Recall that a Weibull law for the lifetime of a system is most simply described by its cumulative hazard function : \(H(t)=\int_{0}^{t}\lambda(T)dT=(t/b)^a , a, b, t>0\)
The heay cables that support a bridge are theorized to each have time to breakage that follows a Weibull law with a=2.5 and b=30 years.
a. Find the hazard function for one of these cables. Is it what we have called an aging system, or a constant hazard system, or a burn in system? Explain.
b. Use the results of a , and our result that the probability of short term failure of a working system is approxamitely lambda(t)deltat, to find roughly the probability that a 40 year old intact cable will fail next month.
c. Find the probability that the cable will last 50 years.