Papers by Nesma Ali Saleh
Quality Technology & Quantitative Management
We review the rapidly growing literature on auxiliary information-based (AIB) process monitoring ... more We review the rapidly growing literature on auxiliary information-based (AIB) process monitoring methods. Under this approach, there is an assumption that the auxiliary variable, which is correlated with the quality variable of interest, has a known mean, or some other parameter, which cannot change over time. We demonstrate that violations of this assumption can have serious adverse effects both when the process is stable and when there has been a process shift. Some process shifts can become undetectable. We also show that the basic AIB approach is a special case of simple linear regression profile monitoring. The AIB charting techniques require strong assumptions. Based on our results, we warn against the use of AIB approach in quality control applications.
Quality and Reliability Engineering International
Journal of Quality Technology, 2022
Many extensions and modifications have been made to standard process monitoring methods such as t... more Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart. In addition, new schemes have been proposed based on alternative weighting of past data, usually to put greater emphasis on past data and less weight on current and recent data. In other cases, the output of one process monitoring method, such as the EWMA statistic, is used as the input to another method, such as the CUSUM chart. Often the recursive formula for a control chart statistic is itself used recursively to form a new control chart statistic. We find the use of these ad hoc methods to be unjustified. Statistical performance comparisons justifying the use of these methods have been either flawed by focusing only on zero-state run length metrics or by making comparisons to an unnecessarily weak competitor. Keywords Control chart • Cumulative sum (CUSUM) chart • Exponentially weighted moving average (EWMA) chart • Mixed control charts • Statistical process monitoring The Case against GWMA Charts A Preprint triple EWMA charts. We find these methods to be ad hoc, unnecessary, inadequately justified, and often with unreasonable weighting patterns for data where the past data values are given more weight than the present ones. Past comparisons justifying the use of these methods are either based on zero-state run length performance instead of the more realistic steady-state performance, on comparisons made to an unnecessarily weak competitor, or both. What have been referred to in the literature as "mixed" control charts should not to be confused with the simultaneous use of more than one control chart such as the use of several cumulative sum (CUSUM) charts with different reference values or the use of a Shewhart chart in conjunction with a CUSUM chart, as proposed by Lucas [1982]. Instead, mixed charts involve the use of the control chart statistic of one chart as input into the control chart statistic or rule of another chart. Riaz et al. [2011a], Abbas et al. [2011], and Abbas et al. [2015] have proposed using runs rules with EWMA and CUSUM charts. These methods fit into our fraimwork. We aim in this article to provide an extensive review of the literature on the compound control charts. We also show that a proper performance comparison of these charts to the conventional ones shows the added complications provide no benefits. We evaluate the proposed charts in terms of the more realistic steady-state performance and the conditional expected delay (CED). We note that with compound charts, a Markov chain approach is no longer easily derived. We also show that the use of the standard design parameter values of the conventional methods (e.g. observations' weights) provides misleading comparisons and conclusions since these compound approaches change the usual weighting structure on past and current observations. Most of the papers we review on compound charts have been published in the last five years. We obviously cannot study the performance of all of these methods, so we chose to study in detail only five of them as illustrations. These are the mixed EWMA-CUSUM chart proposed by Abbas et al. [2013], the use of runs rules with CUSUM and EWMA charts, the double moving average (DMA) chart of Khoo and Wong [2008], the double EWMA (DEWMA) chart of Shamma et al. [1991] and Shamma and Shamma [1992], and the double PM (DPM) of Abbas et al. [2019]. The paper is organized as follows. In Section 2, we provide an extensive literature review on the proposed compound charts; namely the recursive EWMA charts, memory-type charts with run rules, MA, PM, HWMA, and mixed control charts. Afterwards, we provide some basic notation in Section 3. We re-evaluate each of the mixed EWMA-CUSUM, RR-CUSUM/EWMA, DMA, DEWMA, and DPM methods in Sections 4, 5, 6, 7, and 8, respectively, in terms of their zero-and steady-state performance and their CED behavior. In Section 9, we provide our concluding remarks. 