The performance of the hypergeometric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mrow><mml:mi>n</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:math> chart with estimated parameter

Although it is well known that the performance of attribute control charts decreases significantly when assumption process parameters invalid, this prevalent in pertinent literature. However, most practical applications, have to be estimated from a finite in-control Phase I sample, and therefore should evaluated perspective parameters. In paper, we compare run length properties hypergeometric np chart both parameter cases. particular, investigate required number samples new specific allow with p approximately same as case. Moreover, perform comprehensive out-of-control comparison its binomial counterpart. order achieve these objectives, also present approach effectively compute probability distribution sum independent identically hypergeometric-distributed random variables. The proposed approximation reduces computational effort few seconds while keeping remarkable high accuracy only negligible deviations compared exact obtained via convolution.