Proposed Control Chart Research Articles

Construction of Six Sigma-based control chart for interval-valued data

Construction of control charts is straightforward if the data are real-valued. However, there are situations where data are essentially interval-valued in which each observation is represented by minimum and maximum values. While there are only few attempts to develop control charts for interval-valued data, there have been no simple-to-use approaches developed to deal with such type of data. In this article, we propose to make use of the popular Taguchi orthogonal array experiment to first redefine the data for experimental setup and then use Six Sigma control limits to determine overall control limits for interval-valued data. The resulting multiple control limits have inner and outer control limits for simultaneously monitoring minimum and maximum values of the averages of interval-valued data. The proposed control chart is then illustrated using a data set, and conclusions are drawn based on the results. It is observed that the proposed Six Sigma-based control chart for interval-valued data is, in fact, easy-to-use, and it performs better in detecting the out-of-control situations. We have established this using average run length comparisons as well with the traditional charts.

Generalized multivariate EWMA control chart supplemented with bivariate ranked set techniques

ABSTRACT Existing univariate exponential weighted moving average (EWMA) control charts with ranked set schemes are used for monitoring related characteristics independently. Also, existing multivariate EWMA control charts are generally applicable for simple random sampling (SRS) based processes. In this work, a generalized multivariate EWMA control chart is proposed with bivariate ranked set techniques (BVRST) for simultaneously monitoring. Furthermore, an extensive comparative analysis between proposed generalized multivariate EWMA and classical control chart is conducted. In this regard, we have used various performance measures, which cover average run length, median of run length, relative average run length, performance comparison index, and extra quadratic loss. The performance measures are obtained using the Monte Carlo simulation (MCS) approach. Results revealed that the proposed generalized multivariate EWMA control chart has an outstanding detection ability relative to the existing multivariate control charts. Additionally, existing multivariate control charts are found special cases of the proposed control chart. A real-life example from the agriculture field is included in which chemical properties (residual sodium and calcium-magnesium contents) of irrigation water are monitored through the control charts. The results revealed that the proposed control chart is proficient in diagnosing small variations in the chemical characteristics relative to the existing control charts.

Application of Poisson state-space models and shared frailty models for multistage processes surveillance

ABSTRACT There are many applications in actual multistage processes with Poisson data. Control charts are an essential tool for monitoring quality variables in multistage processes. On the other hand, it is not straightforward to adjust a quality variable for the effect of all influential covariates, and ignoring latent variables introduces unobserved heterogeneity which diminishes the detection power of a monitoring scheme. Hence, the present paper proposes two monitoring schemes namely, the GEWMA control chart based on a Poisson state-space model and the modified EWMA control chart based on a shared frailty model in which latent variables are considered in Phase II. In this regard, expectation – maximization and Bayesian algorithms are used to estimate the parameters of the proposed models. A comparison between the two proposed control charts demonstrates that the GEWMA control chart based on a Poisson state-space model performs better than the modified EWMA control chart using the frailty model. Then, comprehensive simulation experiments are conducted to evaluate the performance of the proposed GEWMA. The results show that it performs satisfactorily under different shifts in single and multiple stages. Also, this control chart helps well to identify the out-of-control stage. Finally, a real case in health-care related processes is used to appraise the performance of the proposed monitoring scheme in practice.

Memory type Max-EWMA control chart for the Weibull process under the Bayesian theory

The simultaneous monitoring of both process mean and dispersion, particularly in normal processes, has garnered significant attention within the field. In this article, we present a new Bayesian Max-EWMA control chart that is intended to track a non-normal process mean and dispersion simultaneously. This is accomplished through the utilization of the inverse response function, especially in cases where the procedure follows a Weibull distribution. We used the average run length (ARL) and the standard deviation of run length (SDRL) to assess the efficacy of our suggested control chart. Next, we contrast our suggested control chart's performance with an already-existing Max-EWMA control chart. Our results show that compared to the control chart under consideration, the proposed control chart exhibits a higher degree of sensitivity. Finally, we present a useful case study centered around the hard-bake process in the semiconductor manufacturing sector to demonstrate the performance of our Bayesian Max-EWMA control chart under different Loss Functions (LFs) for a Weibull process. The case study highlights how flexible the chart is to various situations. Our results offer strong proof of the outstanding ability of the Bayesian Max-EWMA control chart to quickly identify out-of-control signals during the hard-bake procedure. This in turn significantly contributes to the enhancement of process monitoring and quality control.

