4.6 Reliability of a manufacturing network. A team of indus trial management uni

Question

4.6 Reliability of a manufacturing network. A team of indus trial management university professors investigated the re liability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems Engineering, March 2013). An example of such a network is a system for producing integrated circuit IC) cards with two production lines set up in sequence. Items (IC cards) first pass through Line 1, then are processed by Line 2. The probability distribution of the maximum capacity level Y of each line is shown in the next table. Assume the lines operate independently.

Explanation / Answer

a) as individual probability falls between 0 and 1 as well sum of probability for each of line is equal to 1; therefore condition is satisfied.

b) for line 1) P(X>30) =P(X=36)=0.95

c)for line 2)P(X>30) =P(X=35)+P(X=70)=0.002+0.996=0.998

d) for probability that a maximum capacity level of 30 item is maintained through out the network

=P(first line has capacity exceeding 30 and second line has capacity exceeding 30 )

=0.95*0.998=0.9481

please revert

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