Engineering statistics confidence intervals

Clearly, this procedure could be repeated for any test statistic previously discussed in this section. The reader is referred to any of a number of engineering statistics texts for developments of F, and t confidence intervals. 

The distinction between confidence intervals and toleranee intervals is (hat civnlidenee interv als refer to estimates of the population statistics (usually the mean) while tolerance intervals are concerned with proportions or fractiles of the population. Thus the term tolerance as used here should be distinguished from the frequently used tolerance in engineering design for dimensions and tUher factors in the construction or manufacture of some object or structure. 

Within the framework of system analysis as an instrument of systems engineering, empirical results are of value only as far as they permit prognoses on the expected behavior of systems for the future. The data on which a system analysis is based constitutes a sort of spot check from the basic totality of the data of all comparable actual or imaginable systems and is thus prone to random variations. I hus mathematical statistics play an eminent role in the evaluation of these data. It permits statements on confidence intervals for derived characteristics and of significance limits for dependencies. Both represent a measure of the degree of uncertainty of the interpretations derived from these data, and knowledge of them is indispensable if wrong conclusions are to be avoided. 

Bayesian Statistics Applications to Earthquake Engineering, Fig. 6 Ninety-five percent confidence interval (Cl) for the spectral density gj(v ), j = 1,2, 3... 

Bayesian Statistics Applications to Earthquake Engineering, Fig. 10 Fragility curves (mean) PfiPSa) and 9S confidence intervals (CIs) for (a) n = 10 and (b) n = 50 records... 

Theoretically, any measurement will produce a set of statistical data and should be so reported if feasible. Let us consider a case study whereby an OEM shaft will be duplicated by reverse engineering. The length of the shaft is measured, and the report shows that the measured data have a nominal distribution with a mean of 250 mm, and a standard deviation of 0.5 mm. The following exemplifies a typical statement reporting this measurement in statistical terms based on the calculations detailed in Equation 6.8a and b. "With a confidence level of 95%, the mean shaft length lies within the confidence intervals between 250.98 and 249.02 mm."... 

The most important statistical subjects relevant to reverse engineering are statistical average and statistical reliability. Most statistical averages of material properties such as tensile strength or hardness can be calculated based on their respective normal distributions. However, the Weibull analysis is the most suitable statistical theory for reliability analyses such as fatigue lifing calculation and part life prediction. This chapter will introduce the basic concepts of statistics based on normal distribution, such as probability, confidence level, and interval. It will also discuss the Weibull analysis and reliability prediction. 

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