Success probability of o-ring

Reference no: EM1314273

In Against All Odds, the TV series on statistics, Bruce Hoadley, a statistician at Bell Communication Research, discusses the catastrophic failure of the Challenger shuttle in 1986. Hoadley estimates that there was a failure probability of .02 for each of the six O-rings (designed to prevent the escape of potentially explosive burning gases from the joints of the segmented rocket boosters).

a. What was the success probability of each O-ring?

b. Given that the six O-rings f u notion independently of each other, what was the probability that all six O-rings would succeed, that is, perform as designed? in other words, what was the success probability of the first O-ring are the second O-ring an*¹the third O-ring, and so forth?

c. Given that you know the probability that all six O-rings would succeed (from the previous question), what was the probability that at least one O-ring would fail?

d. Given the abysmal failure rate revealed by your answer to the previous question, why you might wonder, was this space mission even attempted? According to Hoadley missile engineers thought that a secondary set of O-rings would function independently of the primary set of O-rings. If true and if the failure probability of each of the secondary was the same as that for each primary O-ring (.02), what would be the probability that both the primary and secondary O-rings fall at a particular joint?

e. In fact, under conditions of low temperature, as on the morning of the Challenger catastrophe, both primary and secondary O-rings lost their flexibility, and whenever the primary O-ring failed. Its associated secondary O-ring failed. Under these conditions, what would be the conditional probability of a secondary O-ring failure, given failure of its associated primary O-ring?

Reference no: EM1314273

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