Normal (or Gaussian)
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The two parameters required for the normal distribution are the mean and standard deviation. Normal distributions, which are always symmetric and commonly called bell curves, are important and widely used in the field of statistics and probability. Normal distributions are frequently used to describe equipment that has increasing failure rates with time. The normal distribution is recommended only if failure times can be expressed as a summation of some other random variables. Although the normal distribution is a handy tool for describing all sorts of different data, it allows observations to be negative. Because parts cannot fail before time t = 0, life data is always positive. As a result, the normal distribution does not usually describe life data very well. Most analysts do not even bother to check for a normal fit because life data that follow the normal distribution also generate good Weibull probability plots.
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Lognormal
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The two parameters required for the lognormal distribution are the mean and standard deviation. Although the lognormal distribution is similar to the normal distribution, it assumes that the logarithm of the values of random variables is normally distributed rather than the values themselves. Thus, all values are positive, and the distribution is skewed to the left. The lognormal distribution is probably the most significant competitor to the Weibull distribution. It is frequently used in engineering for metal-fatigue testing, maintainability data (time to repair), chemical-process equipment failures and repairs, some material characteristics and non-linear, accelerating deterioration. When the time to failure results from the multiplication of effects, the lognormal distribution is recommended. For example, in the case of progressive deterioration, a crack forms due to stress, and the stress increases as the crack grows. Non-engineering applications of the lognormal distribution include the analysis of personal incomes, inheritances and bank deposits.
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