Kinerja Grafik X-Bar menggunakan Variabel Parameter dan Double Sampling dengan Pendekatan Rantai Markov


  • Wardatus Syarifah Institut Dirosat Islamiyah Al-Amien Prenduan


double sampling, X-bar graph, markov chain, variable parameter


X-bar control chart is one of the means used to resolve problems or detect specific causes that might occur in the production process. When using charts X-bar, there are situations where the average process can diverge. If the average process of the irregularities, it takes a complex approach involving Markov chains to evaluate the properties of graphs X-bar. In this research discusses the performance of the graph X-bar using Variable Parameters and Double Sampling with Markov chain approach. Stages used is determine the state Variables Parameters and Double Sampling, making a transition matrix for Variable Parameter and Double Sampling, determining Average Time of Cycle and Average Time to Signal, comparison test, conclusions and suggestions. By comparing Variables Parameters and Double Sampling obtained a good method to use for a particular situation on the graph X-bar, that is when a small sample size using Variable Parameters and when a large sample size using Double sampling.


Claro, F.A.E., Costa, A.F.B., Machado, M.A.G., 2008.DOUBLE SAMPLING X ? CONTROL CHART FOR A FIRST ORDER AUTOREGRESSIVE PROCESS. Guaratinguetá, SP: São Paulo State University.

Montgomery, D.C. 2020. Introduction to Statistical Quality Control.USA: John Wiley & Sons, Inc.

Tolver, Anders. 2016. An Introduction to Markov Chains. Denmark: University of Copenhagen

Žitkovic, G., 2010. Introduction to Stochastic Processes. Austin: The University of Texas.

Teoh, W.L., Khoo, M.B.C., 2012. “Optimal Design of the Double Sampling X ?Chart Basedon Median Run Length”.International Journal of Chemical Engineering and ApplicationsVol. 3. Hal.303-306.

Costa, A.F.B, Machado, M.A.G., 2011. “Variable Parameter and Double Sampling X ? Charts in The Presence of Correlation: The Markov ChainApproach”.International Journal Production Economics Vol.130. Hal 224-229.

Ibe, O.C. 2013. Markov Processes for Stochastic Modeling. USA: University of Massachusets

Kirkwood, J. R. 2015. Markov Processes. London. CRC Press Taylor and Francis Group

Qiu, P. 2013. Introduction to Statistical Process Control. USA: University of Florida

Aslam, M., Saghir, A., Ahmad, L. 2020. Introduction to Statistical Process Control. USA: John Wiley & Sons, Inc.