and R control charts based on weighted variance with left-right tail-weighted ratio for skewed distributions

ABSTRACT

The study proposed the average and range control charts by considering the generalized lambda distribution, the percentile-based method, and the weighted variance with left-right tail-weighted ratio for skewed populations. When the underlying distribution is Weibull, Burr, gamma, lognormal, or inverse Gaussian, the proposed control charts have Type I risks, which are closer to 0.27% of the normal distribution, and they do not rapidly vary with sample sizes and the shape of a distribution. Type II risks of the proposed control charts are closer to those of the exact charts than to those of the skewness correction and weighted variance charts.

KEYWORDS:

• Generalized lambda distribution
• Left-right tail-weighted ratio
• Percentile-based method
• Weighted variance

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62P30
• Secondary 62F10

Acknowledgments

The author would like to thank the editor and the referees for their helpful suggestions that led to a clear presentation of my work and the Ministry of Science and Technology of the Republic of China, Taiwan, for financially supporting this research under Contract No. NSC 103-2918-I-244 -001.