Control charts based on linear combinations of order statistics

Abstract

The last 20 years have seen an increasing emphasis on statistical process control as a practical approach to reducing variability in industrial applications. Control charts are used to detect problems such as outliers or excess variability in subgroup means that may have a special cause. We describe an approach to the computation of control limits for exponentially weighted moving average control charts where the usual statistics in classical charts are replaced by linear combinations of order statistics; in particular, the trimmed mean and Gini's mean difference instead of the mean and range, respectively. Control limits are derived, and simulated average run length experiments show the trimmed control charts to be less influenced by extreme observations than their classical counterparts, and lead to tighter control limits. An example is given that illustrates the benefits of the proposed charts. parameters; see, for example, Hunter (1986) and Montgomery (1996). On the other hand, EWMA charts have been shown to be more efficient than Shewharttype charts in detecting small shifts in the process mean; see, for example, Ng & Case (1989), Crowder (1989), Lucas & Saccucci (1990), Amin & Searcy (1991) and Wetherill & Brown (1991). In fact, the EWMA control chart has become popular for monitoring a process mean; see Hunter (1986) for a good discussion. More recently, EWMA charts have been developed for monitoring process variability;

Application of the Regional Flood Frequency Analysis to the Upper and Lower Basins of the Indus River, Pakistan

“…L-moments based regional frequency analysis is practiced all over the world (for example, Guttman et al 1993;Smithers and Schulze 2001;Ben-Zvi and Azmon 1997;Pandey et al 2001;Elamir and Seheult 2001;Jingyi and Hall 2004;Saf 2009;Eslamian and Feizi 2007;Modarres 2007;Norbiato et al 2007;Hussain and Pasha 2009;Castellarin et al 2008;Yang et al 2009) but an important aspect, in the comparison of quality of the quantile estimates obtained at each site from regional approach to that of at-site analysis, is how can we calculate the standard errors of the estimated quantiles at each site of a homogeneous region? In this paper, a relationship provided in Hosking and Wallis (1997) has been explored and standard errors of the estimated flood quantiles at each site of the homogeneous regions have been calculated by extending the results of the simulation experiments related to the accuracy measures of the regional estimates.…”

The EWMA control chart based on robust scale estimators

“…The Expected Points Out of control (EPO) is considered a good measure to show the performance of the control charts used by Elamir and Seheult (2001). The more points out of control limits show that there is a need for corrective action.…”

Monitoring process variability using decile mean standard deviation

“…In this section, a second simulation analysis is performed in order to compare the performance of classical Shewhart S and proposed SD DM ‐control charts. The EW and EPO are good measures for comparing the control charts’ performance utilized by several researchers such as Elamir and Seheult, 23 Saeed and Kamal, 24 and Kashif et al 25 . The Algorithm‐1 is used to find the measures presented in Table 4 as well as to construct the boxplots shown in Figure 1.…”