The normal (Gaussian) distribution is the most widely known distribution, and is given by
| (9.1) |  |
f( T) ? 0, - ? < T < ?, - ? < T < ?, ? T > 0,
where
| T | = | mean of the normal times to failure, hr, |
and
| ? T | = | standard deviation of the times to failure, hr. |
It is a two-parameter distribution with parameters T and ? T, which are the mean and the standard deviation of the times to failure, respectively. Figure 9.1 shows the normal distribution, with the effects on it of a change in the mean and in the standard deviation. Specific characteristics of the normal pdf are the following:
The mean life, or the MTBF, T, is also the location parameter of the normal pdf, because it locates the pdf along the abscissa. It can assume the values of - ? < T < ?. The larger the T the larger is the mean life of the components, or of the equipment, or of the systems. The better the design, or the longer the designed-in life, the greater would be the value of T. The normal pdf is bell shaped and symmetrical about its mean.
The standard deviation, ? T, is also the scale parameter of the normal pdf. As ? T decreases, the pdf
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