Problem 5.58 High priority freight service (Source: Wayne Nelson (1982), Applied Life Data Analysis, John Wiley and Sons, Inc., New York). A high priority freight train required three locomotives for a one–day run. If any one of these locomotives failed the train was delayed and the railroad had to pay a large penalty. Analysis of statistical data indicated that the locomotives failed independently and their failure times could be approximated by an exponential distribution with expected failure times λ−1 = 43.3 days. Thus such a system is a series system.

(a) Compute the reliability of the system.

(b) To reduce the chance of delay the railroad added a fourth locomotive; thus the train was delayed only if two or more locomotives failed. This is an example of a 3-out-of-4 system. Determine the reliability provided by the addition of a fourth locomotive.