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: \( x_{{50}} = \sum\nolimits_{{i = 1}}^{N} {x_{i} /N,} \) when N is the sample size.
- 2.
Standard deviation can be estimated: \( \sigma = \left[ {\sum\nolimits_{{i = 1}}^{N} {(x_{i} - x_{{50}} )^{2} /(N - 1)} } \right]^{{1/2}} \).
- 3.
A more precise value is 15.87Â %.
- 4.
One gm-f equals 9.8 × 10−3 N.
- 5.
A cumulative probability of exactly FÂ =Â 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. (4) is generally used.
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McPherson, J.W. (2013). Gaussian Statistics: An Overview. In: Reliability Physics and Engineering. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00122-7_5
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DOI: https://doi.org/10.1007/978-3-319-00122-7_5
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