Setting Up Acceptability Tolerances - A Case-Study

AbstractCurrent acceptance of goods for color by the United States Army depends on visual comparison against a standard and as many as eight limit samples. The Army wished to have a numerical method of setting color tolerances to be used with instrumental measurement. Preliminary work with the standards and limit samples indicated that acceptability ellipsoids oriented in the hue, chroma, and lightness directions in CIELAB color space should be set up. To establish the tolerances, we selected pairs of samples from a large number of previous submissions by industry. These pairs represented four graduated lightness steps, four graduated chroma steps, and four graduated hue steps. Six observers looked at each pair ten times, randomly interspersed with other pairs, and issued a pass‐or‐fail judgment each time. From these data we established lightness, chroma, and hue tolerance limits. For an olive green and a tan shade, these tolerances were roughly in the ratio 3:2:1; for a dark blue, the ratios were roughly 2:2:1. We wrote simple equations that can be used in order to determine quickly whether a sample passes or fails.