Control Charts For Process Monitoring Research Articles

Mixed Tukey Exponentially Weighted Moving Average-Modified Exponentially Weighted Moving Average Control Chart for Process Monitoring

The goal of this study is to present the mixed Tukey exponentially weighted moving average-modified exponentially weighted moving average control chart (MEME-TCC) for monitoring process location with symmetric and skewed distributions in an attempt to significantly improve detection ability. With the benefits of nonparametric assumption robustness. The average and median run lengths are supporting measurements for assessing the performance of a monitoring scheme using Monte Carlo simulation. Furthermore, the average extra quadratic loss (AEQL), relative mean index (RMI), and performance comparison index (PCI) can all be used to evaluate overall performance criteria. The proposed chart is compared with existing charts such as; EWMA, MEWMA, TCC, MEME, MMEE, and MMEE-TCC. The comparison result shows that the proposed chart is the best control chart for detecting small to moderate shifts among all distributional settings. Nevertheless, the EWMA chart detects large shifts more effectively than other charts, except in the case of the gamma distribution, where MEWMA performs best. The results of adapting the proposed control chart to two sets of real data corresponded to the research findings. Doi: 10.28991/ESJ-2023-07-03-014 Full Text: PDF

Asymmetric Control Limits for Weighted-Variance Mean Control Chart with Different Scale Estimators under Weibull Distributed Process

Shewhart charts are the most commonly utilised control charts for process monitoring in industries with the assumption that the underlying distribution of the quality characteristic is normal. However, this assumption may not always hold true in practice. In this paper, the weighted-variance mean charts are developed and their population standard deviation is estimated using the three subgroup scale estimators, namely the standard deviation, median absolute deviation and standard deviation of trimmed mean for monitoring Weibull distributed data with different coefficients of skewness. This study aims to compare the out-of-control average run length of these charts with the pre-determined fixed value of the in-control ARL in terms of different scale estimators, coefficients of skewness and sample sizes via extensive simulation studies. The results indicate that as the coefficients of skewness increase, the charts tend to detect the out-of-control signal more rapidly under identical magnitude of shift. Meanwhile, as the size of the shift increases under the same coefficient of skewness, the proposed charts are able to locate the shifts quicker and the similar scenarios arise as a sample size raised from 5 to 10. A real data set from survival analysis domain which, possessing Weibull distribution, was to demonstrate the usefulness and applicability of the proposed chart in practice.

New modified exponentially weighted moving average-moving average control chart for process monitoring

The mixed control chart is proposed to improve detection performance with fewer process shifts. In this study, we proposed the modified exponentially weighted moving average - moving average control chart (MMEM), a new mixed control chart for observing the changes in the process mean. Average run length, standard deviation of run length, and median run length can be used to examine the effectiveness of detecting changes in the proposed chart with Shewhart, Moving Average (MA), Modified Exponentially Weighted Moving Average (MEWMA), and Mixed Moving Average - Modified Exponentially Weighted Moving Average (MMME) control charts in parametric and nonparametric distributions that use Monte Carlo simulation. The results demonstrate that the proposed chart outperforms other control charts mostly in the detection of small-to-moderate shifts. To illustrate the application of the proposed chart, chemical process temperature data and dataset on survival times of a group of patients suffering from head and neck cancer disease and treated with radiotherapy were provided, and it was discovered that the proposed chart performs better than other control charts.

A hybrid homogeneously weighted moving average control chart for process monitoring: Discussion

AbstractThe sensitivity of a monitoring scheme depends on many factors including the variance of the charting statistic which is very important in the computation of the control limits. This paper discusses the computation of the variance of the recently proposed hybrid homogeneously weighted moving average (HHWMA) scheme which was based on an incorrect assumption. The correct variance is used to evaluate the run‐length characteristics of the HHWMA scheme. It is observed that the incorrect variance has a significant impact on the sensitivity (or performance) of the HHWMA scheme.

