Statistical material selection

Haugen, E. B. 1982a Modern Statistical Materials Selection - Part 1 Some Basic Concepts. Materials Engineering, 96, July, 21-25. 

Virtually all-classical design equations assume single-valued, real numbers. Such numbers can be multiplied, divided, or otlierwise subjected to real-number operations to yield a single-valued, real number solution. However, statistical materials selection, because it deals witli the statistical nature of property values, relies on tlie algebra of random variables. Property values described by random variables will have a mean value, representing the most typical value, and a standard deviation tliat represents the distribution of values around the mean value. 

Rice, R. C. 1997 Statistical Aspects of Design. In ASM International, ASM Handbook No. 20 - Materials Selection and Design, 10th Edition. OH ASM International. 

The brewer and his customer make a subjective assessment of beer flavour each time they taste but for a more objective appraisal it is usually desirable to submit the beer, with suitable controls, to a taste panel. Taste panels may be used to (/) select qualified judges, (//) correlate sensory with chemical and physical measurements, (Hi) study processing effects, maintain quality, evaluate raw material selection, establish storage stability, and reduce costs, (fv) evaluate quality, and (v) determine consumer reaction [Ij. The types of test used include (/) difference tests, (ii) rank order, (Hi) scoring tests, (iv) descriptive tests, (v) hedonic scaling, and (v/) acceptance and preference tests [1]. Difference tests are most commonly used in the brewing industry, the results of which are readily analysed by statistics. Several forms of difference test are used. The A-not-A form of test is perhaps the simplest. Assessors are first familiarized with a standard A and then presented, in a random manner, either with A again or with the comparative sample B. In the paired-comparison test two samples are presented simultaneously (AA, AB, BA, or BB) and assessors report either there is a difference or there is no difference . 

If, on the other hand, the encounter pair were an oriented structure, positional selectivity could be retained for a different reason and in a different quantitative sense. Thus, a monosubstituted benzene derivative in which the substituent was sufficiently powerfully activating would react with the electrophile to give three different encounter pairs two of these would more readily proceed to the substitution products than to the starting materials, whilst the third might more readily break up than go to products. In the limit the first two would be giving substitution at the encounter rate and, in the absence of steric effects, products in the statistical ratio whilst the third would not. If we consider particular cases, there is nothing in the rather inadequate data available to discourage the view that, for example, in the cases of toluene or phenol, which in sulphuric acid are nitrated at or near the encounter rate, the... 

Selection of appropriate time intei vals for increment extractions relates to property variation (inhomogeneity) within material flow streams. Ten minute extraction intei vals are generally adequate to obtain suitably representative samples from material flows under practical circumstances. Precise determination of extraction intei vals consistent with individual apphcations can be calculatedthrough autocorrelation of historical sampling data, a statistical method described in references (Gy, Pitard). 

Ibis chapter will discuss various reliability issues. The discussion will kept at a philosophical level rather than getting into a statistical analy The statistical analysis is best left to others equipped with the training, toi and the data. Hopefully, this material will give the reader some comn sense insight into the various considerations involved in the selection applicadon of reliable compressors, their drivers, and auxiliary systems. 

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