For a parallel structure of identical components, the system can succeed if at l

Question

For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.19 probability of failure. Complete parts (a) through (c) (a) Would it be unusual to observe one component fail? O Yes O No Would it be unusual to observe two components fail? O Yes O No (b) What is the probability that a parallel structure with 2 identical components will succeed? The probability that a paralilel structure with 2 identical components will sucoeed is (Type an integer or a decimal. Do not round.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999? (Round up to the nearest whole number.)

Explanation / Answer

Ans:

a)P(one component fail)=0.19

No,as probability is >0.05

P(two component fail)=0.19*0.19=0.0361

Yes,as probability is <0.05

b)When there are two components,atleast one component should woek to succeed.

P(succeed)=P(atleast one is working)=1-P(none is working)=1-0.19*0.19=1-0.0361=0.9639

c)

P(succeed)=1-0.19n>=0.9999

0.9999<=1-0.19n

0.19n<=0.0001

n>=6

6 components are needed for P(succeed)>=0.9999

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