Linear profile monitoring using EWMA structure under ranked set schemes

Abstract

In many manufacturing processes, study variable is not the only quality characteristic, but there may exist some explanatory variable(s) that are associated with the study variable. This association may be linear or nonlinear depending on the nature of variables. The term profiling is used for such relationships among study and explanatory variables. Linear profiles are more common options because of their simplicity and coverage of more common scenarios. A popular proposal for the monitoring of linear profiles is EWMA − 3[SRS] chart that detect shifts in the profile parameters including slope, intercept, and error variance. The said chart is designed under simple random sampling. In this study, we have designed and investigated EWMA − 3[τ] chart under the different ranked set sampling strategies (τ) such as ranked set sampling (RSS), median ranked set sampling (MRSS), extreme ranked set sampling (ERSS), double ranked set sampling (DRSS), double median ranked set sampling (DMRSS), and double extreme ranked set sampling (DERSS). We have used average run length (ARL), extra quadratic loss (EQL), relative average run length (RARL), and performance comparison index (PCI) as performance measures for the aforementioned designs of EWMA − 3[τ] chart under different sampling schemes. The computational results of run length properties revealed that the ranked set based EWMA − 3[τ] chart offers better detection ability. More specifically, EWMA − 3[ERSS] and EWMA − 3[DMRSS] serve the purpose in a more efficient way.