Chart For Processes Research Articles

CUSUM charts utilizing reparametrized Birnbaum-saunders model for fault detection and process control

Statistical process control is always intrigued by the design of effective control charts for monitoring production processes and determining assignable causes of variations. It can be challenging to keep track of a positive asymmetric response variable while considering the impact of the input variables. The current work incorporates the Reparametrized Birnbaum Saunders (RBS) model to develop more effective cumulative sum (CUSUM) control charts for analyzing the mean of such a process. We perform a simulation study to evaluate the effectiveness of existing and derived approaches in terms of run length characteristics. The findings showed that when the underlying process distribution is positively asymmetric, the proposed charts provide stronger protection against process alterations as compared to existing methods. Moreover, the suggested control charts are implemented using actual data from a combined cycle power plant.

A control chart for monitoring image processes based on convolutional neural networks

In this paper, the problem of monitoring image processes with spatially correlated pixels over time is considered. An exponentially weighted moving average (EWMA) control chart for monitoring such processes based on a convolutional neural network (CNN) is proposed. A comparison of its performance with a Hotelling's control chart and with a control chart based on generalized likelihood ratio (GLR) approach is conducted through a simulation study. The new method outperforms other methods in most of the cases considered in the simulation study. A technique for mean intensity shift localization based on CNNs is proposed and evaluated.

Control charts for monitoring the capability of unstable process

Stability is an important criterion to be investigated at the early stage of any industrial process and stable processes are usually preferred over unstable ones. But a process can be unstable and nevertheless capable and, therefore, there is a clear need to monitor such situations to ensure an acceptable capability. In this study we introduce, in a first step, a new Shewhart-type control chart for normal processes based on the yield index S pk to monitor the capability of potentially unstable processes and then, in a second step, we extend it using an Exponentially Weighted Moving Average (EWMA) scheme. Moreover, the optimal values of the control parameters are obtained using a nonlinear optimization problem for which the out-of-control average run length is the objective function. The introduced charts’ sensitivity is examined for deterministic shift sizes. Numerical and graphical analyses are given to display the features of the proposed charts. A simulation study shows, how in such a situation, the introduced tool is successful to recognize changes in the process capability.

Memory-type time-between-events charts using nonhomogeneous Poisson process

The traditional time-between-events (TBE) control charts are developed in non-adaptive fashion assuming the Poisson process, where the TBE follows the exponential distribution. However, in many situations we need an adaptive strategy, especially for healthcare or system monitoring. The focus of this study is to introduce new exponentially weighted moving average and cumulative sum adaptive TBE control charts for high-quality processes based on nonhomogeneous Poisson process by assuming the power law intensity. Charts assuming the nonhomogeneous Poisson process are dynamic and can be used where the underlying failure rate may be changing over time. The performance of the proposed control charts is evaluated using the average run length and coefficient of variation of the run length distribution. Three real data examples which correspond to different shape parameters of the power law process are also discussed in the article.

Memory type Bayesian adaptive max-EWMA control chart for weibull processes

The simultaneous monitoring of both the process mean and dispersion has gained considerable attention in statistical process control, especially when the process follows the normal distribution. This paper introduces a novel Bayesian adaptive maximum exponentially weighted moving average (Max-EWMA) control chart, designed to jointly monitor the mean and dispersion of a non-normal process. This is achieved through the utilization of the inverse response function, particularly suitable for processes conforming to a Weibull distribution. To assess the effectiveness of the proposed control chart, we employed the average run length (ARL) and the standard deviation of run length (SDRL). Subsequently, we compared the performance of our proposed control chart with that of an existing Max-EWMA control chart. Our findings suggest that the proposed control chart demonstrates a higher level of sensitivity in detecting out-of-control signals. Finally, to illustrate the effectiveness of our Bayesian Max-EWMA control chart under various Loss Functions (LFs) for a Weibull process, we present a practical case study focusing on the hard-bake process in the semiconductor manufacturing industry. This case study highlights the adaptability of the chart to different scenarios. Our results provide compelling evidence of the exceptional performance of the suggested control chart in rapidly detecting out-of-control signals during the hard-bake process, thereby significantly contributing to the improvement of process monitoring and quality control.

