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16-March-2006
Some Applications of Series Parallel Circuits for Increasing Reliability in Markets and Machines, by Victor Niederhoffer

A breakdown in machines or trades can cause terrible consequences in factories or trades, thus, one of the rules that it is best to follow is to always have multiple paths to extricate oneself from disaster, or more generally to prevent breakdown. I often refer to one of my favorite proverbs in this connection, 'the mouse with one hole is quickly taken', and this one I often follow, never putting on a trade unless there are at least two or three ways I can get out of it with a profit. If there's just one, the mistress will preclude it from occurring and guarantee me a loss.

One analogy as to how to do this comes from electric circuit theory, where parallel wires are often used to provide alternate paths for the input to reach the output, and series paths are used to provide a high chance of a breakdown, as in Christmas tree lights, which are always strung in series. This concept has been employed in reliability theory where parallel paths are often used to increase the chance of exiting a trade, and combinations of series parallel paths with bridges between them are used to maximize the chances of getting from input to output, while using a minimum number of components. An excellent discussion of these series paralled and bridge circuits with particular reference to the exponential, (constant hazard rate), distribution and the Weibull distribution is contained in another book I am reading to increase my knowledge of probability applications, Elementary Applications of Probability Theory by H.C. Tuckwell. The discussion of how to compute the reliability of combined circuits draws on elementary truth table calculations that we are all familiar with from our college logic courses, and it's quite instructive in how to design circuits that give the greatest reliability, or its converse, the least chance of failure.

I asked Doc Castaldo to prepare a brief introduction into reliability theory for the readers, and it appears below.

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