reliability engineering Ralph works in the back room of a commercial credit house. One of the problems under study is designing redundancy into data capture equipment, in order to minimize data processing errors economically. After thinking about this for a while, and shortly before a computer consultant makes a presentation, Ralph goes through the following thought exercise.

a] Suppose the failure rate on a particular process is given by the parameter

f. If three processes are linked in series, a failure will occur only if each of the processes fails. Suppose the failure rate, or failure probability, is f = .02. What is the overall failure rate if two processes are linked in series? What is it if three processes are linked in series? Assume independence across the individual stages.

b] The consultant's literature elaims a failure rate of f = .02. But Ralph knows this is aguess. Suppose, with equal probability, the failure rate is .01 or .03. Determine the overall failure rate when three or two processes are linked together, assuming independence among failure rates and processes.

e] This last exercise troubles Ralph. Does it make sense to treat the uncertainty surrounding f itself as independent? If Ralph guesses f = .01 and f = .03 obtains, eaeh process encounters an f of .03. If this is the case, determine the overall failure rate when three or two processes are linked together.

d] Carefully explain the difference in your answers in [b] and [e] above. What does this teIl you about assuming independence when you are assessing probabilities?AppendixLO1