Fuzzy Heuristics and Decision Tree for Classification of Statistical Feature-Based Control Chart Patterns

Monitoring manufacturing process variation remains challenging, especially within a rapid and automated manufacturing environment. Problematic and unstable processes may produce distinct time series patterns that could be associated with assignable causes for diagnosis purpose. Various machine learning classification techniques such as artificial neural network (ANN), classification and regression tree (CART), and fuzzy inference system have been proposed to enhance the capability of traditional Shewhart control chart for process monitoring and diagnosis. ANN classifiers are often opaque to the user with limited interpretability on the classification procedures. However, fuzzy inference system and CART are more transparent, and the internal steps are more comprehensible to users. There have been limited works comparing these two techniques in the control chart pattern recognition (CCPR) domain. As such, the aim of this paper is to demonstrate the development of fuzzy heuristics and CART technique for CCPR and compare their classification performance. The results show the heuristics Mamdani fuzzy classifier performed well in classification accuracy (95.76%) but slightly lower compared to CART classifier (98.58%). This study opens opportunities for deeper investigation and provides a useful revisit to promote more studies into explainable artificial intelligence (XAI).

Modified EWMA and DEWMA control charts for process monitoring

The modified exponentially weighted moving average (MEWMA) control chart has been proposed in the literature in an effort to improve the performance of the classical EWMA chart. In this article, we study in more detail the MEWMA chart using various values of its additional design parameter and we also propose the double MEWMA (DMEWMA) chart for monitoring shifts in the process mean, under the assumption that the underlying process follows a normal distribution. The statistical performance of the two charts has been evaluated on the basis of the average and standard deviation of run-length performing Monte Carlo simulations. A comparison study versus the EWMA and DEWMA charts indicate that the modified schemes have better detection ability for the range of shifts where a classical chart is not optimal designed. Finally, one real example is given to demonstrate the application of the proposed chart.

The median control chart for process monitoring in short production runs

The implementation of the chart requires a large number of samples from an underlying process model, which poses a major problem in short production runs, like in the fast-paced smart manufacturing environment. In this study, the median chart, as a robust alternative to the chart, is used to efficiently monitor the normal or non-normal processes in short production runs. The sensitivity of the median chart is assessed in terms of the truncated average run length (TARL), truncated standard deviation of the run length (TSDRL) and expected TARL criteria. The in-control and out-of-control run length performances of the and the median charts are compared when sampling from non-normally distributed processes in short production runs. It is found that when a non-normal process is in-control, the median chart outperforms the chart, as the latter possesses smaller in-control TARL and higher in-control TSDRL values. In addition, for a non-normal (heavy-tailed) out-of-control process, the median chart prevails over the chart. An illustrative example is given to explain the implementation of the median chart in short production runs.

A hybrid homogeneously weighted moving average control chart for process monitoring

AbstractSeveral modifications and enhancements to control charts in increasing the performance of small and moderate process shifts have been introduced in the quality control charting techniques. In this paper, a new hybrid control chart for monitoring process location is proposed by combining two homogeneously weighted moving average (HWMA) control charts. The hybrid homogeneously weighted moving average (HHWMA) statistic is derived using two smoothing constants λ1 and λ2. The average run length (ARL) and the standard deviation of the run length (SDRL) values of the HHWMA control chart are obtained and compared with some existing control charts for monitoring small and moderate shifts in the process location. The results of study show that the HHWMA control chart outperforms the existing control charts in many situations. The application of the HHWMA chart is demonstrated using a simulated data.

On a class of mixed EWMA‐CUSUM median control charts for process monitoring

AbstractMonitoring of any manufacturing, production, or industrial process can be controlled and improved by removing these special cause of variations using control charts. Shewhart‐type control charts are effective to control a large amount of special variations, whereas, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts detect small and moderate variations efficiently in the process parameters. Monitoring of location parameter can be done with mean control charts under the assumption that the parameters are known or correctly estimated from in‐control samples and data are free from outliers (but in practice data occasionally have outliers). In this study, we have proposed generalized mixed EWMA‐CUSUM median control charts structures for known and unknown parameters based on auxiliary variables for detecting shifts in process location parameter. The proposed charts are compared with the corresponding charts for the mean, based on contaminated and uncontaminated data. Different performance measures are used to evaluate the performance of proposed control charts and revealed through results that the median‐based charts are more sensitive to detect a shift in process location parameter in the presence of outliers. An illustrative example using real data is also shown for practical consideration.

