Question

Currently, all of Pecan Peanuts’ operations are carried out on two separate production lines, one driven by a new machine and the other by a relatively older machine. Recent monitoring of each machine show that the probability of failure in the new one is 0.20 % and in the old one is 0.80 %. Given that the quality assurance department insists on a probability of 99.999% that at least one machine is working at all times, advise Pecan Peanuts if this condition is being satisfied.

Insert calculation in excel and summarise result approx. 200 word

Answer 1

P(A)	0.2
P(B)	0.8
P() = P(A) * P(B)	0.16
So, P() = 1 - P()	0.84
Let 'A' be the event that the new production line fails and 'B' be the event that the old production line fails. So, we have - P(A) = 0.2 & P(B) = 0.8 As these production lines operate separately, so it can be assumed that both the production lines operate independent of each other. Which gives us - P(A ∩ B) = P(A) * P(B) Where P(A ∩ B) is the probability of occurence of A and B simultaneously. This would give us the probability of both the production lines failing at the same time. So, the required probability is - P(A ∩ B) = 0.2 * 0.8 = 0.16. Thus, there is 16% chance that both the production lines would stop functioning at the same time. Now, the probability of at least one of the production lines working can be obtained using the total probability rule as - Probability of at least one production line working = 1 - probability of none of them working. So, probability of at least one of them working = 1 - P(A ∩ B) = 1 - 0.16 = 0.84. Hence, we can say that there is only 84% chance of at least one of the production lines working. Thus, the estimated value given by quality assurance department is far from the actual value. The probability of at least one machine working at any time is 84% and not 99.999%. So, the condition stated by the quality assurance team is not satisfied.