General control charts for variables

When the distribution of the monitoring statistic used in statistical process control is non-normal, traditional Shewhart charts may not be applicable. A common practice in such cases is to normalize the data, using the Box-Cox power transformation. In this paper, we develop an inverse normalizing transformation (INT), namely, a transformation that expresses the original process variable in terms of the standard normal variable. The new INT is used todevelop a general methodology for constructing process control schemes for either normal or nonnormal environments. Simplified versions of the new INT result in transformations with a reduced number of parameters, allowing fitting procedures that require only low-degree moments (second degree at most). The new procedures are incorporated in some suggested SPC schemes, which are numerically demonstrated.A simple approximation for the CDF of the standard normal distribution, with a maximum error (for z > 0) of +/-0.00002, is a by-product of the new transformations.