Double Exponentially Weighted Moving Average Research Articles

Type‐I censored data monitoring using different conditional statistics

AbstractMonitoring censored data is a challenging task and for this purpose, many control charts have been proposed in the literature using different methodologies. In particular, conditional expected value (CEV) and conditional median (CM) are commonly used to replace the censored observations for efficient monitoring. These central tendency measures do not take into account the variation of the data. Thus, the main aim of the article is to propose control charts for type‐I censored data monitoring using conditional standard deviation (CSD) and compare it with the existing censored data charts. To this end, exponentially weighted moving average (EWMA) and double EWMA (DEWMA) charts are proposed and studied assuming CSD, CEV, and CM statistics for Weibull data. Different size of shifts as well as smoothing parameters are considered to evaluate the effectiveness of the CSD based charts compared to the existing charts. The performance of the charts is assessed using average run length and standard deviation of run length. Based on simulations as well as two real data examples, the results indicated that the new measure CSD perform better than the CEV and CM statistics.

A new double EWMA‐t chart with auxiliary information for the process mean

AbstractIn this paper, we propose an auxiliary‐information‐based (AIB) double EWMA‐ (AIB‐DEWMA‐) chart for monitoring the process mean. The DEWMA‐ chart encompasses the EWMA‐ and AIB‐EWMA‐ charts. The Monte Carlo simulations are used to compute the run length characteristics of the AIB‐DEWMA‐ chart. Based on detailed run length comparisons, it is found that the AIB‐DEWMA‐ chart may uniformly and substantially outperform the AIB‐EWMA‐ chart when detecting different shifts in the process mean. In addition, the AIB‐DEWMA‐ chart is uniformly more sensitive than the DEWMA‐ chart. Similar trends are observed when comparing these control charts with the variable sampling interval feature. A real dataset is also considered to demonstrate the implementation of the proposed chart.

Mixed memory control chart based on auxiliary information for simultaneously monitoring of process parameters: An application in glass field

Cumulative sum (CUSUM) and exponentially weighted moving (EWMA) control charts, known as memory control charts, are famous to monitor a small-to-moderate shift in the process parameters (location and/or dispersion). The EWMA control chart based on auxiliary information denoted as EWMAAIB(1) and EWMAAIB(2) are advanced forms of the classical EWMA control chart to monitor the process location and dispersion, respectively. Likewise, the combined mixed EWMA-CUSUM (CMEC) control chart is used to simultaneously monitor the process parameters. This study presents the CMEC control chart based on auxiliary information, symbolized as CMECAIB control chart for simultaneous monitoring of the process parameters. The proposed CMECAIB control chart used EWMAAIB(1) and EWMAAIB(2) control charts plotting statistics as inputs in the classical CUSUM control charts. The Monte Carlo simulation is used as a computational technique for numerical results. The proposed CMECAIB control chart based on average run length performance measure is evaluated against other control charts such as CMEC, combined double mixed EWMA-CUSUM, combined CUSUM, maximum double EWMA, maximum EWMA based on auxiliary information (MaxEWMAAIB) control and maximum Hybrid EWMA based on auxiliary information (MaxHEWMAAIB) control charts. The comparison revealed the superiority of the proposed CMECAIB control chart. Besides, the CMECAIB control chart performs better as the correlation coefficient increases. Likewise, the proposed CMECAIB control chart has a better diagnostic ability for possible directions of changes against other control charts. It is vital to mention that some existing control charts such as classical CUSUM, CMEC, and maximum CUSUM are special cases of proposed CMECAIB control chart with the specific parameter’s values. Finally, to demonstrate the vitality of the proposed study from a practical point of view, a real-life application in the glass bottle manufacturing industry is also provided for users and practitioners.

