New Lepage-type control charts for joint monitoring of location and scale

Abstract

This paper introduces two new Shewhart Lepage-type control charts for jointly monitoring the location and scale parameters of continuous processes. The first is based on the van der Waerden (VW) and Ansari-Bradley (AB) tests while the other is on the VW and Mood tests. Statistical performances, in terms of average run length (ARL), of these charts are evaluated numerically and compared with that of their two competitor charts in the existing literature under four distributional models for the process output, namely, the normal, lognormal, Laplace, and logistic. The numerical results show that irrespective of the process distribution, one of the proposed charts (based on VW and Mood tests) has the best performance among all the four charts in the detection of simultaneous shifts in both the parameters of all sizes as well as in the detection of shifts in the scale that have not been accompanied by shifts in the location (only-scale shifts) of all sizes. Moreover, the other proposed chart (based on VW and AB tests) performs better than one of the competitor charts in the existing literature for detecting simultaneous shifts as well as only-scale shifts of all sizes. In addition, it performs better than the other competitor chart for detecting the simultaneous shifts consisting of a large location shift and a small scale shift, however, performs worse than that for detecting the simultaneous shifts consisting of a small location shift and a scale shift of any size, as well as for detecting the only-scale shifts of all sizes. All the four charts perform almost similarly in the detection of only-location shifts of all sizes. Regression models are provided for the proposed charts, which facilitate their designs in practice. Finally, the practical implementation of the proposed charts is illustrated through a real-data example.