A Cramér-von Mises test-based distribution-free control chart for joint monitoring of location and scale

- A new distribution-free control chart is proposed.
- It integrates the Cramér-von Mises test and exponentially weighted moving verage.
- It can be used to monitor the location and the scale simultaneously.
- Its control limits and effect of the number of reference samples are provided.
- Its application is illustrated by a real data example.

This paper proposes a new distribution-free control chart by integrating the powerful nonparametric two-sample Cramér-von Mises test and the exponentially weighted moving average control scheme to on-line monitoring. The proposed control chart can be used to monitor the location and the scale parameters of a univariate continuous distribution, simultaneously. The control limits based on Monte-Carlo simulation are provided in a table. The sensitivity analysis of effect of the number of reference samples on the control chart is studied in detail. Comparison results based on Monte-Carlo simulation show that the proposed chart is quite robust to non-normally distributed data, and moreover, it shows satisfactory performance in detecting various process shifts in terms of the average run length and standard deviation of run length. The application of our proposed chart is illustrated by a real data example for automobile engine piston rings.