•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.