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A system contains two components, C and D, connected in

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 37E Chapter 2.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 37E

A system contains two components, C and D, connected in parallel as shown in the diagram.

Assume C and D function independently. For the system to function, either C or D must function.

a. If the probability that C fails is 0.08 and the probability that D fails is 0.12, find the probability that the system functions.

b. If both C and D have probability p of failing, what must the value of p be so that the probability that the system functions is 0.99?

c. If three components are connected in parallel, function independently, and each has probability p of failing, what must the value of p be so that the probability that the system functions is 0.99?

d. If components function independently, and each component has probability 0.5 of failing, what is the minimum number of components that must be connected in parallel so that the probability that the system functions is at least 0.99?

Step-by-Step Solution:

Answer

Step 1 of 4</p>

a) Here C and D are 2 conductors connected parallely  and function independently

     P(C fails)=P(C’)

                    =0.08

     P(C function)=P(C)

                          =1-0.08

                          =0.92

     P(D fails)=P(D’)

                    =0.12

     P(D function)=P(D)

                          =1-0.12

                          =0.88

    P(That the system function)=P(CUD)

                                                =P(C)+P(D)-P(C)P(D)

                                                =0.92+0.88-0.92(0.88)

                                                =0.9904

Step 2 of 4</p>

b) The system C and D both having the probability of failing is P

            P(System function)=0.99

              1-P(System fails) =0.99

                      1-P(C’D’)  =0.99

                                    1-p2 =0.99

                                        p2=1-0.99

                                         p=0.1

     The value of p must be 0.1 so that the probability of system function is 0.99

Step 3 of 4

Chapter 2.3, Problem 37E is Solved
Step 4 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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