Comparing the efficacy of coefficient of variation control charts using generalized multiple dependent state sampling with various run-rule control charts

This paper aimed to develop a coefficient of variation (CV) control chart utilizing the generalized multiple dependent state (GMDS) sampling approach for CV monitoring. We conducted a comprehensive examination of this designed control chart in comparison to existing control charts based on multiple dependent state sampling (MDS) and the Shewhart-type CV control chart, with a focus on average run lengths. The results were then compared to run-rule control charts available in the existing literature. Additionally, we elucidated the implementation of the proposed control chart through concrete examples and a simulation study. The findings clearly demonstrated that the GMDS sampling control chart shows significantly superior accuracy in detecting process shifts when compared to the MDS sampling control chart. As a result, the control chart approach presented in this paper holds significant potential for applications in textile and medical industries, particularly when researchers seek to identify minor to moderate shifts in the CV, contributing to enhanced quality control and process monitoring in these domains.

Optimized two-stage time-truncated control chart for Weibull distribution

In this article, an attribute control chart is proposed when the lifetime of a product follows a Weibull distribution in two-stage sampling, which is based on the number of failures from a truncated life test. The coefficients of the proposed double sampling attribute control chart and the test duration are determined so that the average run length when the process is in control is close to the target value. An overview is reported on how double sampling np control charts work. Tables reporting the out-of-control average run lengths are given for various shift parameters. A case study is given to illustrate the proposed control chart for industrial use. A comparison of two-stage and single-stage sampling of failure of products is discussed.

Time truncated attribute control chart for the generalized Rayleigh distributed quality characteristics and beyond

Purpose First is to develop the time truncated median control chart for the Rayleigh distribution (RD) and generalized RD (GRD), respectively. Second is to evaluate the performance of the proposed attribute control chart which depends on the average run length (ARL) and third is to include real life examples for application purpose of the proposed attribute control chart.Design/methodology/approach (1) Select a random sample of size n from each subgroup from the production process and put them on a test for specified time t, where t = ? × µe. Then, count the numbers of failed items in each subgroup up to time t. (2) Step 2: Using np chart, define D = np, the number of failures, which also a random variable follows the Binomial distribution. It is better to use D = np chart rather than p chart because the authors are using number of failure rather than proportion of failure p. When the process is in control, then the parameters of the binomial distribution are n and p0, respectively. (3) Step 3: The process is said to be in control if LCL = D = UCL; otherwise, the process is said to be out of control. Hence, LCL and UCL for the proposed control chart.Findings From the findings, it is concluded that the GRD has smaller ARL values than the RD for specified values of parameters, which indicate that GRD performing well for out of control signal as compared to the RD.Research limitations/implications This developed control chart is applicable when real life situation coincide with RD and GRD.Social implications Researcher can directly use presented study and save consumers from accepting bad lot and also encourage producers to make good quality products so that society can take benefit from their products.Originality/value This article dealt with time truncated attribute median control chart for non-normal distributions, namely, the RD and GRD, respectively. The structure of the proposed control chart is developed based on median lifetime of the RD and GRD, respectively.

Control charts using half-normal and half-exponential power distributions using repetitive sampling

This manuscript presents the development of an attribute control chart (ACC) designed to monitor the number of defective items in manufacturing processes. The charts are specifically tailored using time-truncated life test (TTLT) for two lifetime data distributions: the half-normal distribution (HND) and the half-exponential power distribution (HEPD) under a repetitive sampling scheme (RSS). To assess the effectiveness of the proposed control charts, both in-control (IC) and out-of-control (OOC) scenarios are considered by deriving the average run length (ARL). Various factors, including sample sizes, control coefficients, and truncated constants for shifted phases, are taken into account to evaluate the performance of the charts in terms of ARL. The behavior of ARLs is analyzed in the shifted process by introducing shifts in its parameters. The superiority of the HEPD-based chart is highlighted by comparing it with both the HND-based ACC and the ACC based on the Exponential distribution (ED) under TTLT using RSS. The results showcase the superior performance of the proposed HEPD-based chart, indicated by smaller ARL values. Additionally, the benefits of another proposed ACC using HND are compared with the ED-based ACC under RSS, further confirming the effectiveness of the HND-based approach through smaller ARLs Finally, the proposed control charts are evaluated through simulation testing and real-life implementation, emphasizing their practical applicability in real-world manufacturing settings.

A nonparametric adaptive EWMA control chart for monitoring mixed continuous and categorical data using self-starting strategy

In the context of big data-driven smart manufacturing, data is often characterized by high dimensionality, numerous variables, and complex associations. As a result, mixed continuous and categorical data are increasingly common. In the case of data that consist of a combination of continuous and categorical variables with unknown distributions, the application of traditional parametric control charts for monitoring purposes becomes challenging. Therefore, a novel nonparametric adaptive exponentially weighted moving average (EWMA) control chart using a self-starting strategy is proposed in this paper. First, the process of converting continuous data into categorical data is conducted using the data categorization method. The log-linear modeling is subsequently employed to investigate the relationships between various variables. Next, a nonparametric adaptive EWMA statistic is constructed to monitor mixed continuous and categorical data, and the self-starting strategy is employed to gradually expand the size of the in-control (IC) dataset and to update the parameters in real time. Then, a numerical simulation is conducted to compare the IC and out-of-control (OC) performance of the proposed chart with other control charts. According to the simulation result, it can be concluded that the proposed chart offers a more effective means of detecting shifts in the production process. Finally, a concrete illustration of an authentic dataset regarding red wine quality is provided to further clarify the effectiveness of the proposed control chart in monitoring mixed continuous and categorical data.

