Exercises 1

Assume we have two redundant shut-down valves, ESDV (emergency shut-down valve) and PSDV (process shut-down valve) that may be used in an emergency situation

Pr(ESDV-failure)=0.01

Pr(PSDV-failure)=0.005

Problem 1:

Find the probability that both valves fail in a critical situation given that the valves fail independently

Problem 2:

Assume that Pr(ESDV-failure| PSDV-failure) = 0.07 = β. Find the probability that both valves fails in a critical situation and compare with Problem 1.

Problem 3:

A component has survivor function R(t) = exp(-(0.01t)²). Find the probability that the component fails before t = 50 (hours). Make a plot of the cumulative distribution function. Hint, use MS Excel.