A Cautionary Tale: Small Sample Size Concerns for Grouped Lifetime Data

ABSTRACT

Often, lifetime data come from experiments where failure times are grouped. The Weibull distribution is a popular distribution for modeling failure times. Maximum likelihood estimation (MLE) has outstanding large sample properties for the Weibull distribution. This article evaluates small sample properties of MLEs for grouped data. We evaluate sample size requirements for MLE asymptotic properties to take effect. We compare type I and type II censoring for pooled experiments and conclude that bias for the shape parameter estimate can be alarmingly high especially for type II censored data. Finally, we investigate the benefits of the pooled analysis.

KEYWORDS:

• lifetime data
• maximum likelihood estimation
• pooled estimates
• type I censoring
• type II censoring
• Weibull distribution