Reliability of the Estimates of the Weibull Parameters



Hideo Hirose


電気学会論文誌A, Vol.110-A, No.12, pp.903-912 (平成2.12)

Trans. IEE of Japan, Vol.110-A, No.12, pp.903-912 (1990.12)

Not only in the field of Electrical Engineering, but in the fields of Mechanical Engineering, Metal Engineering, Pharmacology and Medical Science, the Weibull distribution is widely used in discuss ing the probability distribution of breakdown, failure and lifetime. Therefore, it is very important to estimate the Weibull parameters and percentile points from the actual data. It has been often used the Weibull probability chart to estimate the parameters of the Weibull distribution. That is, the graphical method is taken. This method has a good advantage that we can estimate the parameters easily. On the contrary, there are some disadvantages such as the inaccuracy in estimation and having no confidence. Thus, we have to estimate the parameters with accuracy by the analytical methods such as maximum likelihood estimation method, and then to calculate the reliability of the estimates.
Here, I mainly describe the calculated results of reliability of the estimates of the parameters and percentile points when all the three parameters are unknown, along with the explanation of the theoretical background. In addition, I describe the confidence limit and confidence region with the method of asymptotic normal theory of maximum likelihood estimation comparing with the method of likelihood ratio test.

Key Words



Times Cited in Web of Science:

Cited in Books: