Run-sum control charts for monitoring the coefficient of variation

•We develop the run sum charts for monitoring the coefficient of variation (CV).•The CV is successfully applied in various scientific and societal disciplines.•The ARL, SDRL and EARL formulae are derived through a Markov chain approach.•Optimal designs are based on the deterministic and unknown shift-size conditions.•New optimal charts’ parameters under the zero- and steady-state modes are given. The coefficient of variation (CV) is a unit-free and effective normalized measure of dispersion. Monitoring the CV is a crucial approach in Statistical Process Control when the quality characteristic has a distinct mean value and its variance is a function of the mean. This setting is common in many scientific areas, such as in the fields of engineering, medicine and various societal applications. Therefore, this paper develops a simple yet efficient procedure to monitor the CV using run-sum control charts. The run-length properties of the run-sum CV (RS-γ) charts are characterized by the Markov chain approach. This paper proposes two optimization algorithms for the RS-γ charts, i.e. by minimizing (i) the average run length (ARL) for a deterministic shift size and (ii) the expected ARL over a process shift domain. Performance comparisons under both the zero- and steady-state modes are made with the Shewhart-γ, Run-rules-γ and EWMA-γ charts. The results show that the proposed RS-γ charts outperform their existing counterparts for all or certain ranges of shifts in the CV. The application of the optimal RS-γ charts is illustrated with real data collected from a casting process.