Abstract
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 to develop 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.
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