A sum of squares triple exponentially weighted moving average control chart

AbstractControl charts are widely known quality tools used to detect and control industrial process deviations in statistical process control. In the current paper, we propose a new single memory‐type control chart, called the sum of squares triple exponentially weighted moving average control chart (referred as SS‐TEWMA chart), that simultaneously detects shifts in the process mean and/or process dispersion. The run length performance of the proposed SS‐TEWMA control chart is compared with that of the sum of squares EWMA, sum of squares double EWMA, sum of squares generally weighted moving average, and sum of squares double generally weighted moving average, control charts, through Monte Carlo simulations. The comparisons indicate that the proposed chart is more efficient, than the competing ones, in detecting small shifts in the process mean and/or variability for most of the considered scenarios, while it has comparable performance for some others in identifying large shifts in the process mean and small to large shifts in the process variability. Finally, two illustrative examples are provided to explain the application of the SS‐TEWMA control chart.

On the Development of Triple Homogeneously Weighted Moving Average Control Chart

To detect sustainable changes in the manufacturing processes, memory-type charting schemes are frequently functioning. The recently designed, homogenously weighted moving average (HWMA) technique is effective for identifying substantial changes in the processes. To make the HWMA chart more effective for persistent shifts in the industrial processes, a double HWMA (DHWMA) chart has been proposed recently. This study intends to develop a triple HWMA (THWMA) chart for efficient monitoring of the process mean under zero- and steady-state scenarios. The non-normal effects of monitoring characteristics under in-control situations for heavy-tailed highly skewed and contaminated normal environments are computed under both states. The relative efficiency of the proposed structure is compared with HWMA, DHWMA, exponentially weighted moving average (EWMA), double EWMA, and the more effective triple EWMA control charting schemes. The relative analysis reveals that the proposed THWMA design performs more efficiently than the existing counterparts. An illustrative application related to substrate manufacturing is also incorporated to demonstrate the proposal.

The extended homogeneously weighted moving average control chart

AbstractControl charts are widely applied in many manufacturing processes to monitor the quality characteristic of interest. Recently, a homogeneously weighted moving average (HWMA) control chart was proposed as an improvement of the exponentially weighted moving average (EWMA) chart for efficiently monitoring of small shifts in the process mean. In the present article, we extend the HWMA chart by imitating exactly the double EWMA (DEWMA) technique. The proposed scheme is regarded as double HWMA (DHWMA) control chart. The run‐length characteristics of the proposed chart are evaluated by performing Monte Carlo simulations. A comparison study versus the EWMA, DEWMA, HWMA, mixed EWMA cumulative sum (CUSUM), CUSUM, and GWMA charts indicates that the DHWMA chart is more effective in detecting small to moderate shifts, while it performs similarly with its competitors for large shifts. We also study the robustness of the proposed chart under several nonnormal distributions, and it is shown that the DHWMA chart is in‐control robust for small values of the smoothing parameters. Finally, two examples are given to demonstrate the implementation of the proposed chart.

Distribution‐free triple EWMA control chart for monitoring the process location using the Wilcoxon rank‐sum statistic with fast initial response feature

AbstractThe exponentially weighted moving average (EWMA) control chart is a memory‐type chart known to be more efficient in detecting small and moderate shifts in the process parameter. The double EWMA (DEWMA) chart is an extension of the EWMA chart that is more effective than the latter in the detection of small‐to‐moderate shifts. This paper proposes a new distribution‐free (or nonparametric) triple EWMA (TEWMA) control chart based on the Wilcoxon rank‐sum (W) statistic to improve the detection ability in the process location parameter. Moreover, a new fast initial response (FIR) feature is added to further improve the sensitivity of the new TEWMA chart. The performance of the proposed TEWMA chart with and without FIR features is compared to those of the existing EWMA and DEWMA W charts. It is observed that the TEWMA chart with and without FIR features is superior to the competing charts in most situations. A real‐life illustration is provided to show the application and implementation of the new chart.