A new optimized method in wellbore to improve gas recovery in shale reservoirs

With the scale development of shale gas, the importance of selecting appropriate deliquification process has become increasingly evident in maintaining well productivity and improving shale gas recovery rate. At present, the preferred deliquification process are macro-control plate method and field experience method. The existing methods can only qualitatively select the deliquification process by considering limited influencing factors, resulting in poor process implementation. Based on the results of error analysis, the Gray model was optimized to calculate the pressure distribution in the shale gas wellbore and determine the applicable pressure limit. The W.Z.B. empirical model, which fully considers the influence of wellbore inclination, is used to calculate the gas-liquid carrying situation and determine the applicable liquid carrying limit. By analyzing the technical limits of five commonly used deliquification processes in the Changning shale gas field, namely, plunger lift, optimizing pipe string, gas lift, foam drainage, and intermittent production, a quantitative optimization method for deliquification processes was established. This method was then used to obtain the optimization chart for deliquification processes in shale gas wells. This method was applied in Well Ning 209-X, where the corresponding optimization chart for deliquification processes was drawn based on the production characteristics of the gas well. By quantitatively optimizing the deliquification processes and adjusting to suitable techniques, it effectively guided the production of the gas well and improved the gas field recovery rate.

Robust design of ARMA and ACC charts for imperfect and autocorrelated processes under uncertainty

Occurring disruptions and faults violate the perfectness of a production process in determining Economic Production Quantity (EPQ). Integrating EPQ, Statistical Process Control (SPC), and maintenance terms has brought satisfactory outcomes for such an imperfect process. Under the violated independence assumption, the Autoregressive Moving Average (ARMA) chart has been applied in the integrated models. Under autocorrelation, the extended Acceptance control chart (ACC) has indicated significant reductions in costs. Nevertheless, it has not been applied to any integrated modeling yet. Until now, constant input factors have been considered for modeling imperfect and autocorrelated processes. Uncertainty in estimating those factors can deteriorate the effectiveness of models. We present the first robust design for imperfect and autocorrelated processes under uncertainty. We apply a particle swarm optimization algorithm to provide solutions. The investigations of simple and integrated modeling indicate that applying the ACCs causes better statistical and economic results. Also, a real-life application is presented.

Control charts for processes with variable mean

<p>Despite of strong ability and performance of control charts to control and monitor processes, they have some problems in practical applications. If control chart’s limits are not properly designed then we receive false alarms. For example, several observations may be outside the control limits when the mean of process is in-control. Not considering the variation of the process mean at each sampling time may lead to this error. The process may be adjusted at specific mean but different working conditions and different operators may change mean of the process and it may have a small deviation from its predetermined value and this problem can lead to wrong implementation of control charts. In this paper, the effects of variable mean on control charts are analyzed. It is assumed that the mean of observation varies over time but its probability distribution is normal probability distribution function. It is observed that long-term process mean control chart generates false alarms.<strong></strong></p>

On the design and performance of upper one-sided Shewhart charts for zero-inflated Poisson processes with estimated parameters

ABSTRACT In this work we study the performance of the upper one-sided Shewhart-type control charts for monitoring a zero-inflated Poisson process, in the case of estimated process parameters. In practice, the process parameters are unknown and must be estimated from a Phase I dataset. However, this affects the theoretical performance of a control chart and further investigation is needed to assess how much the performance of the chart is affected. Moreover, practical guidelines are necessary regarding the size of the Phase I sample so as the performance of the control chart in the case of estimated parameters is close to the known parameters case. In this work we use Monte Carlo simulation and evaluate various performance measures that provide useful information on chart’s performance in the case of estimated parameters. Both the in-control and the out-of-control performance are investigated. Moreover, we suggest adjustments to obtain the desired in-control performance, when the size of the Phase I sample is prespecified. The results show that very large Phase I samples are needed in order to make the chart’s performance, in the case of estimated parameters, close to the theoretical one. Using the suggested adjustments, these differences can be significantly reduced.

