Efficient Control Chart for the Process Location Based on Dual-Rank Ranked Set Sampling

Statistical control charts are widely used in monitoring industrial processes. The main purpose of control charts is to detect assignable causes of variation acting on the process based on collected data. Thus, the development of more powerful strategies can lead to faster detection of production problems. In this paper, we introduced the dual rank ranked set sampling (DRRSS), a recently proposed strategy based on ranked set sampling, in the design of control charts. A Shewhart type control chart was developed and its performance evaluated through extensive simulations. Samples were simulated from normal and non-normal distributions, considering distributions with different levels of kurtosis, skewness, and contamination. The performance of the proposed chart was evaluated through different run length metrics. The simulation results allowed us to verify that the DRRSS control chart has greater power than its simple random sampling and RSS for different sample sizes and shifts in the process mean. The robustness of DRRSS control charts to imperfect ranking was also addressed. An application based on water quality data illustrates the development of a DRRSS control charts and corroborates the previous findings.