This is implemented in Excel via the formulaĪs described in Weibull Distribution, we call Goal Seek by selecting Data > What If Analysis|Goal Seek and then filling in the dialog box that appears in Figure 1. We can now use Excel’s Goal Seek capability to find β. We initially set the value of the β parameter in cell H4 to some guess, i.e. Cell E6 contains the formula on the left side of the equation that we derived above to find the β parameter, namely =GAMMALN(1+2/H4)-2*GAMMALN(1+1/H4)-LN(E3^2+E4^2)+2*LN(E3). In particular, cells E3 and E4 contain the formulas =AVERAGE(B4:B15) and STDEV.S(B4:B15). We implement these equations in Excel as shown in Figure 1. Using algebra, we can now eliminate α to obtain As we saw in Weibull Distribution, once we do this, we can estimate the scale and shape parameters based on the fact thatĮstimating μ by x̄ and σ by s, it then follows that We can estimate the mean μ and standard deviation σ of the population from the data in Figure 1. Find the scale and shape parameters that best fit the data.įigure 1 – Fitting a Weibull distribution We believe that the data fits a Weibull distribution. The time to failure is shown in range B4:B15 of Figure 1. Elsewhere, we show two other approaches using the maximum likelihood method and regression.Įxample 1: Twelve robots were operated until they failed. We illustrate the method of moments approach on this webpage. Given a collection of data that may fit the Weibull distribution, we would like to estimate the parameters which best fit the data.
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