A nonparametric triple exponentially weighted moving average sign control chart

AbstractNonparametric control charts are used in process monitoring when there is insufficient information about the form of the underlying distribution. In this article, we propose a triple exponentially weighted moving average (TEWMA) control chart based on the sign statistic for monitoring the location parameter of an unknown continuous distribution. The run‐length characteristics of the proposed chart are evaluated performing Monte Carlo simulations. We also compare its statistical performance with existing nonparametric sign charts, such as the cumulative sum (CUSUM), exponentially weighted moving average (EWMA), generally weighted moving average (GWMA), and double exponentially weighted moving average (DEWMA) sign charts as well as the parametric TEWMA‐ chart. The results show that the TEWMA sign chart is superior to its competitors, especially for small shifts. Moreover, two examples are given to demonstrate the application of the new scheme.

A triple exponentially weighted moving average control chart for monitoring time between events

AbstractTime between events (TBE) charts are used in high‐yield processes where the rate of occurrences is very low. In the current article, we propose a triple exponentially weighted moving average control chart to monitor TBE (regarded as triple exponentially weighted moving average TEWMA‐TBE chart) modeled by a gamma distribution. One‐ and two‐sided schemes of the proposed chart are designed and compared with the double EWMA DEWMA‐TBE and EWMA‐TBE charts. It is shown that the lower‐ and two‐sided TEWMA‐TBE charts outperform its competitors, especially for small to moderate downward shifts, while the upper‐sided TEWMA‐TBE chart has very good detection ability for small shifts. We also study the robustness of the proposed chart when the true distribution is a Weibull or a lognormal and it is found that the TEWMA‐TBE chart has better robustness properties than its competitors, especially for small shifts. Two illustrative examples from airplane accidents and earthquakes are also provided to display the application of the proposed chart.

Economic Design of X̅ Control Chart under Double EWMA

Designing of parameters plays an important role in economic design of control charts for lowering the cost and time. Manipulating sample size (n) and sampling interval (h), the effect of double exponentially weighted moving average (DEWMA) model was studied for the Economic Design (ED) of X̅ control chart. Optimum sizes and level were obtained when the characteristics of an item possesses DEWMA model. When shifts are uncertain the optimal design for DEWMA chart should be more conservative and should be implemented for benefiting the consumers as well as producers.

Auxiliary information based maximum EWMA and DEWMA charts with variable sampling intervals for process mean and variance

The maximum EWMA (ME) and maximum double EWMA (MDE) charts are used to detect joints shifts in mean and variance of a normal process. In this paper, we propose the ME and MDE charts using the variable sampling interval (VSI) feature. In addition, the VSI feature is also attached with auxiliary information based (AIB) ME and MDE charts. Using Monte Carlo simulations, the run length characteristics of these control charts are computed. Based on detailed run length comparisons, it is found that the ME and MDE (AIB-ME and AIB-MDE) charts with VSI are more sensitive than those with fixed sampling interval. A real dataset is considered to demonstrate the implementation of proposed charts.

A novel approach to monitor simple linear profiles using individual observations

In some quality control applications, quality of a product or process may be characterized effectively by a functional relationship between one or more variables that is typically referred to as a profile. In this paper, we propose four control charts, namely the maximum CUSUM (MaxCUSUM), maximum Crosier CUSUM (MaxCCUSUM), maximum EWMA (MaxEWMA) and maximum double EWMA (MaxDEWMA) charts, for monitoring the parameters of a Phase II simple linear profile using the individual observations. In addition, the sensitivities of these control charts are also enhanced with the variable sampling interval feature. The Monte Carlo simulation method is used to compute the zero-state and steady-state run length characteristics of the proposed charts. The run length comparisons reveal that the MaxCCUSUM (MaxDEWMA) chart is slightly more sensitive than the MaxCUSUM (MaxEWMA) chart. A real dataset is also considered to support the theory.

