1. A machine has a time-to-first-failure distribution that is Weibull with β = 2.10 and θ = 620
operating hours. Assume an average usage of the machine of 150 hours per year.
(a) The manufacturer of the machine offers a 10-year warranty if the customer purchases their
10-year service plan. The service plan will replace all worn parts each year, thus restoring the
machine to "as-good-as-new" condition. Compare the machine reliability at 10 years with and
without the service plan.
(b) The repair time distribution of the machine is lognormal with a shape parameter of 0.60 and a
median repair time of 8 hours. The service centre advertises that if you bring them a broken
machine, it will be repaired by the same the following workday. Find the MTTR and the
percent of repairs that are completed within an 8-hour workday.
(c) Failure of a broken machine results in minimal repair that can be described by the following
intensity function (a nonhomogeneous process): ρ(t) = 6.0 × 10-6 t1.15 with t measured in
operating hours. Assume that the customer does not accept the service plan in (a).
(i) What is the expected number of failures that will occur over 10 years?
(ii) What is probability of at least one failure during the tenth year?
(iii) What is the MTBF (instantaneous) at the end of the 10th year?
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