Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes

Abstract

The nonparametric (distribution-free) control charts are robust alternatives to the conventional parametric control charts when the form of underlying process distribution is unknown or complicated. In this paper, we consider two new nonparametric control charts based on the Hogg–Fisher–Randle (HFR) statistic and the Savage rank statistic. These are popular statistics for testing location shifts, especially in right-skewed densities. Nevertheless, the control charts based on these statistics are not studied in quality control literature. In the current context, we study phase-II Shewhart-type charts based on the HFR and Savage statistics. We compare these charts with the Wilcoxon rank-sum chart in terms of false alarm rate, out-of-control average run-length and other run length properties. Implementation procedures and some illustrations of these charts are also provided. Numerical results based on Monte Carlo analysis show that the new charts are superior to the Wilcoxon rank-sum chart for a class of non-normal distributions in detecting location shift. New charts also provide better control over false alarm when reference sample size is small.

Keywords:

• average run length
• control chart
• false alarm rate
• HFR statistic
• Savage statistic
• Wilcoxon rank-sum

Additional information

Funding

This work was primarily supported by the XLRI – Xavier School of Management. An early version of the work was supported by IIM Udaipur, under the project # SP-01.