Suppose the failure time history of a component

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 ?(t) = exp(?+?t). Estimate the model parameters ? and ? 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 [? = 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 ? 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 ?.