Question Help structure of identical components, the system can succeed if at le

Question

Question Help structure of identical components, the system can succeed if at least one of the components scaeds Assume that components each other and that each component has a 0.16 probability of failure. Complete parts (a) dntyof ndep (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 No (b) What is the probability that a paraliel structure with 2 identical components wil The probability that a paralel structure with 2 identical components will succed is (Type an integer or a decimal. Do not round) Tools (c) How many components would be needed in the structure so that the probabilty the system will succeed is greater than 0 997 Click to select your answerls). oast due MyMathlab Module 2 Practice exam (optoral. No ered Type here to search 5 3 2 wIE

Explanation / Answer

a) Probability of one component failing is computed here as:

= 2*0.16*(1 - 0.16) = 0.2688 > 0.05 therefore this is not unusual here.

Probability that two components fails is computed here as:

= 0.162 = 0.0256 < 0.05 , therefore this is an unusual event here.

b) Probability that a parallel structure with 2 components succeed is computed here as:

= 1 - Probability that both components work

= 1 - 0.0256

= 0.9744

Therefore 0.9744 is the required probability here.

c) Let the number of components required here be n. Then, we have here:

Probability of success > 0.9999

1 - 0.16n > 0.9999

0.16n < 0.0001

n > Ln(0.0001) / Ln(0.16)

n > 5.03

Therefore minimum number of components required here would be 6

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