On developing an exponentially weighted moving average chart under progressive setup: An efficient approach to manufacturing processes

AbstractThe exponentially weighted moving average (EWMA) control chart is a memory chart that is widely used in process monitoring to spot small and persistent disturbances in the process parameter(s). This chart requires normality of the quality characteristic(s) of interest and a smaller choice of smoothing parameter. Any deviations from these conditions affect its performance in terms of efficiency and robustness. For the said two concerns, this study develops a new mixed EWMA chart under progressive setup (mixed EWMA–progressive mean [MEP] chart). The proposed MEP chart combines the advantages of robustness (under nonnormal scenarios) and high sensitivity to small and persistent shifts in the process mean. The performance of the proposed MEP control chart is evaluated in terms of average run length and some other characteristics of run length distribution. The assessment of the proposed chart is made under standard normal, student's t, gamma, Laplace, logistic, exponential, contaminated normal and lognormal distributions. The performance of the proposed MEP chart is also compared with some existing competitors including the classical EWMA, the classical cumulative sum (CUSUM), the homogenously weighted moving average, the mixed EWMA–CUSUM, the mixed CUSUM–EWMA and the double EWMA charts. The analysis reveals that the proposal of this study offers a superior design structure relative to its competing counterparts. An application from substrates manufacturing process (in which flow width of the resist is the key quality characteristic) is also provided in the study.

Maximum weighted adaptive CUSUM charts for simultaneous monitoring of process mean and variance

ABSTRACT In this paper, we propose maximum weighted adaptive Crosier CUSUM (MaxWACCUSUM) charts with three different unbiased estimators of the process mean and variance shifts for joint monitoring of the mean and variance of a normal process. The MaxWACCUSUM charts provide an overall good performance for detecting a range of joint mean and dispersion shift sizes. The run length characteristics of the proposed charts are computed using the Monte Carlo simulation method. A detailed comparative study is conducted to compare the run length performances of the proposed and existing charts. It is found that the MaxWACCUSUM charts are more sensitive than the maximum EWMA, double EWMA and CUSUM charts when detecting a range of joint shift sizes. Real datasets are considered to support the theory.

A Double Generally Weighted Moving Average Chart for Monitoring the COM-Poisson Processes

Generalized exponentially weighted moving average (EWMA) and double EWMA (DEWMA) charts based on the Conway–Maxwell–Poisson (CMP or COM-Poisson) distribution, also known as the GEWMA and CMP-DEWMA charts, are effectively used for monitoring the counts of non-conformities in a process. To further enhance their performance, this study utilizes design and adjustment parameters to develop generally weighted moving average (GWMA) and double GWMA charts, also known as the CMP-GWMA and CMP-DGWMA charts, to monitor COM-Poisson attributes. Numerical simulations indicate that the CMP-DGWMA chart outperforms its prototype CMP-DEWMA and CMP-GWMA charts in detecting small location and dispersion shifts, as well as both shifts together, in terms of average run lengths. Finally, an example is provided to demonstrate the efficiency of the proposed CMP-DGWMA chart and its counterparts.

Design of a run‐to‐run controller based on discrete sliding‐mode observer

AbstractIn this study, a run‐to‐run controller based on a discrete sliding‐mode observer (DSMO) is presented for photolithography manufacturing processes. A second‐order DSMO is introduced to estimate the process disturbances caused by tool aging and preventive maintenance. The proposed controller is constructed by applying DSMO estimation to the deadbeat control law and the stable region is discussed. Numerical simulations and an industrial case demonstrated the performance of the proposed algorithm. It is observed that the proposed controller has a superior performance over the exponentially weighted moving average (EWMA) and double EWMA (dEWMA) controller under the first‐order integrated moving average disturbance with shift or drift. This superiority is maintained when the system contains a certain plant‐model mismatch. Moreover, the tolerance of the proposed controller for metrology delay is better than that of the dEWMA controller.

