Email this article A comparison of Process Capability Measures for Seasonal and Non-Seasonal Autoregressive Auto-Correlated Data
Abstract
The process capability indices give a measure of how a process suits within the specification limits. Traditionally, the main assumptions are used in calculating these indices that the measurements for the specified characteristic are independent and normally distributed. In this paper we investigated the distributional properties in terms of Bias, MSE and empirical distribution for the sample version of the most common three process capability measures namely; when the process data are autocorrelated following seasonal or non-seasonal first-order autoregressive process. We have found that the characteristics of those estimators are negatively affected by the autocorrelation data, especially for the multiplicative seasonal AR model. Besides, we found that the empirical distributions of the three sample capability measures are positively skewed and leptokurtic, a fact which is true when the data are independent and normal.
References
Alzoubi, A. (2013). "On the Distributional Properties of Some Process Capability Measures for Autocorrelated Data". Unpublished Master thesis, Yarmouk University, Jordan.
Chou, Y. M. and Owen, D .B. (1989). "On the Distributions of the Estimated Process Capability Indices", Communications in Statistics: Theory and Methods, 18(12): 4549-4560.
Cryer, J.D., and Chan, K. (2008). Time Series Analysis with Application in R, Second Edition, Springer.
Guevara, R., and Vargas, J. (2007). "Comparison of Process Capability Indices under Autocorrelated Data", Revista Colombiana de Estadistica, 30(2): 301 - 316.
Kotz, S., Pearn, W. L. and Johnson, N. L. (1993). "Some process capability indices are more reliable than one might think", Journal of the Royal Statistical Society, Series C: Applied Statistics, 42(1): 55-62.
Montgomery, D. (2001). Introduction to statistical quality control, Fourth Edition. John Wiley and Sons.
Pearn, W.L and Kotz, S. (2006). Encyclopaedia and Handbook of Process Capability Indices, Comprehensive Exposition of Quality Control Measures. World Scientific Publishing, Singapore.
Pearn, W. L. and Lin, G. H. and Chen, K. S. (1998). "Distributional and inferential properties of the process accuracy and process precision indices", Communications in Statistics: Theory and Methods, 27(4): 985-1000.
R Core Team (2017). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.URL: https://www.R-project.org/.
Shore, H. (1997). "Process capability analysis when data are autocorrelated", Quality Engineering, 9: 615–626.
Steiner, S., Abraham, B., and Mackay, J(1997). "Understanding process capability Indices", IIQR Research Report, no.2, University of Waterloo, Canada.
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