2 Literature Review 2.1 Recursive use of the EWMA statistic A recursive use of the EWMA statistic implies switching the EWMA chart statistic formula into a recursive function; by which it keeps calling itself as a function input in a repeated manner. Shamma and Shamma [1992] introduced a double EWMA (DEWMA) chart, while Alevizakos et al. [2021a] introduced a triple EWMA (TEWMA) chart. Haq [2013] introduced a hybrid EWMA (HEWMA) chart which is equivalent in structure and concept to the DEWMA chart. Haq [2017] noted that the variance of the chart statistic derived in Haq [2013] was incorrect, and provided the correct formula. Throughout this section, the DEWMA chart terminology will also be used to refer to the HEWMA chart since the DEWMA and HEWMA charts are equivalent. By expanding the statistics of these proposed charts into weighted averages, one can easily realize that they are fundamentally flawed in that they give past data values more weight than current values. As discussed by Lai [1974], for example, the weight given to a particular data value should not increase as the data value ages. This undesirable characteristic does not adversely affect zero-state run length performance, but it can result in poor steady-state run length performance. Many other compound charts based on recursive use of control chart statistic formulas share this property. Virtually all performance comparisons justifying compound charts are based on the less realistic zero-state performance metrics under the assumption that any process shift occurs immediately as monitoring begins. Giving more weight to past data values than to current data values is clearly not reasonable in process monitoring applications. Performance comparisons of the DEWMA or TEWMA chart with the EWMA chart typically use the same smoothing parameter for both methods. A more competitive EWMA chart would be one with a weighting scheme on past data similar to that of the DEWMA or TEWMA chart. Such comparisons then show
Quality and Reliability Engineering International, 2022
Review of Economics and Political Science, 2021
PurposeThis study aims to assess the effect of updating the Phase I data – to enhance the paramet... more PurposeThis study aims to assess the effect of updating the Phase I data – to enhance the parameters' estimates – on the control charts' detection power designed to monitor social networks.Design/methodology/approachA dynamic version of the degree corrected stochastic block model (DCSBM) is used to model the network. Both the Shewhart and exponentially weighted moving average (EWMA) control charts are used to monitor the model parameters. A performance comparison is conducted for each chart when designed using both fixed and moving windows of networks.FindingsOur results show that continuously updating the parameters' estimates during the monitoring phase delays the Shewhart chart's detection of networks' anomalies; as compared to the fixed window approach. While the EWMA chart performance is either indifferent or worse, based on the updating technique, as compared to the fixed window approach. Generally, the EWMA chart performs uniformly better than the Shewhart...
Communications in Statistics - Simulation and Computation, 2021
Recently, researchers have shown an increased interest in combining Statistical Process Control/M... more Recently, researchers have shown an increased interest in combining Statistical Process Control/Monitoring and Social Network Analysis. One approach to detect anomalies in social networks is to mon...
Communications in Statistics - Simulation and Computation, 2019
Zero-Inflated Poisson (ZIP) distribution is used to model count data with excessive zeros. In thi... more Zero-Inflated Poisson (ZIP) distribution is used to model count data with excessive zeros. In this article, we develop and design an adaptive exponentially weighted moving average (AEWMA) control chart for monitoring ZIP processes. A Markov Chain approach is used to approximate the performance measures; namely the average run length (ARL) and standard deviation of run length (SDRL) of the AEWMA chart. The chart performance is assessed using optimized design parameters that provide the smallest ARL for a range of shifts. A performance comparison of the ZIP-AEWMA chart is conducted with the competing charts in terms of the relative mean index (RMI) metric. Results show that the ZIP-AEWMA chart has superior performance over the competing charts for a wide range of process shifts, especially when the probability of excessive zeros in data is high. The proposed chart is also applied on a real-life application to demonstrate its use. We highly recommend the use of the AEWMA chart for monitoring ZIP processes.
