Simultaneous monitoring of linear profile parameters under progressive setup

In many manufacturing or service processes, we come across different quality characteristics that govern the process behavior. These characteristics are categorized as the main quality characteristics (study variables) and the supporting or explanatory characteristics. There is always a possibility that some of the explanatory variables offer a relationship with the study variable which is known as profiles. The monitoring of study variable which is linearly associated with an explanatory variable is termed as simple linear profiles. In this study, we intend to design an efficient memory type structure based on progressive mean for the simultaneous monitoring of linear profile parameters. The performance of proposed scheme (PM_3) and its counterparts (i.e. EWMA_3 chart, Hotelling T2 chart, EWMA/R chart and Shewhart_3 chart) are evaluated using some useful performance measures such as average run length (ARL), relative average run length (RARL), sequential relative average run length (SRARL), extra quadratic loss (EQL) and sequential extra quadratic loss (SEQL). In the presence of shifts in linear profile parameters, the findings depict that PM_3 chart has better detection ability as compared to counterpart charts. A case study related to Queen size problem is also discussed to highlight the importance of the newly proposed control chart.