title: Enhanced cumulative sum charts for monitoring process dispersion.
abstract: The cumulative sum (CUSUM) control chart is widely used in industry for the detection of small and moderate shifts in process location and dispersion. For efficient monitoring of process variability, we present several CUSUM control charts for monitoring changes in standard deviation of a normal process. The newly developed control charts based on well-structured sampling techniques - extreme ranked set sampling, extreme double ranked set sampling and double extreme ranked set sampling, have significantly enhanced CUSUM chart ability to detect a wide range of shifts in process variability. The relative performances of the proposed CUSUM scale charts are evaluated in terms of the average run length (ARL) and standard deviation of run length, for point shift in variability. Moreover, for overall performance, we implore the use of the average ratio ARL and average extra quadratic loss. A comparison of the proposed CUSUM control charts with the classical CUSUM R chart, the classical CUSUM S chart, the fast initial response (FIR) CUSUM R chart, the FIR CUSUM S chart, the ranked set sampling (RSS) based CUSUM R chart and the RSS based CUSUM S chart, among others, are presented. An illustrative example using real dataset is given to demonstrate the practicability of the application of the proposed schemes.
authors.affiliation: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia; Preparatory Year Mathematics Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
authors.forename: Mu'azu Ramat
authors.initials: MR
authors.lastname: Abujiya
authors.affiliation: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
authors.forename: Muhammad
authors.initials: M
authors.lastname: Riaz
authors.affiliation: Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia.
authors.forename: Muhammad Hisyam
authors.initials: MH
authors.lastname: Lee
mesh_terms: D007221:Industry; D013223:Statistics as Topic