The ENBIS‐21 quality and reliability engineering international special issue

The ENBIS-21 Quality and Reliability Engineering International Special Issue is related to the contributions to the 21st Annual Conference of the European Network for Business and Industrial Statistics (ENBIS) held online from 13 to 15 September, 2021. The topics covered by the 12 papers included in this special issue fall within the scope of ENBIS, whose ultimate goal is to bridge the gap between methodology and application in the field of business and industrial statistics and foster networking between statisticians in academic and commercial settings. It becomes evident from the papers on this issue that classical methods of industrial statistics are still having a wide range of applications and expansions towards complex and big data structures as well as they are increasingly cross-fertilized by artificial intelligence and machine learning perspectives and approaches. The issue is opened by the contribution of Yang et al.1 in the Statistical Process Monitoring (SPM) of data in the form of tensors. The authors develop a hierarchical in-situ process monitoring approach for anomaly detection, which is applied to thermal video streams acquired during a metal additive manufacturing process for highly complex parts. A more traditional SPM approach based on generalized likelihood ratio (GLR) control charts is elaborated by Rizzo and Di Bucchianico2 to set up tailor-made monitoring for high-purity (high-quality) processes and deals with issues arising in GLR control charts for discrete processes. Along the line of developing statistical methods for complex data structures, Gril et al.3 set up a tensor-on-tensor regression model able to dynamically predict repetitive human motions helpful in avoiding unwanted collisions at the interface with robots in industrial assembly tasks. Chuquin et al.4 present a straightforward extension of the K-means clustering to spatially correlated functional data, with an application in the analysis of the normalized difference vegetation index in a large region of Ecuador. From a more general perspective, Vanacore et al.5 address the problem of assessing prediction performance in the multi-class classification of imbalanced data sets. In the optimal Design of Experiments (DoE) Pesce et al.6 offer new results that are oriented to bias reduction in large datasets and protection against confounders. Whereas, Kirchhoff et al.7 use DoE as the initial solution for the optimization of shift planning in high-bay warehouse operations based on Gaussian process models with low-rank correlation kernels. Risk assessment and management is the topic of the following three papers. Testik and Unlu8 compare traditional and fuzzy failure modes and effect analysis to rank risks in different areas of testing and calibration laboratories. Meynaoui et al.9 deal with an accidental scenario in a sodium-cooled fast nuclear reactor by means of a global sensitivity analysis of the input parameter distribution used in numerical simulator outputs to model physical phenomena. Lai and Zwetsloot10 offer a data-driven ensemble ranking system of product quality, which is validated in the identification of high-risk manufacturers in a solar industry case study. The final two papers are devoted to the Reliability and Maintenance of repairable systems. El-Aroui and Gaudoin11 propose a general goodness-of-fit test for imperfect repair models that has the favorable property of being asymptotically distribution-free for renewal and power law processes. Fouladirad et al.12 develop a new bounded transformed gamma process model to describe and predict degradation phenomena by relaxing the typical assumption that the degradation level can grow indefinitely, which is often unrealistic for technological units. The proposed model is also applied to a set of wear measures of cylinder liners that equip a diesel engine for marine propulsion. We are deeply grateful to the journal staff for their professional assistance in the editorial process, as well as to the anonymous referees for the time and effort spent to provide careful and constructive comments, and to all the authors, who made revisions on a very tight timescale.

New statistical process control charts for overdispersed count data based on the Bell distribution.

