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MIL-HDBK-338 15 OCTOBER 1984 5.2.2 STATISTICAL DISTRIBUTIONS USED IN RELIABILITY MODELS There are many standard statistical distributions which may be used to model the various reliability parameters. It has been found that a relatively small number of statistical distributions satisfies most needs in reliability work. The particular distribution used depends upon the nature of the data, in each case. Following is a short summary of some of the distributions most commonly used in reliability analysis, criteria for their use, and examples of application. Figures 5.2.2-1 and 5.2.2-2 are summaries of the shape of common failure density, reliability, and hazard rate functions for the distributions described. Each distribution will be described in more detail, with reliability examples, in the following sections. 5.2.2.1 CONTINUOUS DISTRIBUTIONS 5.2.2.1.1 NORMAL (OR GAUSSIAN) DISTRIBUTION There are two principal applications of the normal distribution to 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. The other application deals with 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 f,t, = ^ exph (^)2] (5-22) where u = the population mean o = the population standard deviation, which is the square root of the variance. 5-7

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