A profile is a functional relationship, between two or more variables, used to monitor the process performance and its quality. The relationship may be linear or nonlinear depending upon the situation. Linear profiling methods with a fixed-effect model are commonly used under simple random sampling (SRS). In this article, we propose linear profiles monitoring methods under a new ranked set sampling (RSS) scheme named as Neoteric RSS (NRSS). The new profiling methods are proposed under all the three popular structures, namely Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA). The study proposal considers both classical and Bayesian setups. We have investigated the detection ability of newly proposed classical charts (i.e., Shewhart_NRSS(C), CUSUM_NRSS(C), EWMA_NRSS(C) charts) and Bayesian charts (i.e., Shewhart_NRSS(B), CUSUM_NRSS(B) and EWMA_NRSS(B) charts). An extensive simulation study showed that the proposed charts have better detection ability for perfect NRSS scheme, while Bayesian control charts showed superiority over its classical counterpart under both perfect and imperfect NRSS. The significance of the proposed study is further highlighted using the real data study of chemical gas sensors from the chemical industry.