1)a) A parallel system has the same components having reliability of 0.5. Determine the minimum number of components if the system reliability should be at least 0.99?
b) A system consists of 4 components is parallel system needs that at least 3 out of 4 must functions.
i) What is the system reliability if each component has a reliability of 0.9 and
ii) What is the system reliability if 5 components are there to perform the same functions?
2) Consider the system in the figure given below is which success needs that at least one of the path AC, BD, AED, BEC is good. Evaluate a general expression for system success and the reliability of the system if each component has reliability of 0.99.
In one component repairable model with stats space diagram and the corresponding rates of transition are shown. If stats 2 is an absorbing stats evaluate the expected number of intervals the system can resides in other state. And also derive the formula used.
3) Estimate the limiting state probabilities using STPM approach for the given ex.
The failure rates of three components are 0.05 f/yr, 0.01 f/yr and 0.02 f/yr respectively. And their average repair times are 20 hours, 15 hours and 25 hours respectively. Evaluate the system failure rate, average repair time and unavailability if all the three components must operate for system success. And derive the formulas used.