A novel approach for estimating the ARL-BIAS severity of shewhart p-charts

Abstract

[EN] The Shewhart p-Chart is a widely used and taught control chart that monitors the process fraction of nonconforming, p. The control limits of this chart are computed from an equation derived from the central limit theorem that assumes the parameters p and sample size, n, provide a good approximation of the binomial to the normal distribution. It is known that if the approximation is poor the chart becomes ARL-biased with a consequent deterioration of its process improvement detection capability. Hence, if one is to use this chart its ARL-biased severity ought to be established in advance. Three parameters are used to estimate a chart's ARL-bias severity, namely the in-control ARL, the relative ARL-bias and the maximum out of control ARL. However, calculating these parameters is a task that requires of lengthy calculations that often entails the use of specialised software. In this paper we present a new approach that facilitates the estimation of the bias severity, this approach consists of a closed-form equation that eases the calculations of the ARL-bias parameters and of a graphical method that permits assessing a p-Chart's ARL-bias severity level according to the severity zone in which its n and p values fall into.