On developing linear profile methodologies: A ranked set approach with engineering application

Linear profiles are quite popular in establishing relationships among different variables associated with each other in an ongoing process. Control charting methodologies for these linear profiles are used to monitor and improve the performance of a process. The commonly used Phase I methodologies of linear profiles are mostly based on simple random selection procedures. In this study, we intend to improve the existing Phase I profile methods by considering different ranked set strategies including ranked set sampling (RSS), median RSS (MRSS) and extreme RSS (ERSS). The profile monitoring is considered in terms of three main parameters namely slope, intercept and error variance for efficient detection of any assignable cause(s). We have used probability to signal as a performance measure in our study. A real-life application of the proposed methods is also presented in this study using real data from electrical engineering related to a grid-connected photovoltaic system.