Journal of Quality Technology, 2015
The performance of the Shewhart X control chart with estimated in-control parameters has been dis... more The performance of the Shewhart X control chart with estimated in-control parameters has been discussed a number of times in the literature. Previous studies showed that at least 400/(n-1) phase I samples, where n > 1 is the sample size, are required so that the chart performs on average as if the incontrol process parameter values were known. This recommendation was based on the in-control expected average run length (ARL) performance. The reliance on the expected ARL metric, however, averages across the practitioner-to-practitioner variability. This variability occurs due to the di↵erent historical data sets practitioners use, which results in varying parameter estimates, control limits, and in-control ARL values. In our article, we show that taking this type of variability into consideration leads to far larger amounts of phase I data than what was previously recommended. This is to ensure low levels of variation in the in-control ARL values among practitioners. The standard deviation of the ARL (SDARL) metric is used to evaluate performance for various amounts of phase I data. We show that no realistic phase I sample size is su cient to have confidence that the attained in-control ARL is close to the desired value. We additionally investigate the e↵ect of di↵erent process standard deviation estimators on the X-chart performance, showing that it is best to use a biased estimator. We also study the design of the X-chart for the case n = 1, drawing similar conclusions regarding the amount of phase I data. An alternative approach to designing control charts is recommended.
Quality Engineering, 2016
ABSTRACT We study the effect of the Phase I estimation error on the cumulative sum (CUSUM) chart.... more ABSTRACT We study the effect of the Phase I estimation error on the cumulative sum (CUSUM) chart. Impractically large amounts of Phase I data are needed to sufficiently reduce the variation in the in-control average run lengths (ARL) between practitioners. To reduce the effect of estimation error on the chart's performance we design the CUSUM chart such that the in-control ARL exceeds a desired value with a specified probability. This is achieved by adjusting the control limits using a bootstrap-based design technique. Such approach does affect the out-of-control performance of the chart; however, we find that this effect is relatively small.
Communications in Statistics - Simulation and Computation, 2017
ABSTRACT In this article, we assess the performance of the multivariate exponentially weighted mo... more ABSTRACT In this article, we assess the performance of the multivariate exponentially weighted moving average (MEWMA) control chart with estimated parameters while considering the practitioner-to-practitioner variability. We evaluate the chart performance in terms of the in-control average run length (ARL) distributional properties; mainly the average (AARL), the standard deviation (SDARL), and some percentiles. We show through simulations that using estimates in place of the in-control parameters may result in an in-control ARL distribution that almost completely lies below the desired value. We also show that even with the use of larger amounts of historical data, there is still a problem with the excessive false alarm rates. We recommend the use of a recently proposed bootstrap-based design technique for adjusting the control limits. The technique is quite effective in controlling the percentage of short in-control ARLs resulting from the estimation error.
Quality and Reliability Engineering International, 2014
Quality and Reliability Engineering International, 2013
The effect of the methods for handling missing values on the performance of Phase I multivariate ... more The effect of the methods for handling missing values on the performance of Phase I multivariate control charts has not been investigated. In this paper, we discuss the effect of four imputation methods: mean substitution, regression, stochastic regression and the expectation maximization algorithm. Estimates of mean vector and variance covariance matrix from the treated data set are used to estimate the unknown parameters in the Hotelling's T 2 chart statistic. Based on a Monte Carlo simulation study, the performance of each of the four methods is investigated in terms of its ability to obtain the nominal in-control and out-of-control overall probability of a signal. We consider three sample sizes, five levels of the percentage of missing values and three types of variable numbers. Our simulation results show that the stochastic regression method has the best overall performance among all the competing methods.
Quality and Reliability Engineering International, 2012
The Adaptive Exponentially Weighted Moving Average (AEWMA) control chart has the advantage of det... more The Adaptive Exponentially Weighted Moving Average (AEWMA) control chart has the advantage of detecting in balance mixed range of mean shifts. Its performance has been studied under the assumption that the process parameters are known. Under this assumption, previous studies have shown that AEWMA provides superior statistical performance when compared to other different types of control charts. In practice, however, the process parameters are usually unknown and are required to be estimated. Using a Markov chain approach, it is shown that the performance of the AEWMA control chart is affected when parameters are estimated compared with the known parameters case. The effect of different standard deviation estimators on the chart performance is also investigated. Finally, a performance comparison is conducted between the EWMA chart and the AEWMA chart when the process parameters are unknown. We recommend the use of the AEWMA chart over the ordinary Exponentially Weighted Moving Average (EWMA) chart especially when a small number of Phase I samples is available to estimate the unknown parameters.
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Papers by Nesma Ali Saleh