Joint economic design of EWMA control charts for mean and variance

Abstract

Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by adding constraints associated with in-control and out-of-control average run lengths. The quality related production costs are calculated using Taguchi's quadratic loss function. The optimal values of smoothing constants, sampling interval, sample size, and control chart limits are determined by using a numerical search method. The average run length of the control scheme is computed by using the Markov chain approach. Computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and/or variance increase, and higher values of quality loss coefficient lead to shorter sampling intervals. The sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an EWMA-based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance.

Robust economic and economic-statistical design of EWMA control chart

“…This issue is suggested by authors like Linderman and Choo [23] and Serel [18] as a future research, and this paper follows this idea. GA algorithm is used to solve the optimization models and the results are compared with the best procedure in the literature.…”

“…The economic design of EWMA control charts has been investigated by several authors such as Ho and Case [17]. Joint economic design of EWMA control [18]. Serel [19] proposed economic design of EWMA control charts based on loss function.…”

Fuzzy MaxGWMA chart for identifying abnormal variations of on-line manufacturing processes with imprecise information

“…Therefore, in this paper, we take both randomness and fuzziness into consideration. Furthermore, as the extensions of the traditional exponential weighted moving average assume that the interested variable is normally distributed (Eyvazian et al, 2008;Gan, 1995;Khoo et al, 2010;Serel and Moskowitz, 2008;Vargas et al, 2004), the data set used in this study should be tested for its normal distribution before relevant control charts are constructed. Runs test is considered as one of the good methods to test for the randomness of not only crisp data (Walpole et al, 2012) but also fuzzy numbers (Buckley, 2006).…”

Control charts limits flexibility based on the equipment conditions

“…In these equations t X is the sample mean at t (Serel & Moskowitz, 2008), T L the maximum or minimum admissible for each variable or parameter, E  the variable E standard deviation, n the sample dimension, λ the weight constant (0 ≤ λ ≤ 1) and ∆ s the safety factor. The Modified EWMA limits are Alert Level (AL) and Upper Control Level (UCL) for these charts are given by equations (3) and (4).…”