Circular error probability

In the military science of ballistics, circular error probable (CEP) (also circular error probability or circle of equal probability) is a measure of a weapon system's precision. It is defined as the radius of a circle, centered on the mean, whose boundary is expected to include the landing points of 50% of the rounds. That is, if a given bomb design has a CEP of 100 metres (330 ft), when 100 are targeted at the same point, 50 will fall within a 100 m circle around their average impact point. (The distance between the target point and the average impact point is referred to as bias.)

The original concept of CEP was based on a circular bivariate normal distribution (CBN) with CEP as a parameter of the CBN just as μ and σ are parameters of the normal distribution. Munitions with this distribution behavior tend to cluster around the mean impact point, with most reasonably close, progressively fewer and fewer further away, and very few at long distance. That is, if CEP is n meters, 50% of rounds land within n meters of the mean impact, 43% between n and 2n, and 7% between 2n and 3n meters, and the proportion of rounds that land farther than three times the CEP from the mean is approximately 0.32%.

CEP is not a good measure of accuracy when this distribution behavior is not met. Precision-guided munitions generally have more "close misses" and so are not normally distributed. Munitions may also have larger standard deviation of range errors than the standard deviation of azimuth (deflection) errors, resulting in an elliptical confidence region. Munition samples may not be exactly on target, that is, the mean vector will not be (0,0). This is referred to as bias.

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