An offshore oil extraction and processing platform has been operated out in the
ID: 3228860 • Letter: A
Question
An offshore oil extraction and processing platform has been operated out in the North Sea for the last 36 years. It has been recorded that every two years on average 7 major disputes occur among the workers ending with severe injuries of one or two workers. (7%) a) Assume occurrence of such major disputes follows a Poisson process, then, what is the probability of at least one such event will occur in every two months for a given year? (7%) b) It has been also noticed that the occurrence of disputes among the workers is strongly correlated with the communication network problems of the platform with the outer world mostly due to severe weather conditions. Over the last 36 years, there have been 9 significant storm events that have hourly average wind speeds exceeding 30 m/s at least once. The probability of having a failure in the communication system during such an event is 50%. If the occurrence of such a storm is assumed to follow a Poisson process, then, what is the probability that there will be no failure in the communication system associated with such storms within the next 2 years?
Explanation / Answer
By the historical data, it has been observed that on average that every two years witness 7 major disputes, or that on average we have 3.5 major disputes per year.
Let X denote the number of events every two months. Then, the probability of at least one event every two months is
P(X>1| ext{two months}) =1- P(X=0| ext{two months}) = 1-e^{-3.5 imes 1/6}=0.442
Now, the probability of at least one event every two months throughout the year is then 0.4426 = 0.0075.
b) Now, probability of a significant storm during an year is P(S) = 9/36 = 0.25, and that the probability of failure in communication systems (F) during the storm is 0.5, that is, P(F|S) = 0.5.
Under the assumption of Poisson process, the probabilty of no storms over the next two years is
P( ext{ no storms } ) = e^{-0.25 imes 2} = 0.6065