Statistical Confidence Level and Interval

For a normal distribution, the probability that a measurement falls in the interval of n standard deviation, no, of the mean, x, can be calculated by Equation 6.6. This equation quantitatively calculates the confidence level (the probability) of finding the measurement within a defined confidence interval, from p - no to p + no. 

Conversely, for a given confidence level, the confidence interval can be calculated by Equation 6.7  

Confidence Level Corresponding to Specific Confidence Interval of a Normal Distribution  

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 statistics of test results and measured data might be critical to part reliability analysis in machine design and reverse engineering. In some cases the method of probabilistic fracture mechanics along with the statistical data is preferred over deterministic fracture mechanics in failure prevention analysis. However, a simple average value, that is, 250 mm for the shaft length in the above example, is usually sufficient in most calculations 

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