TABLE OF CONTENTS The normal (Gaussian) distribution is the most widely known distribution and is given by
| (7.1) |  |
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, i.e. the mean and the standard deviation, respectively. Figure 7.1 shows the normal distribution, with the effects on it of a change in the mean and in the standard deviation. Some of the specific characteristics of the normal pdf are the following:
One of the two parameters, the mean, or the mean life or the MTBF, T, is also the location parameter of the normal pdf as it locates the pdf along the abscissa. It can assume 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 second parameter is the standard deviation, ? T, which is also the scale parameter of the normal pdf. As ? T decreases,...