Poisson distribution is a popular discrete model used to describe counting information, from which traditional control charts involving count data, such as the c and u charts, have been established in the literature. However, several studies recognize the need for alternative control charts that allow for data overdispersion, which can be encountered in many fields, including ecology, healthcare, industry, and others. The Bell distribution, recently proposed by Castellares et al. (2018), is a particular solution of a multiple Poisson process able to accommodate overdispersed data. It can be used as an alternative to the usual Poisson (which, although not nested in the Bell family, is approached for small values of the Bell distribution) Poisson, negative binomial, and COM-Poisson distributions for modeling count data in several areas. In this paper, we consider the Bell distribution to introduce two new exciting, and useful statistical control charts for counting processes, which are capable of monitoring count data with overdispersion. The performance of the so-called Bell charts, namely Bell-c and Bell-u charts, is evaluated by the average run length in numerical simulation. Some artificial and real data sets are used to illustrate the applicability of the proposed control charts.

A side-sensitive synthetic chart for the multivariate coefficient of variation.

Control charts for the coefficient of variations (γ) are receiving increasing attention as it is able to monitor the stability in the ratio of the standard deviation (σ) over the mean (μ), unlike conventional charts that monitor the μ and/or σ separately. A side-sensitive synthetic (SS) chart for monitoring γ was recently developed for univariate processes. The chart outperforms the non-side-sensitive synthetic (NSS) γ chart. However, the SS chart monitoring γ for multivariate processes cannot be found. Thus, a SS chart for multivariate processes is proposed in this paper. A SS chart for multivariate processes is important as multiple quality characteristic that are correlated with each other are frequently encountered in practical scenarios. Based on numerical examples, the side-sensitivity feature that is included in the multivariate synthetic γ chart significantly improves the sensitivity of the chart based on the run length performance, particularly in detecting small shifts (τ), and for small sample size (n), as well as a large number of variables (p) and in-control γ (γ0). The multivariate SS chart also significantly outperforms the Shewhart γ chart, and marginally outperforms the Multivariate Exponentially Weighted Moving Average (MEWMA) γ chart when shift sizes are moderate and large. To show its implementation, the proposed multivariate SS chart is adopted to monitor investment risks.

On designing TEWMA-Tukey control charts for normal and non-normal processes using single and repetitive sampling schemes

Technology advancement and the need to produce quality products have necessitated the development of more efficient process monitoring schemes. In the form of a combined triple EWMA (TEWMA) and Tukey control chart (TCC), this study is an analogous attempt to develop a better charting framework for normal and non-normal data using single and repetitive schemes. The proposed and competing charts are compared based on average run length, standard deviation of the run length and median run length criteria under both zero-state and steady-state conditions. The proposed charts display dominance in detecting mean shifts in both directions not only for symmetric distributions but they are also robust for skewed distributions in that they are devoid of the average run length biased problem. The proposed charts beat the Tukey and Shewhart charts under the repetitive scheme. The TEWMA-TCC under the repetitive scheme has emerged as the best chart under all distributional setups. The steady-state findings of the TEWMA-TCC and its repetitive variant are as beneficial as those of the zero-state results, if not more. A practical application for the proposed designs in the surveillance of industrial production index data in the aerospace manufacturing is illustrated. The proposed charts issue more and earlier signals in the Phase-II process compared with their existing counterparts, most notably the two Tukey charts, i.e. the TCC and EWMA-TCC. Hence, quality and industrial engineers can rely on the proposed charts in process monitoring.

Bivariate copula-based CUSUM charts for monitoring conditional nonlinear processes with first-order autocorrelation

This paper considers the bivariate copula-based first-order Markov models to describe nonlinear dependence in autocorrelated data. Then the cumulative sum (CUSUM) charts based on log-likelihood ratio are developed to monitor the mean shifts. The performance of the proposed CUSUM charts is studied in both linear and nonlinear time series under weak, moderate and strong dependence by numerical simulations. Comparisons with the AR(1) model-based CUSUM and EWMA charts are present under the same range of scenarios. Simulation results show that the Clayton copula-based CUSUM charts are more effective to almost all the mean shifts and further have an obvious advantage in strong dependence. An example from chemical production is given to illustrate the implementation of the proposed control scheme.

