You are an engineer responsible for maintaining the manufacturing system illustr

Question

You are an engineer responsible for maintaining the manufacturing system illustrated below, where p represents the percent of the time a specific machine is operational. According to theory, the entire manufacturing system should be operating approximately 77.5% of the time. From recent efficiency reports, it appears that this is not correct. You suspect that there is a significant amount of dependence between Machine 4 and Machine 5, with respect to whether they are operational. In order to test this hypothesis, you have collected data every hour over the course of the last month regarding whether Machine 4 and Machine 5 were operational. This data can be found in the file, "Q4.xlsx", where a 0 represents that the machine was not operating and a 1 represents that the machine was operating. Using this information, determine a new approximation for the percent of time the manufacturing system is operational.

Explanation / Answer

Given M1, M2 and M3 are parellel configuration.

Let these 3 components are replaced by the new component A

P(A) = 1 - [1-P(M1)][1-P(M2)][1-P(M3)]

= 1 - [1-0.85][1-0.9][1-0.95]

=1 - 0.00075 = 0.99925

Let Components M4 and M5 are in parellel configuration and replaced by the new component B

P(B) = 1 - [1-P(M4)][1-P(M5)]

= 1 - [1 - 0.7][1-0.9]

= 1 - 0.03 = 0.97

The component A , B and M6 are series configuration.

The reliability of entire system is

Rs(t) = P(A)P(B)P(M6) = 0.99925*0.97*0.8 = 0.775418

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