Consider a machine that operates continuously, and can fail in three different ways. If the machine is operational at time t, then a type i failure (i = 1, 2, 3) will occur in the time interval (t, t h) with probability pi(h), where pi(h) = ih o(h) as h 0. Failure can only occur when the machine is operational. Upon failure, repair will start immediately, whose duration is an exponential random variable with mean depending on the type of failure. The mean repair time for a type i failure (i = 1, 2, 3) is 1/i . When the repair is finished, the machine will start operating immediately. Let X(t) be the state of the machine at time t, where the state indicate whether or not the machine is functioning, and if not, the type of failure being addressed. That is, 0 = no failure (operating), 1 =type-1 failure, 2 =type-2 failure, and 3 =type-3 failure