Design of Nonparametric Extended Exponentially Weighted Moving Average – Sign Control Chart

The present research introduces the EEWMA-Sign chart, which incorporates the extended exponentially weighted moving average control chart with the sign control charts to detect small changes in procedures. This is a nonparametric control chart that can overcome the constraints imposed by normal assumptions. The average run lengths serve as supporting examinations for comparing the effectiveness of a monitoring scheme to the EEWMA and EWMA control charts via Monte Carlo Simulation. Besides a specific range of shift sizes, the expected ARL (EARL) remains an instrument to assess the efficiency of control charts. The overall result demonstrates that the proposed chart is the most suitable control chart for detecting small shifts between Normal, Lognormal, and Laplace distributional scenarios. Nonetheless, the EWMA chart recognizes large shifts more efficiently than others. Adapting the proposed control chart to the flow width dataset produced results consistent with the research findings.

A novel Bayesian Max-EWMA control chart for jointly monitoring the process mean and variance: an application to hard bake process

In this article, we introduce a novel Bayesian Max-EWMA control chart under various loss functions to concurrently monitor the mean and variance of a normally distributed process. The Bayesian Max-EWMA control chart exhibit strong overall performance in detecting shifts in both mean and dispersion across various magnitudes. To evaluate the performance of the proposed control chart, we employ Monte Carlo simulation methods to compute their run length characteristics. We conduct an extensive comparative analysis, contrasting the run length performance of our proposed charts with that of existing ones. Our findings highlight the heightened sensitivity of Bayesian Max-EWMA control chart to shifts of diverse magnitudes. Finally, to illustrate the efficacy of our Bayesian Max-EWMA control chart using various loss functions, we present a practical case study involving the hard-bake process in semiconductor manufacturing. Our results underscore the superior performance of the Bayesian Max-EWMA control chart in detecting out-of-control signals.

Incorporating principal component analysis into Hotelling [formula omitted] control chart for compositional data monitoring

In the manufacturing industry, compositional data (CoDa) is a vital quality characteristic to be monitored. The proposed study has introduced a Hotelling T2 control chart using principal component analysis to monitor CoDa explicitly. The proposed method overcomes the limitations of previous approaches by utilizing isometric log-ratio transformation to map the CoDa into unrestricted real space. A Monte Carlo simulation procedure is employed to evaluate the performance of the proposed multivariate control chart. The simulation involves varying combinations of the number of variables (p) and subgroup sizes to obtain metrics such as the average run length when the process is out-of-control (OOC) and the upper control limit. The article presents a comprehensive analysis of the proposed control chart’s statistical performance. These visual aids facilitate a deeper understanding of the method’s effectiveness in detecting OOC conditions in CoDa. Furthermore, two illustrative examples using synchronous machines and components of electronic scrap are provided to illustrate the practical implementation and effectiveness of the Hotelling T2-based principal component control chart for p=5-part and p=12-part CoDa in real-world scenarios.

Design and Analysis of Extended Exponentially Weighted Moving Average Signed-Rank Control Charts for Monitoring the Process Mean

In the real world, a nonparametric control chart is a powerful substitute for enhancing outcome quality, although the fundamental procedure characteristic often fails to match the distribution assumptions. This study aims to construct and evaluate an extended exponentially weighted moving average control chart based on signed-rank statistics (EEWMA-SR) for recognizing changes in procedures. According to the study, the proposed chart proves more potent recognition of shifts in the process mean, predominantly small shifts, than the other control charts by the average run length in Monte Carlo simulation. Applying the proposed control chart to an actual dataset yielded events that corroborated the study discoveries.

Monitoring of manufacturing process using bayesian EWMA control chart under ranked based sampling designs

Control charts, including exponentially moving average (EWMA) , are valuable for efficiently detecting small to moderate shifts. This study introduces a Bayesian EWMA control chart that employs ranked set sampling (RSS) with known prior information and two distinct loss functions (LFs), the Square Error Loss function (SELF) and the Linex Loss function (LLF), for posterior and posterior predictive distributions. The chart's performance is assessed using average run length (ARL) and standard deviation of run length (SDRL) profiles, and it is compared to the Bayesian EWMA control chart based on simple random sampling (SRS). The results indicate that the proposed control chart detects small to moderate shifts more effectively. The application in semiconductor manufacturing provides concrete evidence that the Bayesian EWMA control chart, when implemented with RSS schemes, demonstrates a higher degree of sensitivity in detecting deviations from normal process behavior. Comparison to the Bayesian EWMA control chart using SRS, it exhibits a superior ability to identify and flag instances where the manufacturing process is going out of control. This heightened sensitivity is critical for promptly addressing and rectifying issues, which ultimately contributes to improved quality control in semiconductor production.

