One-sided control charts for the mean of positively skewed distributions

Abstract

Traditional control charts for the mean are based on the normal process assumption. However, in reality there are many situations in which the process populations are non-normal. This paper proposes a new control charting technique for the mean of positively skewed distributions. The charting procedure is described in detail. Some existing robust control charts are reviewed and the properties of these control schemes are compared with the proposed method. A simulation study shows that the proposed control charting method has good robust performance and can detect process shifts e Y ciently.

Improved one‐sided control charts for the mean of a positively skewed population using truncated saddlepoint approximations

“…A graphical comparison of the upper tail of the densities ofX for n = 3 observations, i.e. f (2) x (x),f (3) x (x),f (4) x (x),gx(x) and x ∈ [14,18], is given in Figure 3. It is noted that higher order TS approximations more closely follow the exact pdf on the tail, which indicates a potential better performance in terms of type 1 error rates.…”

“…This approach is quite popular as it results in charts that are easy to use and provides type 1 and 2 errors somewhat close under a Gaussian assumption. A sampling of such charts include synthetic control charts 2 , skewness correction (SC) methods 3 , Edgeworth-based charts 4 , improved exponentially weighted moving average (IEWMA) charts 5 , and modifiedX charts using Weighted Variance (WV) and Weighted Standard Deviation (WSD) methods 6,7 . Notwithstanding, these heuristic charts often quickly lose accuracy as the degree of skewness goes up and/or the subgroup size goes down, as will be shown in Section 5.2 of this paper.…”

Enhancing R Control Chart Performance in Monitoring Process Dispersion using Scaled Weighted Variance Method for Skewed Populations

“…The last approach is to use heuristic methods to design control charts such as the and R charts based on the Weighted Variance (WV) X method proposed by Bai and Choi (1995), control chart X using Scaled Weighted Variance (SWV-) chart X proposed by Castagliola (2000), the , EWMA and X CUSUM charts based on the Weighted Standard Deviation (WSD) method suggested by Chang and Bai (2001), the and R charts based on the Skewness X Correction (SC) method presented by Chan and Cui (2003), a multivariate synthetic control chart for monitoring the process mean vector of skewed populations using weighted standard deviations suggested by Khoo et al (2009b), a multivariate EWMA control chart using weighted variance method by Atta et al (2014) and comparing the Median Run Length (MRL) performances of the Max-EWMA and Max-DEWMA control charts for skewed distributions by Teh et al (2014). Other works that deal with univariate control charts for skewed distributions include that of Wu (1996), Nichols and Padgett (2005), Tsai (2007), Dou and Sa (2002), Chen (2004) and Yourstone and Zimmer (1992). In this study, the R control chart is developed by using the Scaled Weighted Variance (SWV) method suggested by Castagliola (2000).…”

Measurement error effect on the power of control chart for Zero truncated Negative Binomial Distribution (ZTNBD)

“…In industries, a conventional inspecting tool is to construct control charts to realize whether a process is in control or not [9]. A control chart is a statistical system developed with the objective of inspection after which,the statistical stability of a process is checked.…”