An Analysis of the Mean Chart Under OC Function for Correlated Data
DOI:
https://doi.org/10.13052/jrss0974-8024.1625Keywords:
Correlation, X-bar chart, operating characteristic (OC) curve, average run length (ARL)Abstract
In this paper, we determine and illustrate the effects of correlation between the observations on the operating characteristics curve, Type-I error and Average Run length. In addition, for different correlated coefficient the control limits have been developed. To study the effect of correlated observations the OC curves, Type-I error, ARL and factor A have been worked out using various equation and values are given in Tables 1 to 4. To give a visual comparison of OC function and ARL, curves have been drawn in Figures 1 to 6. It is found that correlation between observations seriously affected the OC, Type-I error, ARL and factor A for the mean chart when standards are known. When the center line and control limits are based on the large value. Thus, it will be healthy contribution in manufacturing process which tracks important product characteristics in industry.
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References
Lin, H. R., Chou, C. Y. and Chen, C. H. (2003): The effect of correlation on the economic design of warning limit X-bar charts; The International Journal of Advanced Manufacturing Technology, Vol. 22, pp. 3–4.
Che Dinetal, N.S., Abdul Samad, N.A.F. and Chin, S.Y. (2011): Fault detection and diagnosis for Gas Density Monitoring using multivariate statistical process control. Journal of applied sciences, 11: 2400–2405.
Singh J. R, Sankle R., and M. Ahmad Khanday (2013): Variables Sampling Plan for Correlated Data. Journal of Modern Applied Statistical Methods, Vol 12, Issue 2.
Zameer Abbas, Hafiz Zafar Nazir, Noureen Akhtar. Muhammad Riaz, and Muhammad Abid (2020): On designing a progressive mean chart for efficient monitoring of process location. Quality and Reliability Engineering. April 2020, DOI: 10.1002/qre.2655.
Shewhart, W.A. (1939): Statistical methods from the viewpoint of Quality Control, Republished in 1986 by Dover Publications New York: 12, 54.
Fearell, E. B. (1953): Control Charts using Median & Mid Ranges, Industrial Quality Control, 9:30–32.
Che Dinetal, N.S., Abdul Samad, N.A.F. and Chin, S.Y. (2011): Fault detection and diagnosis for Gas Density Monitoring using multivariate statistical process control. Journal of applied sciences, 11: 2400–2405.
Manzoor A. Khanday and J. R. Singh (2020): Economic Design of X̄ Control Chart under Double EWMA. Journal of Modern Applied Statistical Methods.
