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Unformatted text preview: 36 Lectures on Stat-613 (Reliability) Dr. Hanan M. Aly Lecture 4 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 The pdf of the normal distribution is given by: 2 1 ( ) 2 1 ( ) 2 t t t f t e f(t) 0, - < t < , - < t < , T > 0 where: It is a two-parameter distribution with parameters (or t ) and T , i.e . the mean and the standard deviation, respectively. 37 Normal Statistical Properties The Normal Mean, Median and Mode The normal mean or MTTF is actually one of the parameters of the distribution, usually denoted as . Since the normal distribution is symmetrical, the median and the mode are always equal to the mean, = = . The Normal Standard Deviation As with the mean, the standard deviation for the normal distribution is actually one of the parameters, usually denoted as T. The Normal Reliability Function The reliability for a mission of time T for the normal distribution is determined by: 2 1 ( ) 2 1 ( ) ( ) 2 t t t t t R t f t dt e dt 1 ( ) t...
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- Spring '11
- Normal Distribution, Dr. Hanan M. Aly Lecture