Reintegration of auxiliary information based control charts

Abstract

During the last decade, auxiliary information based (AIB) control charts have gained a lot of popularity for process monitoring. These charts are proved efficient for early detection of shifts in process parameters like location and dispersion. A recent study has pointed out few concerns related to AIB control charts which were already highlighted in earlier studies one way or the other. In reply to that, we reiterate the initial classification of processes by Hawkins (1993) namely non-cascading processes where the change in one variable may not affect the other variable. Under the non-cascading situations, AIB control charts are designed with the assumption that auxiliary variable remains stable even if there is a shift in study variable. This assumption is true for some processes. On the other hand, in many non-cascading processes where the auxiliary variable can experience a shift, the performance of AIB control charts is highly affected specially when the auxiliary variable(s) and study variable are strongly correlated. This study proposes a modified AIB control charting structure that safeguards the detection ability and the run length properties in case auxiliary variable experiences a shift. In addition, the usual AIB and classical Shewhart charts become a special case of the proposed chart. For several values of design parameter, the in control and out of control performance of proposed chart is evaluated in terms of average run length. It is observed that the proposed modified AIB control chart is capable of increasing its robustness against any shift in the auxiliary variable through a design parameter. An extensive comparative analysis revealed that the newly proposed modified AIB control chart has capability to absorb a shift of any size in auxiliary variable, maintaining the gain in terms of efficiency. An illustrative example is also included to support the finding of our study.