Computer Methods for Estimating Weibull Parameters in Reliability Studies

In an earlier paper³ which appeared in this Transactions, the author showed in the appendixes two methods of estimating the shape and scale parameters of a Weibull distribution from a set of life testing data. They are: (I) the method of least squares for the transformed data, and (II) the method of maximum likelihood for ungrouped data. It was pointed out that since the method of least squares was the simpler of the two, it could be used as a first approximation for getting the maximam likelihood estimate which involves solving, by trial and error, two simultaneous transcendental equations. As a measure of simplifying the computation of the analysis, the author suggested fixing the shape parameters at m = 1.7, when studying the reliability of electron tubes. This value of m = 1.7 was an average value based upon the life experience data, then available to the author, of some 2,000 electron tubes. With the wide popularity and availability of electronic computer, the above simplifications are no longer necessary, though still desirable for reasons explained in the text. This paper describes two additional methods for which the computers are almost indispensable. They are: (III) the method of maximum likelihood for grouped data, and (IV) the method of minimized chi-squares. For the sake of discussion, the two previous methods (I and II) are briefly reviewed.