Mean and Variance Adjustment of the Average Control Chart by Shape Parameter Using Bayesian Estimation of the Inverse Gaussian Distribution
Article Sidebar
Main Article Content
Abstract
This research aims to develop the average control chart ( ) using the shape parameter of the Inverse Gaussian Distribution by Bayesian Estimation for estimating mean and variance, and to compare the process potential capability (Cp) and the actual process capability index (Cpk) for Monte Carlo simulation with 10,000 replications assuming that the specification is 0.001. The result shows that the process potential capability (Cp) and the actual process capability index (Cpk) of the Adjusted
using Bayesian Estimation of the shape parameter of the Inverse Gaussian Distribution for estimating mean and variance have more capability than the
under the normal distribution when the sample size is less than 30. For the sample size of 30, the two control charts have the indifferent capability process.
Keywords: Adjusted ; Bayesian Estimation; shape parameter; Inverse Gaussian Distribution
Corresponding author: Tel.: 02-4416083, 0863623508
E-mail: kittisak.jang@rmutr.ac.th, kittisakaj1986@gmail.com
Article Details
Copyright Transfer Statement
The copyright of this article is transferred to Current Applied Science and Technology journal with effect if and when the article is accepted for publication. The copyright transfer covers the exclusive right to reproduce and distribute the article, including reprints, translations, photographic reproductions, electronic form (offline, online) or any other reproductions of similar nature.
The author warrants that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.
Here is the link for download: Copyright transfer form.pdf
References
Sant’Anna, Â.M.O. and ten Caten, C.S., 2012. Beta control charts for monitoring fraction data. Expert Systems with Applications, 39(11), 10236-10243.
Cooper, R. And Van Vliet, B., 2012. Whole distribution statistical process control in high frequency trading. Journal of Trading, 7(2). 1-23.
Hoyle, D., 2017. ISO 9000 Quality Systems Handbook-updated for the ISO 9001: 2015 Standard: Increasing the Quality of an Organization’s Outputs. London: Routledge.
Quesenberry, C.P.,1997. SPC Methods for Quality Improvement. New York : Wiley.
Khoo, M.B., 2004. A moving average control chart for monitoring the fraction non‐conforming. Quality and Reliability Engineering International, 20(6), 617-635.
De Oliveira, G.S., Knautz, J.S., Sherwani, S. and McCarthy, R.J., 2012. Systemic magnesium to reduce postoperative arrhythmias after coronary artery bypass graft surgery: a meta-analysis of randomized controlled trials. Journal of Cardiothoracic and Vascular Anesthesia, 26(4), 643-650.
Ryan, T.P. and Schwertman, N.C., 1997. Optimal limits for attributes control charts. Journal of Quality Technology, 29(1), 86-98.
Rungruang, S., 2013. An efficiency comparison of fraction nonconforming control charts. Veridian E-Journal, 6(3), 860-876.
Chhikara, R.S. and Folks, J.L., 1977. The Inverse Gaussian distribution as a lifetime model. Technometrics, 19(4), 461-468.
Samaniego, F.J., 2010. A Comparison of the Bayesian and Frequentist Approaches to Estimation. New York: Springer Science & Business Media.
Lindley, D.V., 1980. Approximate Bayesian methods. Trabajos de Estadística Y de Investigación Operativa, 31(1), 223-245.
Jangphanish, K. and Kornpetpranee, S., 2016. Monte Carlo simulation for comparing the parameters Inverse Gaussian Distributions estimated by Bayesian Estimation using Gamma and Weibull Prior Distribution. KKU Science Journal,45(1), 200-213.
AIAG, 2005. Statistical Process Control. 2nd ed. (Thai Edition). Daimler Chrysler, Ford Motor Company and General Motors Corporation, pp. 72-102.