Phase I control chart based on a kernel estimator of the quantile function

To measure the statistical performance of a control chart in Phase I applications, the in-control average run length (ARL) is the most frequently used parameter. In typical start up situations, control limits must be computed without knowledge of the underlying distribution of the quality characteristic. Assumptions of an underlying normal distribution can increase the probability of false alarms when the underlying distribution is non-normal, which can lead to unnecessary process adjustments. In this paper, a control chart based on a kernel estimator of the quantile function is proposed. Monte Carlo simulation was used to evaluate the in-control ARL performance of this chart relative to that of the Shewhart individuals control chart. The results indicate that the proposed chart is more robust to deviations in the assumed underlying distribution (with respect to the in-control ARL) and results in an alternative method of designing control charts for individual units.