Some theoretical comments regarding the run-length properties of the synthetic and runs-rules monitoring schemes – Part 2 : Steady-state

In 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.

Part of this work was supported by the SARCHI Chair at the University of Pretoria. Sandile Shongwe’s research was supported in part by the National Research Foundation (NRF) and Department of Science and Technology’s Innovation Doctoral scholarship, Grant number: 95208 as well as Department of Statistics’ STATOMET and Marien Graham’s research was supported in part by the NRF (Thuthuka program), Grant number: 94102.

http://www.tandfonline.com/loi/ttqm20

2019-05-23

Science, Mathematics and Technology Education

Statistics