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{{template:LDABOOK|9|The Normal (Gaussian) Distribution}}
#REDIRECT [[The_Normal_Distribution]]
 
 
The normal distribution, also known as the Gaussian distribution, is the most widely-used general purpose distribution. It is for this reason that it is included among the lifetime distributions commonly used for reliability and life data analysis. There are some who argue that the normal distribution is inappropriate for modeling lifetime data because the left-hand limit of the distribution extends to negative infinity. This could conceivably result in modeling negative times-to-failure. However, provided that the distribution in question has a relatively high mean and a relatively small standard deviation, the issue of negative failure times should not present itself as a problem. Nevertheless, the normal distribution has been shown to be useful for modeling the lifetimes of consumable items, such as printer toner cartridges. 
 
{{normal probability density function}}
 
{{normal statistical properties}}
 
{{characteristics of the normal distribution}}
 
{{normal distribution estimation of the parameters}}
 
{{normal distribution confidence bounds}}
 
{{nd bayesian confidence bounds}}
 
==General Examples==
 
'''Example 8:'''
{{Example: Normal General Example (RRX Plot)}}
 
 
'''Example 9:'''
{{Example: Normal General Example (RRX QCP)}}
 
 
'''Example 10:'''
{{Example: Normal General Example (RRX Report)}}
 
 
'''Example 11:'''
{{Example: Normal General Example Interval Data}}
 
 
 
'''Example 12:'''
{{Example: Normal General Example Complete Data}}
 
 
'''Example 13:'''
{{Example: Normal General Example Suspension Data}}
 
===  Example 14===
Suppose our data set includes left and right censored, interval censored and complete data as shown in the following table.
 
====  Solution to Example 14====
This data set can be entered into Weibull++ by selecting the data type Times to Failure, with Right Censored Data (Suspensions), with Interval and Left Censored Data and with Grouped Observations.
 
The computed parameters using maximum likelihood are:
 
::<math>\begin{align}
  & \widehat{\mu }= & 48.11 \\
& {{{\hat{\sigma }}}_{T}}= & 26.42. 
\end{align}</math>
 
 
For rank regression on x:
 
::<math>\begin{align}
  & \widehat{\mu }= & 49.99 \\
& {{{\hat{\sigma }}}_{T}}= & 30.17. 
\end{align}</math>
 
 
For rank regression on y:
 
::<math>\begin{align}
  & \widehat{\mu }= & 51.61 \\
& {{{\hat{\sigma }}}_{T}}= & 33.07. 
\end{align}</math>

Latest revision as of 08:44, 3 August 2012

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