Statistics for Maintenance Modelling: Renewal Processes

# Calculating the Renewal Function Analytically: Exponential Distribution (2)¤

Now:

Prob(N(t) = k) = Prob(N(t) k) - Prob(N(t) (k + 1))

= (t)k /k! (using the equation on the previous screen)

Since E[X] = xf(x) dx,

M(t) = kProb(N(t) = k) = (t) (t)j / j! = t

as the sum (t)j / j! = (since ex = 1 + x + x2/2! + ... xn/n! = )

This tells us that the expected number of events in time t is just the interval t times the rate of occurrence, .