Abstract
The Gaussian distribution (normal or bell-shaped distribution) is a widely used statistical distribution and it is generally used as the foundation for statistical quality control. Simply measuring the time-zero values of a parameter (resistor values, mechanical tolerances, children heights, class grades on a test, etc.) can result in a distribution of values which can be described by a normal distribution.
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Notes
- 1.
Mean can be estimated: \(x_{50} = \sum\limits_{i = 1}^N {x_i } /N\), where N is the sample size.
- 2.
Standard deviation can be estimated: \(\sigma = \left[ {\sum\limits_{i = 1}^N {(x_i - x_{50} )^2 } /(N - 1)} \right]^{1/2} .\)
- 3.
A more precise value is 15.87%.
- 4.
One gm-f equals 9.8×10−3 Newton.
- 5.
A cumulative probability of exactly F=1 cannot be plotted. Therefore, in order to ensure that all 25 data points can be plotted, then an unbiased estimate of the cum F is needed. In reliability physics and engineering, Eq. (5.4) is generally used.
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Larsen, R.: Engineering with EXCEL, 2nd Ed., Pearson/Prentice Hall Publishing, (2005).
Miller, I. and J. Freund: Probability and Statistics for Engineers, Prentice Hall Publishing, (1977).
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McPherson, J. (2010). Gaussian Statistics — An Overview. In: Reliability Physics and Engineering. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6348-2_5
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