0.9*0.8*0.3*0.6 + 0.9*0.8*0.3*0.4 + 0.1*0.8*0.7*0.6 + 0.9*0.2*0.7*0.6 + 0.1*0.2*0.7*0.6) + 0

= 57

Expected percentage output is 57%

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