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.