The Component, Stochastic Program Flow Graph Parallel-Redundant System - Mathematics Assignment Help

Assignment Task -                 
 

The Component

1.)a)Consider a two-component parallel-redundant system with distinct failure rates λ1 and λ2 respectively. Upon failure of a component, a repair process is invoked with their respective repair rates μ1 and μ2.

• Find the probability of proper operation of the system assuming that a failure of a component while another is being repaired causes a system failure.
• Compute the steady-state availability assuming that the failure of a component while another is being repaired is not catastrophic.

b)For the stochastic program flow graph (shown below), compute the average number of times each vertex si is visited, and assuming that the execution time of si is given by ti = 2i+1 time units, find the average total execution time τ of the program.

c) A two-component active redundant system can be repaired only after both units have failed. Only one unit can then be repaired at a time. The units have constant failure rates λ1 and λ2, respectively. If the system repair rate, r, is assumed to be constant, what is the steady-state availability?

2.) A radar unit consists of two primary components: a power supply and a transceiver. The power supply has a constant failure rate of 0.0031 failures per operating hour and takes an average of 5 hrs. (mean) to repair (constant repair rate). The transceiver fails an average (mean) of every 100 operating hours (constant failure rate) and takes 3 hrs. to repair (constant repair rate). What is the point availability of the radar unit after 10 hrs. of use? How much does this differ from the steady-state availability? If two radar units are operating in parallel (high-level active redundancy), what are the point, interval (after 10 hrs.), and steady-state availability?

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