In the figure it gives the component reliability and relationships for a particu

Question

In the figure it gives the component reliability and relationships for a particular system, with the specific probabilities given in the following table.

what is the overall system reliability?

show work

Pa = 0.91
Pb = 0.85
Pc = 0.92
Pd = 0.93
Pe = 0.87
Pf = 0.97
Pg = 0.99
Ph = 0.72
Pi = 0.87

reliability distribution fro this data (report results using the text definition for beta). 6. The figure below gives the component reliability and relationships for a particular system, with the specific probabilities given in the following table. What is the overall system reliability? Pa 0.91 Pb 0.85 Pc 0.92 Pd 0.93 Pe 0.87 Pf 0.97 Pg 0.99 Ph 0,72 0.87 7- You to determine if a given process s in control for the mean value of a characteristic. You sample s items, random ly, each hour for 24 hours and the results given in the Problem workshoet of the Test 4 Data fila a. Using the appropriate process control chart, determine if rhis prmniil

Explanation / Answer

Reliability of Pc and Pb(parallel)

Pbc = 1 - (1-Pb)(1-Pb) = 1 - (0.08)(0.15) = 0.988

Reliability of Pd and Pe (series)

Pde= 0.93*0.87 = 0.8091

Reliability of Pbc and Pde (parallel)

Pbcde = 1 - (0.012)(0.1909) = 0.9977092

Reliability of Pg and Ph (parallel)

Pgh = 1 - (0.01)(0.28) = 0.9972

Reliability of the whole system =

reliability of Pa and Pbcde and Pf and Pgh and Pi (series) =

                  = 0.91 * 0.9977092 * 0.97 * 0.9972 * 0.87 = 0.7640444510399938

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