A mathematical technique for maximizing the reliability in a parallel flow system of electronic units is presented. The failure rate is used as the measure of reliability, and reliability is maximized when the failure rate is minimized. An expression for the system failure rate as a function of individual unit flow rates is derived. This expression, subject to the constraint that the sum of the individual unit flows must equal the system flow rate, forms the basis for this analysis. The method of Lagrange multipliers is applied to minimize the failure rate and determine the optimum distribution of flow within the system. Comparisons are made to failure rates for two other flow distributions. 1. Flow based on maximum allowable junction temperature. 2. Flow proportional to unit power dissipation.

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