Note: Please see attachment for more clarification.
1. Suppose the failure time history of a component is given (where downward -facing arrows indicate failure times):
a. Assume the failure process follows a NHPP with λ(t) = exp(α+βt). Estimate the model parameters α and β using the MLE.
b. What is the expected number of failures from the current time until 72 months?
c. Check if the failure process has a time trend [α = 0.1]. If it does not, find the ROCOF.
2. Suppose the following data were observed in a repairable system:
a. Assume the failure process follows a renewal process and the interarrival time have
Estimate the parameter α based on the failure data. (Hint: find the MLE)
b. Now, assume that the failure process follows a renewal process with an exponentially distributed interarrival time Estimate the value of α.