Question

- At The exponential density function in the previous problem: t20 is often used to model the failure of equipment components. That is, the probability that a particular component will fail within time T is given by: f(t)= le- Pf =ff(odt 0 Reliability is defined as the probability that a component will not fail in time T, i.e. R=1-P, a) what is the expected (average) lifetime of a component in terms of 2 ? b) if an electronic component has the average lifetime of 10,000 hrs, for what time span might we expect its reliability to be 0.99 ?

Answer 1

det T denotes the life time of equipmei components The pdf of Tas f(t) = delt i 420 - S f (t) at Pr ť at е dt at O A700 Pf - - eat and R : l-Pf е edt &70 Radio

@ E(T) = Se ft let o = ale zatat [are ca Hence the expected lifetime of a a componeng as a E(T) = á

b Given = 10000 -4 a = 10 t ܢܛܼ > . 10000 and R = 0.99 0.99 ē 10000 Log(0-99) t = -10l Log (0.99) t = 100.5034 Hence the lime span is 100.5034 3 hours.