Literature Review on Control Charts for Autocorrelated Processes

This research aims to present a literature review (LR) on control charts for autocorrelated processes, intending to contribute to the scientific knowledge of the process management area. The article was constructed having a research question defined ex-ante, elaborated based on the literature, where a research protocol adapted from Tranfield, Denyer, and Smart (2003) was systematized according to the methodological rigor demanded in the literature review, which resulted in the composition of the research corpus. The research corpus was evaluated in detail using the bibliometric packages HistCite, VOSviewer, package R and Iramuteq. It was evaluated the validity of the 3 bibliometric laws were verified: Lotka's Law, Bradford's Law, and Zipf's Law based on the authors’ citation and co-citation techniques. This study is considered as relevant and original since it is the first literature review on control charts for autocorrelated processes. The results confirmed the 3 classical bibliometric laws for the researched corpus. As a practical implication, this review provides support for quality management scholars to unlock potential research gaps. The main limitation of the work refers to the composition of the textual corpus, given that databases of national journals were not consulted due to the difficulty in terms of compatibility of the software used in this research.

Statistical design of an adaptive synthetic X¯$\bar{X}$ control chart for autocorrelated processes

AbstractThis paper aims to design a variable parameters synthetic control chart for first‐order AR(1) autocorrelated data following a Gaussian process. To improve the statistical performance in detecting small changes and maintaining a low false alarm rate, the variable parameters control chart was combined with the Conforming Run Length (CRL) sub‐chart to determine when to implement tight or relaxed control and intervene to identify an assignable cause. The statistical design of the proposed chart was performed under a discrete‐time Markov chain approach and a non‐linear programming mathematical model to obtain, using a genetic algorithm (GA), the values of the design parameters that minimise the average time to signal the out‐of‐control state (). A sensitivity analysis was performed to examine the behaviour of the in the face on changes in the parameters. Also, a performance evaluation was conducted to compare the proposed chart with other adaptive synthetic charts, the synthetic control chart and the chart developed by Costa and Machado. Our results indicate that this proposal is faster to detect small changes in the process mean considering the autocorrelation of the data.

Statistical process control of overdispersed count data based on one‐parameter Poisson mixture models

AbstractThe Poisson distribution is a discrete model widely used to analyze count data. Statistical control charts based on this distribution, such as the and charts, are relatively well‐established in the literature. Nevertheless, many studies suggest the need for alternative approaches that allow for modeling overdispersion, a phenomenon that can be observed in several fields, including biology, ecology, healthcare, marketing, economics, and industry. The one‐parameter Poisson mixture distributions, whose literature is extensive and essential, can model extra‐Poisson variability, accommodating different overdispersion levels. The distributions belonging to this class of models, including the Poisson‐Lindley (PL), Poisson‐Shanker (PSh), and Poisson‐Sujatha (PSu) models, can thus be used as interesting alternatives to the usual Poisson and COM‐Poisson distributions for analyzing count data in several areas. In this paper, we consider the class of probabilistic models mentioned above (as well as the cited three members of such a class) to develop novel and useful statistical control charts for counting processes, monitoring count data that exhibit overdispersion. The performance of the so‐called one‐parameter Poisson mixture charts, namely the ‐, ‐, and ‐ charts, is measured by the average run length in exhaustive numerical simulations. Some data sets are used to illustrate the applicability of the proposed methodology.

