THE DRAWBACKS OF EMPLOYING MAXIMUM LIKELIHOOD ESTIMATION IN WEIBULL ANALYSIS

 Introduction

 It is well known that the maximum likelihood method of parameter estimation can lead to extremely biased results in many problems. This is especially true for small samples --- for example, the classical sample estimate of variance of a Gaussian population is biased, and is corrected by changing the divisor in the mean sum of squares to N - 1 in place of the maximum likelihood divisor N.

This problem of bias in the maximum likelihood method is even more serious in the case of Weibull parameter estimation. The purpose of this issue ( Volume 4, Bulletin 4: August, 1974) of the Statistical Bulletin is to give quantitative empirical formulas for the amount of bias in the maximum likelihood method of Weibull analysis, by taking the more unelegant MEDIAN RANK LEAST SQUARES METHOD as the method which gives reasonable and practical answers. (See the Improved New Increment Technique and the Standard New  Increment Technique for Weibull Analysis to see the difference.)

 Specimen No. Running Time
 Status
 1   302 Hours
 Failed
 2   450 Hours
 Suspended
 3   740 Hours
 Failed
 4   800 Hours
 Suspended
 5   900 Hours
 Suspended
 6 1,005 Hours 
 Failed
 7 1,300 Hours
 Suspended
 8 1,410 Hours
 Failed
Note: N = 8 Observations

Table 1 - Data Obtained on Test Specimen

Improved New Increment Least Squares Regression Method

Standard New Increment  Least Squares Regression Method

Maximum Likelihood Method