Reliability function

1. Consider the following reliability function, where t is in hours:(a)Find the reliability after 100 operation hours; after 1000 operating hours.(b)Derive the hazard rate function. Is it an increasing or a decreasing failure rate?2.The PDF for the time to failure in years of the drive-train on a Regional Transit Authority bus is given by(a)Show that the hazard rate function is increasing, indicating continuous wearout over time.(b)Find the MTTF.(c)Find the median time to failure.(d)Find the mode of the failure distribution.3.The reliability of a turbine blade can be represented by the following:where t0 is the maximum life of the blade.(a)Show that the blades are experiencing wearout.(b)Compute the MTTF as a function of the maximum life.(c)If the maximum life is 2000 operating hours, what is the design life for a reliability of 0.90?4.A household appliance is advertised as having more than a 10-yr life. If the following is its PDF, determine its reliability for the next 10 yr if it has survived a 1-yr warranty period.What is its MTTF without the warranty period, and what is its MTTF after the warranty period assuming it has still survived?

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