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Question 1.
A machine has a time-to-first-failure distribution that is Wgibull with 0 = 2.15 and 6 = 600 operating hours. Assume an average usage of the machine of 100 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 6 hours. The service centre advertises that if you bring them a broken machine, it will be repaired by 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): p(/) = 6.0 x 10-6 Z1.15 with t measured in operating hours. Assume that the customer does not accept the service plan in (a).
(j) 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?
Question 2.
An essential part of a manufacturing process is the factory assemble and integration linking (FAIL) system. Unfortunately this system has experienced numerous failures over the years under a minimal repair concept that is a nonhomogeneous Poisson process having an intensity function of p£/) = 1.15 x 10-7 fl .20 with t measured in operating hours. The system averages 3000 operating hours a year and is currently five years old. When the system fails, the repair time, is lognormal with 6.0 hours and 5 = 1.23.
(a) When the system was new, its manufacturer offered a 600-operating-hour warranty. What is the system reliability during the warranty period?
(b) What are the expected numbers of failures through the first five years of the system?
(c) How many failures are expected in the next two year (year 6 and year 7 of the FAIL system)?
(d) When the system fails, what percentage of repairs will be completed within a single 8-hour shift?
(e) When the system fails, it takes a crew of two to repair it. If the labour rate is $50 per hour and based upon the MTTR, what is the maintenance cost of the FAIL system during its 6th year of operation?
(f) If the cost of the system is $20,000, what is its optimal (minimum cost) replacement time?
(g) Management group believes that a preventive maintenance (PM) program may be cost effective. A PM consists primarily of replacing certain parts having a cost of $650 and thus restoring it to as-good-as-new condition. If it takes one technician 4 hours to do this, what is the optimum (minimum cost) PM interval?
Question 3.
A company operates an equipment that is essential in the manufacture of their products. This machine has been in operation for four years (1000 operating days). In order to plan for next year’s production levels, the availability of the machine must be determined. The company works a single 8-hour shift, 300 days out of one year. Relevant failure and maintenance data collected over this period is:
Failures: Minimal repair with a power law intensityfunction having a = 0.000125 and b = 1.650 with time measured in operating days
i Repairs: Repair time is lognormal with /med = 2.5 days and 5 = 0.70 A
Scheduled maintenance: preventive maintenance of downtime of one day ey ery five weeks (30 operating days).
(a) What is the mean system downtime over the first four years?
(b) Based upon both schedule and unscheduled maintenance, determine the expected availability of the equipment over the coming year the next 250 operating days).
(c) If the machine costs $30,080 to replace and a failure costs S200, when should the machine be replaced?

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