(Solved) Problem A circuit-board is assembled using four identical components (numbered 1 through 4) 12 their youth phase (3:. constant failure rate) with

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Problem A circuit-board is assembled using four identical components (numbered 1 through 4) 12
their youth phase (3:. constant failure rate) with MTTF , y _ in“, .( f-‘w determined above.) The overall life of the board is reflected by the reliability diagram given below,
(Note: components 1 and 2 occur at two places). 999‘s» 3'“? Write down its structure function W35) egplicitly in terms of the states xi.
Determine all of its path sets. Identify the minimal path sets. GE: there will be 3) Redraw the diagram as a parallel structure of the minimum path series structures, and generate its structure function.
Determine the reliability function Rf!) for each minimal path set.
Using (e) above, determine the R(r) of the circuit-board, and determine its reliability at 30 seconds.
If the MW of each component in the highest reliable path set is increased by 25%, what would be the board’s reliability at 30 seconds?l (this increase is ONLY
for this question)
Determine all of its (the board’s) cut sets. Identify the minimal cut sets.
Redraw the diagram as a series structure of the minimum cut parallel structures, and generate its structure filnction. WCafl the path sets of (c) above ‘units’ a, b, and c. 1.
2. Using the numerical value for )1, determine the MW of each unit.
Ignore the unit with the least reliability (a judgment call may be involved here).
You now have an active parallel system with two units. Assume that both these
units can be repaired as and when they occur with a constant repair rate of
1* =1.5;" y -
i. Draw the state transition diagram for this system.
ii. Determine the transition matrix M in P = W.
iii. Determine numerically the steady-state probability state vector 350°)-
iv. Determine the steady-state probability of the system’s operation.


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Mar 27, 2022





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