Some theoretical comments regarding the run-length properties of the synthetic and runs-rules X¯ monitoring schemes – part 2: steady-state. Issue 2 (4th March 2019)

• Record Type: Journal Article
• Authors: Shongwe, Sandile C.; Graham, Marien A.
• Is Part Of: Quality technology & quantitative management. Volume 16:Issue 2(2019)
• Page Start: 190
• Page End: 199
• Publication Date: 2019-03-04
• Subjects: Average run-length (ARL) -- overall performance -- runs-rules charts -- steady-state -- synthetic charts -- transition probability matrix (TPM); Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2017.1389142
• Languages: English
• ISSNs: 1684-3703

Abstract

Abstract: 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 X ¯ 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 X ¯ 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 X ¯ schemes in practice and in further academic research.