Equations such as CIE94 and CMC are now in common use to set instrumental tolerances for industrial color control. A visual experiment was performed to generate a data set to be used in evaluating typical industrial practices. Twenty-two observers performed a pass-fail color tolerance experiment for a single high-chroma yellow color. Thirty-two glossy samples varying in all three CIE-LAB dimensions were compared with a single standard. A near-neutral anchor pair was used to define the quality of match criterion. The pooled pass data were used to fit a 95% confidence ellipsoid. The chromaticness dimension was well estimated by either CMC or CIE94. The lightness dimension was poorly estimated by either equation. Evaluating the sampling distribution of the 32 test samples via a covariance matrix revealed a poor sampling, particularly in the Delta L*Delta b* plane. This sampling may have biased the visual experiment. The visual data were used to optimize various color-difference equations based on CIE94 and CMC, where the l:c and total color difference were adjustable parameters. Several methods of optimization are described including minimizing the number of instrumental wrong decisions and logistic multiple-linear regression. Some methods require only pass response data, while other require both pass and fail data. Because industrial tolerances are usually based on a single observer, ellipsoids were fitted for three observers to demonstrate the large variability between observers in judging color differences. It was concluded that when tolerances need to be set based on a single observer＇s visual responses of samples not well distributed about the standard, typical industrial occurences, one should only adjust the tolerance magnitude based on a statistically valid equation such as CIE94. One should not change l:c or derive a new ellipsoid.