Shongwe, Sandile CharlesGraham, Marien Alet2018-09-172018Shongwe S.C., Graham M.A. 2018, 'Some theoretical comments regarding the run-length properties of the synthetic and runs-rules monitoring schemes – Part 2: Steady-state', Quality Technology and Quantitative Management, NYP.1684-370310.1080/16843703.2017.1389142http://hdl.handle.net/2263/66573In this paper, the long term (also known as the steady-state mode) run-length theoretical properties of the four different types of synthetic and runs-rules monitoring schemes, that were empirically analysed in part 1 of this research work. That is, using the Markov chain imbedding technique (thoroughly discussed in Part 1 of this work), the closed-form expressions of the steady-state initial probabilities and average run-length (ARL) vectors are derived; so that the corresponding steady-state ARL and overall performance expressions, of each of the four different types of the synthetic and runs-rules monitoring schemes, may be formulated. Since there is very little literature on steady-state analysis of the synthetic and runs-rules charts, the closed-form expressions derived here will ease the understanding and implementation of the different types synthetic and runs-rules schemes in practice and in further academic research.en© 2018 International Chinese Association of Quantitative Management. This is an electronic version of an article published in Quality Technology and Quantitative Management, vol. x, no. y, pp. z-zz, 2018. doi : 10.1080/16843703.2017.1389142. Quality Technology and Quantitative Management is available online at: http://www.tandfonline.com/loi/ttqm20.Average run-length (ARL)Overall performanceRuns-rules chartsSteady-stateSynthetic chartsTransition probability matrix (TPM)Statistical process controlMarkov processesPostprint Article