The theoretical underpinnings of standard least‐squares (LS) regression analysis are based on the assumption that the independent variable (often thought of as x ) is measured without error as a design variable. The dependent variable (often labeled y ) is modeled as having uncertainty or error. Both independent and dependent measurements may have multiple sources of error. Thus, the underlying least‐squares regression assumptions can be violated. Reduced major axis (RMA) regression is specifically formulated to handle errors in both the x and y variables. It is an alternative to least squares and demonstrates the importance of understanding the assumptions underlying statistical procedures.

Maximum likelihood estimation of the two-parameter Weibull distribution is straightforward; however, there are multiple methods for maximum likelihood estimation of the threeparameter Weibull. The third parameter for the three-parameter Weibull distribution shifts the origin from 0 to some generally positive value sometimes called the location, threshold, or minimum life. This article initially evaluates twelve statistical packages for four real-world datasets including oil spill data from the Gulf of Mexico. The different methods used by the packages result in fairly major differences in the estimated parameters between the statistical packages. Some statistical packages do not offer three-parameter Weibull estimation. Other software attempts the estimation in only certain cases. This may have major implications for those needing to estimate or apply the results of a three-parameter Weibull distribution that is used frequently in practice. A subset of the twelve packages is subsequently analyzed in detail based on an experimental design using pseudo-random Weibull datasets. This article also discusses the most common estimation method employed, which is maximizing a profile log-likelihood function.

No abstract

Cortest Columbus is investigating the long-term performance of container materials used for high-level waste packages as part of the information needed by the Nuclear Regulatory Commission to assess the Department of Energy's application to construct a geologic repository for high-level radioactive waste. In one task of the program, a cyclic potentiodynamic polarization (CPP) technique was used to evaluate the corrosion behavior of the candidate container materials. In order to evaluate the expected range of environmental variables, a statistical experimental design approach was used. A Resolution IV experimental design for 15 variables was selected. The variables included temperature, pH, species present in the groundwater, and those generated by radiolysis. Complete matrices of CPP tests, which consist of tests in 33 environments, were performed on two candidate container materials; Type 304L Stainless Steel and Incoloy Alloy 825. In these tests, both alloys exhibited a wide range of behavior; including passive behavior, pitting and active corrosion. For each alloy, the environmental variables that affected corrosion behavior were identified.