Weighted standard deviation method for X and S control charts

Yıl 2019, Cilt: 68 Sayı: 2, 1377 - 1386, 01.08.2019

Derya Karagöz

https://doi.org/10.31801/cfsuasmas.530462

Cited By: 1

Öz

A Shewhart chart based on normality assumption is not appropriate for skewed distributions since its Type-I error rate is inflated. This study presents X and S control charts for monitoring the process variability for skewed distributions. We propose Weighted Standard Deviation (WSD) X and S control charts. Standard deviation estimator is applied to monitor the process variability for estimating the process standard deviation, in the case of the WSD X and S control charts as this estimator is simple and easy to compute. Unlike the Shewhart control chart, the proposed charts provide asymmetric limits in accordance with the direction and degree of skewness to construct the upper and lower limits. The performances of the proposed charts are compared with other heuristic charts for skewed distributions by using Simulation study. The Simulation studies show that the proposed control charts have good properties for skewed distributions and large sample sizes.

Anahtar Kelimeler

Weighted standard deviation, lognormal distributions, X and S control charts

Kaynakça

• Bai, D.S., and Choi, I.S., 1995, X and R Control Charts For Skewed Populations, Journal Of Quality Technology, 27:120-131.
• L.K. Chan, and H.J. Cui, 2003, Skewness Correction X and R Charts for Skewed Distributions, Naval Research Logistics, 50, 1-19.
• Chang, Y.S., and Bai, D.S.,2001, Control Charts for Positively Skewed Populations with Weighted Standard Deviations, Quality and Reliability Engineering International, 17: 397-406.
• Choobineh, F., and Ballard, J.L., 1987, Control-Limits of QC Charts For Skewed Distributions Using Weighted Variance, IEEE Transactions on Reliability, 473-477.
• Karagöz, D., and Hamurkaroğlu C., 2012, Control Charts for Skewed Distributions: Weibull, Gamma, and Lognormal, Metodoloski zvezki - Advances in Methodology and Statistics, 9.2: 95-106.
• Koo, M.B., Atta, A.M.A. and Chen C.H., 2009, Proposed X and S Control Charts for Skewed Distributions, Proceedings of the 2009 IEEE IEEM.
• Montgomery, D.C., 1997, Introduction to Statistical Quality Control. John Wiley&Sons. Inc., USA.