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Statistics and Probability Knowledge There are two principal applications of the
normal distribution to engineering and reliability. One
application deals with the
analysis of items which exhibit failure due to wear, such as
mechanical devices. Frequently
the wear-out failure distribution is sufficiently close to
normal that the use of this distribution
for predicting or assessing reliability is valid.
Another
application is in the analysis of manufactured items and their
ability to meet specifications.
No two parts made to the same specification are exactly alike.
The variability of parts
leads to a variability in systems composed of those parts. The
design must take this part variability
into account, otherwise the system may not meet the
specification requirement due to the
combined effect of part variability. Another aspect of this
application is in quality control procedures. The basis for the use of normal
distribution in this application is the central limit theorem
which states that the sum of a large number of identically
distributed random variables, each with finite mean and
variance, is normally distributed.
Thus, the variations in value of electronic
component parts, for example, due to manufacturing are
considered normally distributed.
The failure
density function for the normal distribution is:
Where:
= The population mean
 =
Population standard deviation, which is the square root of the
variance.
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