Boolean Sum can be converted into arithmetic sumwhen we obtain a non-overlapping expression
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Non-overlapping expression using K-map
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F & M METHOD
L. Fratta & V. Montanari
Discuss boolean algebra approach for determining terminal reliability
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Algorithm
• Determine all paths
• Write down the corresponding boolean expression
• Determine non-overlapping simplification
• Transform into mathematical expression
• Substitute reliability values
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Algorithm
Step 1: Let S be the set of all simple paths between the terminal nodes. Construct a Boolean sum of products f, where each product corresponds to a path S and whose factors are exactly the noncomplemented variables corresponding to the arcs in the path
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Algorithm
Let P = 0
Step 2: If f has no terms, stop
Step 3: Select any term A of f
Step 4: Let A’ be the arithmetic monomial which is equivalent to A
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Algorithm
Let P = P + A’
Step 5: Let A’.f --> f and reduce f to a sum of products. Go to step 2.