Tham khảo tài liệu 'designing capable and reliable products episode 1 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Statistical methods for probabilistic design 145 of the 3-parameter Weibull distribution. The procedure for the 3-parameter Weibull distribution is more complex as you would expect due to the distribution being modelled by three rather than two parameters. Essentially it requires the determination of the expected minimum value xo a location parameter on the x-axis. As shown in Appendix X the linear rectification equations are a function of ln x XÓ where xo xmin the minimum variable value on the data. We don t know the value of xo initially but by searching for a value of xo such that when ln x XÓ is plotted against lnln l l Fị the correlation coefficient is its highest value will give a reasonably accurate answer. The process can be easily translated to computer code to speed up the process. Determining the parameters for the common distributions can also be done by hand using suitably scaled probability plotting paper a straight line through the data points being determined by eye as described earlier. See Lewis 1996 for examples of probability plotting graph paper for some of the statistical distributions mentioned. Further improvement in the selection of the best linear rectification model can be performed by comparing the uncertainty in model fit as determined from the standard error of the data Nelson 1982 . Also the use of confidence limits in determining the uncertainty in the estimates from linear regression is useful for assessing the nature of the data particularly when small samples are taken and or when outlying data points control the gradient of the regression line. Confidence limits are generally wider than some inexperienced data analysts expect so they help avoid thinking that estimates are closer to the true value than they really are. A discussion of their application in data analysis can be found in Ayyub and McCuen 1997 Comer and Kjerengtroen 1996 Nelson 1982 and Rice 1997 . Example - fitting a Normal distribution to a set of existing data We .
