A One-Sided EWMA Control Chart for Monitoring Process Means

A comparison of CUSUM, EWMA, and temporal scan statistics for detection of increases in poisson rates

“…Robinson and Ho 30 examined a one-sided control limit for a conventional EWMA chart. A discussion and comparison of the existing one-sided EWMA charts can be found in Shu et al 31 . Gan 32 introduced a modified version of the EWMA chart to monitor the mean shift of a process away from the Poisson distribution.…”

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

“…A paper by Borror et al 11 analyzes the Average Run Length (ARL) performance of a traditional EWMA chart under populations with skewed densities, following which Shu et al 5 specifies a one-sided IEWMA chart that monitors for shifts only in the direction of skewness by resetting observations in the opposite direction to the target value. In both these papers, it was assumed that the mean and variance of the population were known; yet as noted by Jones 12 and Jensen et al 13 , the ARL performance of EWMA charts may be significantly overestimated when these population parameters are rather only estimates from data.…”

“…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.…”

Generalized autoregressive and moving average models: control charts, multicollinearity, and a new modified model

“…Whenever C i,t > h i , the process is considered out-of-control. In general, the distribution of the transformed statistics are not Gaussian (and this was confirmed for all these statistics excepting the deviance residual in Alencar et al 21 ). Due to this fact, the parameters (k, h) of CUSUM charts were exhaustively searched by simulation when the process is in-control and out-of-control.…”

“…The first four statistics are transformations of the original count data to achieve a standardized normal distribution (one is based on the deviance residuals as proposed in Alencar et al 21 ); and the last two are derived from the ratio of likelihood functions. All statistics are summarized in Table 1 and detailed in Alencar et al 21 . …”