Development of Univariate Control Charts for Non-Normal Data

Abstract

In this study, a new control chart methodology was developed to address statistical process monitoring issue associated with non-normally distributed process variables. The new method (NM) was compared aginst the classical Shewhart control chart (OM) using synthetic datasets from normal and non-normal distributions as well as over an industrial example. The NM involved taking the difference between the specified probability density estimate and non-parametric density estimate of the variable of interest to calculate an error value. Both OM and NM were found to work well for normally distributed data when process is in-control and out-of control situation. Both methods could be returned back to normal operation upon feeding in control data. In case of non-normally distributed data, the OM failed significantly to detect small shifts in mean and standard deviation, however the NM maintained its performance to detect such changes. In the application to an industrial case (data were obtained from a local cement manufacturer about a 90 micrometer sieve fraction of the final milled cement product), the NM methodology outperformed the OM by recognizing the change in the mean and variance of the measured parameter. The data were tested for its distribution and were found to be non-normally distributed. Violations beyond the control limits in the new developed technique were easily observed. The NM was found to successfully operate without the necessity to apply run rules.