Reintegration of Auxiliary Information Based Control Charts

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) into two mechanisms namely cascade versus non-cascade processes. AIB control charts are designed under the assumption that auxiliary variable remains stable even if there is a shift in study variable. This assumption is true for non-cascading processes where the shift in one variable does not necessarily affect the other variables. On the other hand, in cascading processes where a shift in the parameters of study variable affects the auxiliary variable(s), the performance of AIB control charts is deteriorated 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