What is the reliability that bank loans will be processed ac

What is the reliability that bank loans will be processed accurately if each of the five clerks shown in the chart has the reliability shown?

What is the reliability that bank loans will be processed accurately if each of the five clerks shown in the chart has the reliability shown?

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Solution

Answer to Question 17.9 :

Reliability of the subsystem when two clerks are connect in series ( in middle row ) = 0.95 x 0.95 = 0.9025

We now move to bigger subsystem in which following units are connected in PARALLEL;

-Unit with reliability 0.95

-Above subsystem with reliability 0.9025

- Unit with reliability 0.95

Reliability of this bigger subsystem

= 1 – ( 1 – 0.95) x ( 1 – 0.9025) x ( 1 – 0.95)

= 1 - ( 0.05 x 0.0975 x 0.05)

= 1 -0.000243

= 0.99975

We are now at the last stage when we have a simplified system consisting of following in SERIES:

Reliability of the above bigger subsystem 0.99975

Unit with reliability of 0.95

Thus, reliability that the bank loans will be processed = 0.99975 x 0.95 = 0.94976

RELIABILITY THAT THE BANK LOANS WILL BE PROCESSED ACCURATELY = 0.94976

RELIABILITY THAT THE BANK LOANS WILL BE PROCESSED ACCURATELY = 0.94976