Sensor-Based Recurrence Analysis of Energy Efficiency in Machining Processes

Manufacturing industry incurs a large portion of energy consumption and carbon emission in the economy. Traditionally, smart energy management depends on aggregated measures from billing information, as well as physics-based models, empirical results derived from extensive experiments, which tend to be limited in the ability for real-time monitoring of energy efficiency. There is an urgent need to develop energy monitoring solutions for more transparency about energy use. This paper presents a new sensor-based approach for recurrence analysis of continuous power signals and multi-state modeling of energy efficiency in the machining process. First, we leverage the recurrence plot to characterize the nonlinear variations in power signals and further help delineate different states in the machining process, thereby providing statistics of energy consumption in each state. Second, we compute the composite index of energy efficiency for each workpiece and then develop multivariate statistical control charts for process monitoring of continuous production of workpieces. Third, after an anomaly is detected, we propose the orthogonal decomposition approach to diagnose the root cause of abnormal states in the energy use. The proposed methodology is evaluated and validated on real-world manufacturing of shaft-like parts in a machine shop. Experimental results show that the prediction error of energy efficiency from sensor-based models is within 5% from the ground truth, which show great potentials to implement sensor-based monitoring and analysis of real-time energy efficiency in the manufacturing process.

Shewhart control chart for monitoring the mean of Poisson mixed integer autoregressive processes via Monte Carlo simulation

Most control charts for process monitoring assume independence among observations and that the nature of the characteristics of interest is continuous. However, these assumptions are often violated in practice, include industrial engineering applications. For integer-valued autocorrelated processes, usual control charts have a poor performance. Time-series modeling and modified control limits play a fundamental role in such circumstances. In this paper, we propose a Shewhart control chart for monitoring the mean when observations can be modeled as a first order Poisson mixed integer autoregressive model - POMINAR(1) process. The performance of the proposed approach is investigated based on in-control and out-of-control average run lengths (ARL0 and ARL1, respectively) in different scenarios. Both the determination of the control limits and the evaluation of the chart are done through computational studies using Monte Carlo simulations. Practical use of the proposed approach is illustrated with two real examples for monitoring crime data and network traffic.

Robust bootstrap control charts for percentiles based on model selection approaches

Abstract This paper presents two model selection approaches, namely the random data-driven approach and the weighted modeling approach, to construct robust bootstrap control charts for process monitoring of percentiles of the shape-scale class of distributions under model uncertainty. The generalized exponential, lognormal and Weibull distributions are considered as candidate distributions to establish the proposed process control procedures. Monte Carlo simulations are conducted with various combinations of the percentiles, false-alarm rates and sample sizes to evaluate the performance of the proposed robust bootstrap control charts in terms of the average run lengths. Simulation results exhibit that the two proposed robust model selection approaches perform well when the underlying distribution of the quality characteristic is unknown. Finally, the proposed process monitoring procedures are applied to two data sets for illustration.

On designing a robust double exponentially weighted moving average control chart for process monitoring

A double exponentially weighted moving average chart has been proven more efficient for monitoring process mean in comparison to the classical exponentially weighted moving average chart. We, in this article, made a careful investigation on how well this scheme performs with the presence of disturbances in the process under consideration. This investigation was motivated in exploring the scheme with some robust statistic, as the mean estimator performs woefully. We also evaluated the effects of parameter estimation on the phase II assuming the parameters are unknown. Adopting a 20% trimmed mean of trimeans (robust) reveals the effect of parameter estimations. We substantiated these claims by applying the scheme on a real-life data set. The findings of the study pronounced the trimean estimator to be the best of all the five estimators used, including the mean.

Design of an attribute np control chart for process monitoring based on repetitive group sampling under truncated life tests

ABSTRACTIn this paper, an attribute control chart under repetitive group sampling is designed for monitoring the production process where the lifetime of the product is considered as quality of the product. We assume that the lifetime follows the Pareto distribution of second kind with known shape parameter. The performance of the proposed chart is evaluated by average run length. The control limits coefficients as well as the repetitive group sampling parameter such as sample size are determined such that the in-control average run length is as close as to the specified average run length. Out-of-control average run length is also reported for different shift constants with corresponding optimal parameters. In addition, performance of proposed control chart is compared with the performance of existing chart. An economical designing of proposed control chart is also discussed.

