Consider a variation of the two-state availability model (Example 8.6) so that thetime

Chapter 8, Problem 1

(choose chapter or problem)

Consider a variation of the two-state availability model (Example 8.6) so that thetime to failure is a k-stage hypoexponentially distributed random variable withparameters 1, 2,...,k and the repair times are exponentially distributed withparameter . Compute the steady-state availability. Recall that the time to failureof a hybrid k-out-of-n system (which includes the class of parallel redundant,standby redundant, and TMR systems) is hypoexponentially distributed. Themodel of this example thus gives the steady-state availability for this class ofsystems, provided that the repair process cannot begin until the system breaksdown. Show that the availability of such a system is obtained from the two-statemodel by substituting for , from the equation1 = ki=11i