Comparing the Maximum Likelihood Method and a Modified Moment Method to fit a Weibull distribution to aircraft engine failure time data.
Woods, W. Max
Larson, Harold J.
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This thesis provides a comparison of the accuracies of two methods for fitting a Weibull distribution to a set of aircraft engines time between failure data. One method used is the Maximum Likelihood Method and assumes that these engine failure times are independent. The other method is a Modified Method of Moments procedure and uses the fact that if time to failure T has a Weibull distribution with scale parameter lambda and shape parameter beta, then T(beta) has an exponential distribution with scale parameter lambda(beta). The latter method makes no assumption about independent failure times. A comparison is made from times that are randomly generated with a program. The program generates times in a manner that resembles the way in which engine failures occur in the real world for an engine with three subsystems. These generated operating times between failures for the same engine are not statistically independent. This comparison was extended to real data. Although the two methods gave good fits, the Maximum Likelihood Method produced a better fit than the Modified Method of Moments. Explanations for this fact are analyzed and presented in the conclusions
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