On enhanced sensitivity of nonparametric EWMA control charts for process monitoring

Control charts are popular tounderols for process monitoring and are mainly classi ed into memory and memory-less structures. Exponentially Weighted Moving Average control charts (EWMA) are widely used for the detection of small shifts in process parameters. The traditional design structures of these types of charts rely on the stringent assumption of normality. In practice, quality characteristics generally do not follow normality; hence, alternative charting structures are needed. Nonparametric control chart is one such alternative that do not depend on the mentioned distributional assumption(s). This study deals with nonparametric EWMA charts for an ecient detection of smaller shifts in location. We have investigated asymptotic, time-varying, and Fast Initial Response (FIR) based time varying control limits for nonparametric EWMA charts. We have considered two variants of FIR with time varying limits for nonparametric EWMA structure. A variety of run length properties have been investigated for performance evaluations. It is observed that FIR-based nonparametric EWMA charts with time-varying limits are quite sensitive to detecting smaller shifts, and they o er attractive run length properties. A real-life example is also provided to illustrate the application of the time-varying and FIR-based nonparametric EWMA control charts.

An Economic Design of A Modified Synthetic Double Sampling Control Chart for Process Monitoring

An Economic Design of A Modified Synthetic Double Sampling Control Chart for Process Monitoring

Robust point location estimators for the EWMA control chart

In practice, the EWMA control chart for process monitoring is based on parameters estimated from a retrospective data set representing the process characteristic under study. This data set may contain contaminated observations, which in turn can affect the estimates and hence the control chart’s performance. We study the problem of estimating the location when the data set may or may not contain contaminated observations. We compare six point estimators proposed in the SPC literature. The quality of the estimators is evaluated in terms of estimation accuracy. Moreover, we study the impact of the estimators on the performance of the EWMA control chart based on the different location estimators.

The variable sampling interval run sum [formula omitted] control chart

Traditional control charts for process monitoring are based on taking samples from the process at fixed length sampling intervals. More recently, research works focused on the use of variable sampling intervals (VSIs), where the lengths of the sampling intervals are varied according to the process quality. A short sampling interval is considered when the process quality indicates a possible out-of-control situation while a long sampling interval is considered, otherwise. In this paper, the VSI run sum (RS) X‾ chart is proposed with its optimal scores and parameters determined using an optimization technique to minimize the out-of-control average time to signal (ATS) or the adjusted average time to signal (AATS). A Markov-chain method is used to evaluate both the ATS and AATS of the proposed chart, for the zero and steady state cases, respectively. Results show that the VSI RS X‾ chart is considerably more efficient than the basic RS X‾ chart. The VSI RS X‾ chart performs generally well compared with other competing charts, such as the standard X‾, synthetic X‾, exponentially weighted moving average (EWMA) X‾, VSI X‾ and VSI EWMA X‾ charts. The sensitivity of the VSI RS X‾ chart can be enhanced further by adding more scoring regions or a head-start feature. An illustrative example is presented to explain the implementation of the proposed VSI RS X‾ chart.

On designing a new Tukey-EWMA control chart for process monitoring

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are used to detect smaller shifts in process parameters. The usual EWMA and CUSUM charts depend on the normality assumption for a better detection ability. This study proposes an efficient EWMA control chart based on the spirit of Tukey control chart, especially designed for skewed distributions. The performance of the proposed and the competing charts is measured using different length properties such as average run length (ARL), standard deviation of run length (SDRL), and median run length (MDRL). We have observed that the proposed chart is quite efficient at detecting process shifts of smaller magnitude, especially for skewed distributions. For practical considerations, the proposed chart is implemented at aerospace manufacturing data on industrial production index.

Robust Tukey–CUSUM Control Chart for Process Monitoring

In real world scenarios, we continuously inspect the performing behavior of different features of processes. A change in the process parameters may affect the product quality and therefore needs a timely identification. For this purpose we have designed new memory structure based on Tukey control chart (TCC) under cumulative sum (CUSUM) setup. The proposed chart, namely Tukey‐CUSUM, combines the feature of TCC with CUSUM design for improved detection of shifts for normal and non‐normal data. The performance of the study proposal is evaluated through different measures based on run length including ARL, EQL, PCI and RARL. We have observed that the proposed Tukey‐CUSUM design is quite robust and efficient, especially using asymmetrical decision intervals for different process models. An application example is also provided to illustrate the study proposal. Moreover, sample selection is always of great concern for practitioners so we have included a brief description of the steps for sample selection with reference to process monitoring. Copyright © 2015 John Wiley & Sons, Ltd.