On median control charting under double sampling scheme

Abstract

Standard Shewhart control charts are often based on the assumption that the observations follow a specific parametric distribution, such as the normal, and outlier-free samples are initially selected to construct control limits for future monitoring of process parameters, e.g., location, dispersion, etc. The median is a popular measure of location which is more robust than mean for heavily skewed distributions. In ideal circumstances (where all the underlying assumptions such as normality and independence are met), the median chart is shown to be less efficient that the mean chart. To overcome the efficiency loss of the median chart, this study presents a set of auxiliary information-based median type Shewhart charts based on parent normal, t and gamma distributed process environments under double sampling scheme. The performance of these charts is evaluated in terms of run length (RL) characteristics such as: average run length (ARL), median run length (MDRL), standard deviation of the run length distribution (SDRL), extra quadratic loss (EQL) and relative ARL (RARL). Moreover, the effects of Step 1 sample size and contaminated environments are examined on the ARL performance of different median-based charting structures, under double sampling scheme. Illustrative examples are also provided to explain the working of the said charts.