Efficient Phase II Monitoring Methods for Linear Profiles under the Random Effect Model

A profile is a functional relationship between two or more variables used to monitor the process performance and its quality. Sometimes, the aforementioned relationship is linear or nonlinear depending upon the situation. A monitoring method based on the linear profiles is known as linear profiling which is commonly used due to its simplicity and efficacy. Linear profiling methods have been studied by many researchers with a fixed effect model. However random effect model provides a more suitable interpretation as compared to the fixed effect model under different real-time monitoring methods. Therefore in this article, we are intended to propose a linear profiling EWMA method (mathrm {EWMA}mathrm {[R]} -3 chart) and mathrm {MEWMA}mathrm {[R]} chart based on the random effect model using different ranked set sampling techniques such as ranked set sampling (RSS), extreme RSS (ERSS), median RSS (MRSS), double RSS (DRSS), double ERSS (DERSS) and double MRSS (DMRSS). The ranked set sampling (RSS) schemes are not only cost-effective method but also an efficient mechanism as compared to simple random sampling. A designed simulation study used Average Run Length (ARL) as an evaluation measure to witness the detection ability of newly offered mathrm {EWMA}mathrm {[R]} -3 chart, mathrm {MEWMA}mathrm {[R]} chart and existing mathrm {EWMA}mathrm {[SRS]} -3 chart. The extensive simulation showed that the proposed mathrm {EWMA}mathrm {[R]} -3 chart and mathrm {MEWMA}mathrm {[R]} chart have superiority to detect faults in the process compared to a competitive counterpart. The results are further justified with real data application related to a combined cycle power plant.