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• Maximum likelihood method (MLE) (Cohen(1991))—Single DL • ROS Methods for normal, gamma, and lognormal distributions—Multiple DLs Note: ProUCL 4.0 can be used to generate columns consisting of detected data and extrapolated NDs obtained using a ROS method(normal, lognormal, and gamma). • Kaplan-Meier(KM)method(Kaplan-Meier(1958))—Multiple DLs • Winsorization method • DL/2 substitution(DL/2) method—not a recommended method. The DL12 method is included for historical reasons only. Note on the Use of DL/2 and Other Substitution Methods • The use of DL/2 (and DL)method is not recommended in statistical procedures that may be used in decision-making processes. Therefore, it is suggested to avoid the use of the DL/2 method(and other substitution methods such replacement of NDs by `0', `DL')to estimate the EPC terms and BTVs. • Also,the use of the substitution methods is not recommended in hypothesis testing approaches. • However,the substitution methods such as the DL/2 method may be used in graphical and exploratory methods to gain visual information about the data distributions and outliers. Several graphical methods (e.g., boxplots, Q-Q plots) based upon DL/2 method are available in ProUCL 4.0. ProUCL 4.0 can compute several parametric and nonparametric UCLs with a confidence coefficient (CC) specified in the interval [0.5, 1.0) including the commonly used CC level 0.95. However, since in most environmental applications (e.g., estimation of EPC), a 95% UCL of mean is used,therefore, ProUCL 4.0 makes recommendations for the most appropriate 95% UCL (s)that may be used to estimate the EPC terms based upon data sets with ND observations. The theory behind those recommendations can be found in Singh, Maichle, and Lee (EPA, 2006). Using the estimates of mean and standard deviation, or extrapolated NDs obtained using one of the ROS methods listed above, ProUCL 4.0 computes UCLs of the means using the following methods. • Tiku's UCL method(Tiku(1967 and 197 1))—Single DL • Ad hoc UCL methods using Student's t-statistic on ML estimates and KM estimates • Ad hoc UCL methods based upon Land's H-statistic—Single DL • Gamma UCL—Bootstrap UCL on gamma ROS • Nonparametric Chebyshev UCL based upon KM estimates • Bootstrap (percentile, standard bootstrap, bootstrap t, and bias-corrected accelerated (BCA)) methods on ROS methods and KM estimates.