Run-to-run control of batch production process in manufacturing systems based on online measurement

Run-to-run control is an important and effective method for quality control of batch production process in manufacturing systems. Most of current run-to-run control methods are investigated based on offline sampled measurement due to the limitation of measurement technology. The sampled measurements cannot represent each run, thus lead to performance deterioration of run-to-run control methods. The development of new measurement technologies provides great opportunities to improve product quality, since all data of each run is obtained by online measurement. This paper presents a systematic run-to-run control method for batch production process in manufacturing systems based on online measurement. Firstly, a single-input-single-output process model of multiple workpieces (MSISO) is built and a MSISO double exponentially-weighted-moving-average (EWMA) controller is proposed. The proposed MSISO double EWMA controller updates control recipe of current run based on all output data of its previous run. Then, the stability analysis of the proposed MSISO double EWMA controller is conducted to obtain the sufficient conditions for the asymptotic stability of the control process in manufacturing systems. Mean square error (MSE) is used to evaluate the quality control performance. The results of simulation experiments and a case study show that the proposed method can effectively improve the control performance for batch production process in manufacturing systems when compared to other run-to-run-based methods.

A Nonparametric Repetitive Sampling DEWMA Control Chart Based on Linear Prediction

Distribution-free control charts can be useful in statistical process control (SPC) when only limited or no information about the distribution of the data of the process is available. In this paper, a linear prediction related double exponentially weighted moving average (DEWMA) sign control chart using a repetitive sampling scheme (RSNPDEBLP) has been considered for a binomially distributed process variable to improve the efficiency of detecting small drifts in its place of small changes. The proposed RSNPDEBLP control chart is assessed in average run length (ARL) for the various values of sample sizes. The efficiency of the proposed RSNPDEBLP control chart is compared with the existing EWMA and DEWMA sign control charts using single sampling and repetitive sampling schemes in terms of ARLs. When there are small changes in the process after the stabilization period, the proposed control chart is used to control small trends rather than small shifts.

An Efficient Mixed-Memory-Type Control Chart for Normal and Non-Normal Processes

Statistical process control techniques are commonly used to monitor process performance. Control charting technique is the most sophisticated tool of SPC and is categorized as memory-less and memory-type control charts. Shewhart-type control charts have low efficiency in detecting the small changes in the process parameters and named as memory-less control charts, and memory-type control charts (for example cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts) are very sensitive to small persistent shifts. In connection with enhancing the performance of CUSUM and EWMA charts, an efficient variant of memory-type charts for the location parameter is developed based on mixing the double exponentially weighted moving average (DEWMA) chart and CUSUM chart by performing exponential smoothing twice. Performance of the proposed efficient variant is compared with existing counterparts under normal and non-normal (heavy tails and skewed) environments. The study also provides an industrial application related to the monitoring of weights of quarters made by mint machine placed into service at U.S. Mint. From theoretical and numerical studies, it is revealed that proposed variant of memory-type charts outperforms the counterparts in detecting shifts of small and moderate magnitude.

Monitoring of zero‐inflated Poisson processes with EWMA and DEWMA control charts

AbstractThe zero‐inflated Poisson (ZIP) distribution is an extension of the ordinary Poisson distribution and is used to model count data with an excessive number of zeros. In ZIP models, it is assumed that random shocks occur with probability p, and upon the occurrence of random shock, the number of nonconformities in a product follows the Poisson distribution with parameter λ. In this article, we study in more detail the exponentially weighted moving average control chart based on the ZIP distribution (regarded as ZIP‐EWMA) and we also propose a double EWMA chart with an upper time‐varying control limit to monitor ZIP processes (regarded as ZIP‐DEWMA chart). The two charts are studied to detect upward shifts not only in each parameter individually but also in both parameters simultaneously. The steady‐state performance and the performance with estimated parameters are also investigated. The performance of the two charts has been evaluated in terms of the average and standard deviation of the run length, and compared with Shewhart‐type and CUSUM schemes for ZIP distribution, it is shown that the proposed chart is very effective especially in detecting shifts in p when λ remains in control (IC) and in both parameters simultaneously. Finally, one real example is given to display the application of the ZIP charts on practitioners.