Design of a robust T2 control chart, a re‐sampling approach

AbstractIn constructing any control chart, the sample size and the number of samples taken are important issues. When destructive tests are applied to collect data, the sample size and the number of subsamples are usually limited. Lack of sufficient observations affects parameters estimates. Re‐sampling techniques are always suggested to increase the accuracy of parameters estimates. Also, the presence of outlying observations severely affect re‐sampling and the estimates of the underlying distribution parameters. The limited sample size, limited number of subsamples and presence of outliers are more important in multivariate process analysis. In this study, bootstrap re‐sampling technique and robust estimators of mean vector and variance‐covariance matrix are simultaneously utilized to design a multivariate robust T2 control chart to address the three problems in hand. The performance of the proposed robust T2 control chart is evaluated and compared to the Hotelling T2 control chart by means of average run length (ARL). Simulation results indicate that the suggested robust T2 control chart outperforms the Hotelling T2 in presence of outliers and similarly when there is no outlier. Design of robust control chart for processes generating auto‐correlated data applying bootstrap re‐sampling technique is an area for further research.

An adaptive exponentially weighted moving average control chart for poisson processes

The Adaptive Exponentially Weighted Moving Average (AEWMA) control chart is known to be effective in detecting range of shifts simultaneously. Moreover, the AEWMA chart is known to diminish the inertia effect. The AEWMA chart is usually investigated while assuming that the monitored process follows a continuous distribution; commonly the normal distribution. In practice, however, monitored data could be of a discrete-type. We aim in this study to propose a discrete-version from the AEWMA chart; namely the Poisson AEWMA chart. The chart is compared with its counterparts; the Poisson EWMA chart and Poisson CUSUM chart using the ARL and RMI metrics. Our results show that the Poisson AEWMA chart performs more efficiently in detecting shifts of various sizes with an RMI value approaching zero. The Poisson CUSUM chart has the worst performance. Moreover, the proposed Poisson AEWMA chart is capable of detecting shifts faster than an approach based on normal approximation even for large values of the mean defects. In addition, the superiority of the Poisson AEWMA chart in diminishing the inertia effect is illustrated through a numerical example. The example shows that the Poisson AEWMA chart is capable of detecting out of control situations very fast even if the chart statistic is in a disadvantageous position before a shift occurs.

A trimmed EWMA control charts for non-normal processes

The traditional exponentially weighted moving average (EWMA) control chart is very popular in statistical process control (SPC) for detecting small shifts in process mean and variance. It performs well under the assumption of normality but when data violate this assumption, a modified approach is needed. In this paper, we proposed a variable control chart for monitoring the process mean by modifying the traditional EWMA control chart for non-normal processes based on the modified trimmed standard deviation (MTSD). The proposed EWMA control charts are based on three different heuristic methods, namely, the Trimmed Exponentially Weighted Moving Average (T-EWMA) control chart, the Trimmed Weighted Standard Deviation Exponentially Weighted Moving Average (TWSD-EWMA) control chart and the Trimmed Weighted Variance Exponentially Weighted Moving Average (TWV-EWMA) control chart. The performances of the control charts under study are evaluated via a Monte-Carlo simulation study by calculating expected out-of-control points and expected widths under non-normal distributions (i.e. Gamma and Exponential). Also, since the EWMA statistic $${Z}_{i}$$ is sensitive to detect mean shifts in the process, the out-of-control average run length ( $${ARL}_{1}$$ ) is considered in the simulation as a best tool to measure the sensitivity. The simulation studies are being carried out for the purpose and results showed that the proposed trimmed control charts performed well for non-normal processes in terms of their shorter expected widths, more number of expected out-of-control points and quick out-of-control signals as compared to non-trimmed versions of control charts. Moreover it is also observed that as weighing constant $$\lambda$$ increases, the sensitivity of the proposed trimmed control charts increases. For illustration purposes, a real-life data set from a public service industry is analyzed which confirming our conclusions from the simulation analysis. Consequently, for estimating of the process mean when the distribution of the data is non-normal, we recommend the trimmed versions of EWMA control charts for the practitioners to be used.