There are 3 Signal-to-Noise ratios of common interest; (I) SMALLER-THE-BETTER : n = -10 Log10 [ mean of sum of squares of measured data ] This is usually chosen for all undesirable characteristics like ” defects ” etc for which the ideal value is zero. Also, when an ideal value is finite and its maximum or minimum value is defined (like maximum purity is 100% or maximum Tc is 92K or minimum time for making a telephone connection is 1 sec) then the difference between measured data and ideal value is expected to be as small as possible. The generic form of S/N ratio then becomes, n = -10 Log10 [ mean of sum of sqaures of {measured – ideal} ] (II) LARGER-THE-BETTER : n = -10 Log10 [mean of sum squares of reciprocal of measured data] This case has been converted to SMALLER-THE-BETTER by taking the reciprocals of measured data and then taking the S/N ratio as in the smaller-the-better case.(III) NOMINAL-THE-BEST : n = 10 Log10 (square of mean / variance )This case arises when a specified value is MOST desired, meaning that neither a smaller nor a larger value is desirable. Examples are; (i) most parts in mechanical fittings have dimensions which are nominal-the-best type. (ii) Ratios of chemicals or mixtures are nominally the best type. e.g. Aqua regia 1:3 of HNO3:HCL Ratio of Sulphur, KNO3 and Carbon in gun powder (iii) Uniformity in deposition /growth /plating /etching thickness.
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