Distribution-free double exponentially and homogeneously weighted moving average Lepage schemes with an application in monitoring exit rate

Two new distribution-free Lepage-type statistical process monitoring schemes are proposed. One is the double exponentially weighted moving average Lepage scheme, and the other is the homogeneously weighted moving average Lepage scheme. For the past ten years, the distribution-free schemes for jointly monitoring both the location and scale parameters of a process draw an abundance of attention from the researchers. The Lepage statistic is a famous single statistic employed in the distribution-free joint monitoring schemes. The Lepage-type schemes have been widely explored, modified, and improved by researchers recently. The in-control robustness of the distribution-free schemes renders flexibility in its implementation, and they are now playing a pivotal role in the new era of intelligent monitoring. Also, the double exponentially and homogeneously weighted moving average schemes are widely explored in recent years. One of the new charting plans combines the distribution-free approach for joint monitoring and the notion of the double exponentially weighted moving average. Another proposed scheme blends the concepts of distribution-free simultaneous monitoring with the homogeneously weighted moving average. Implementation designs based on both the time-varying and steady-state control limits are considered. A homogeneously weighted moving average Lepage scheme with the time-varying control limit is better than its counterpart with the steady-state control limit in reducing the rate of early false alarms. In general, the double exponentially weighted moving average scheme performs well in detecting small to moderate shifts in the process. The proposed schemes are illustrated with an industrial application in monitoring the e-commerce activity, precisely the online shopper's intention. Some concluding remarks and future research problems are presented.