Parameter Estimation for the Weibull Distribution

The time to electric breakdown, and the electric field necessary to result in breakdown of solid insulation, seem to be best represented by a Weibull probability distribution. This tutorial paper reviews the graphical method of estimating the parameters of the Weibull distribution. It also presents the method of Maximum Likelihood as an objective technique, developed by statisticians for improving the estimates of the Weibull parameters, especially for censored experiments. Procedures for calculating confidence intervals are also given. It is shown in an example that the confidence intervals can be very wide for sample sizes commonly used in dielectric life tests.

[1]  Dielectric permittivity and breakdown characteristics of polymer-mica composites , 1976, 1976 IEEE International Conference on Electrical Insulation.

[2]  A. Cohen,et al.  Multi-Censored Sampling in the Three Parameter Weibull Distribution , 1975 .

[3]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[4]  Andrew C. Gorski.  Beware of the Weibull euphoria , 1968 .

[5]  R. Kaneko,et al.  Statistical considerations on impulse breakdown characteristics of cross-linked polyethylene insulated cables , 1975, IEEE Transactions on Power Apparatus and Systems.

[6]  Charles E. Antle,et al.  Statistical Inference From Censored Weihull Samples , 1972 .

[7]  W.J. McNutt,et al.  The combined effects of thermal aging and short-circuit stresses on transformer life , 1976, IEEE Transactions on Power Apparatus and Systems.

[8]  G. Cran,et al.  Graphical estimation methods for Weibull distributions , 1976 .

[9]  G. Bahder,et al.  Criteria for determining performance in service of crosslinked polyethylene insulated power cables , 1976, IEEE Transactions on Power Apparatus and Systems.

[10]  B. Epstein,et al.  The Theory of Extreme Values and Its Implications in the Study of the Dielectric Strength of Paper Capacitors , 1948 .

[11]  William Q. Meeker,et al.  Weibull Percentile Estimates and Confidence Limits from Singly Censored Data by Maximum Likelihood , 1976, IEEE Transactions on Reliability.

[12]  A. Cohen,et al.  Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples , 1965 .

[13]  E. Occhini,et al.  High voltage cables with extruded insulationߞStatistical controls and reliability evaluation , 1975, IEEE Transactions on Power Apparatus and Systems.

[14]  S. Boggs,et al.  Dielectric Permittivity, Conductivity, and Breakdown Characteristics of Polymer-MICA Composites , 1977, IEEE Transactions on Electrical Insulation.

[15]  Nancy R. Mann,et al.  Simplified Efficient Point and Interval Estimators for Weibull Parameters , 1975 .

[16]  Nancy R. Mann,et al.  Design of Over-Stress Life-Test Experiments When Failure Times Have the Two-Parameter Weibull Distribution , 1972 .