A generalized Conforming Run Length control chart for monitoring the mean of a variable

The attribute Conforming Run Length (CRL) control chart has attracted increasing research interests in Statistical Process Control (SPC). It decides the process status based on the interval or distance between two nonconforming units. This article proposes a Generalized CRL chart (namely GCRL chart) for monitoring the mean of a measurable quality characteristic x under 100% inspection. To run a GCRL chart, each unit will be classified as a passing or nonpassing unit depending on whether the sample value of x falls within or beyond a pair of lower and upper inspection limits LIL and UIL. When a nonpassing unit is detected, the GCRL chart checks the distance between the current and last nonpassing units in order to determine the process status (in control or out of control). The inspection limits LIL and UIL are determined by an optimization design. The GCRL chart not only solves a dead-corner problem suffered by the conventional CRL chart, but also considerably outperforms the latter for detecting mean shifts. The most interesting finding is that the attribute GCRL chart excels the variable X chart to a significant degree in SPC for variables. It suggests that the simple attribute chart may replace the variable chart in some SPC applications. The design of the GCRL chart has to be carried out by a computer program, but the design can be completed almost in no time in a personal computer.