Performance Analysis of Interval Type-2 Fuzzy X¯ and R Control Charts

Statistical process control (SPC) is one of the most powerful techniques for improving quality, as it is able to detect special causes of problems in processes, products and services with a remarkable degree of accuracy. Among SPC tools, X¯ and R control charts are widely employed in process monitoring. However, scenarios involving vague, imprecise and even subjective data require a type-2 fuzzy set approach. Thus, X¯ and R control charts should be coupled with interval type-2 triangular fuzzy numbers (IT2TFN) in order to add further information to traditional control charts. This paper proposes a performance analysis of IT2TFN and X¯ and R control charts by means of average run length (ARL), standard deviation of the run length (SDRL) and RL percentile. Computer simulations were carried out considering 10,000 runs to obtain ARL, SDRL and the 5th, 25th, 50th, 75th and 95th RL percentiles. Simulation results reveal that the proposed control charts increased fault detection capability (speed of response) and slightly reduced the number of false alarms in processes under control. Moreover, it was observed that, in addition to superior performance, IT2TFN X¯-R control charts proved to be more robust and flexible when compared to traditional control charts.

Adaptive EWMA control chart for monitoring the coefficient of variation under ranked set sampling schemes

In this study, we introduce an Adaptive Exponentially Weighted Moving based Coefficient of Variation (AEWMCV) control chart, designed to address situations where the process mean fluctuates over time and the standard deviation of the process changes linearly with the process mean. To enhance the efficiency and effectiveness of the control chart, we integrate the ranked set sampling method and its modified schemes, such as Simple Random Sampling, Quartile RSS, Median RSS, and Extreme RSS. The performance of the proposed AEWMCV control chart and the studied CV control charts are evaluated using the Average Run Length and Standard Deviation of Run Length metrics. Our findings reveal that the proposed control chart outperforms the existing CV control charts, especially in detecting slight to moderate changes in the process CV. To illustrate the practical applicability of the suggested control chart, we present an example demonstrating its use on a real dataset. The results highlight the superior performance of the AEWMCV control chart in accurately detecting and responding to changes in the process CV. In conclusion, our study introduces an innovative AEWMCV control chart that combines ranked set sampling and its modified schemes to enhance performance in scenarios with fluctuating process means and changing standard deviations. The proposed control chart proves to be more effective in detecting subtle variations in the process CV compared to traditional CV control charts. This research provides a valuable contribution to the field of control chart methodology, especially when dealing with challenging or costly data collection scenarios.

Error detection through modified phase II process monitoring under different classical estimators

In real life, the distribution of the errors during any life testing of products or process does not meet the assumption of normality. Statistical process control (SPC) is defined as the use of statistical techniques to control a process or production method. SPC tools and procedures can help to monitor process behavior, discover problems in internal systems, and find solutions for production issues. To identify and remove the variation in different reliability processes and to monitor the reliability of machines where the number of errors follows skewed distributions, we develop control charts to keep the process in control. For such situations, we have modified the existing control charts such as Shewhart control chart, exponentially weighted moving average (EWMA), hybrid exponentially weighted moving average (HEWMA) and extended exponentially weighted moving average (EEWMA) control charts. The current study introduced classical estimator based modified control charts for phase-II monitoring by assuming that the errors occur during the process follow skewed distribution called Beta Lehmann 2 Power function distribution (BL2PFD). The proposal for these control charts is based on the percentile estimator. We have compared all these control charts using Monte Carlo simulation studies and real-life applications to compare the proposed control charts. This study shows that an EEWMA control chart based on PE performs better than Shewhart, EWMA and HEWMA control charts, when the underlying distribution of the errors in process monitoring follows BL2PFD. These findings can be useful for researchers and practitioners in dealing with production errors and optimizing the output.

A New Sine-Based Distributional Method with Symmetrical and Asymmetrical Natures: Control Chart with Industrial Implication

Control charts are widely used in quality control and industrial sectors. Because of their important role, researchers are focusing on the development of new control charts. According to our study, there is no significant amount of published work on control charts using trigonometrically generated distribution methods. In this paper, we contribute to this interesting research gap by developing a new control chart using a sine-based distributional method. The proposed distributional method (or family of probability distributions) may be called a new modified sine-G family of distributions. Based on the new modified sine-G method, a novel modification of the Weibull distribution, namely, a new modified sine-Weibull distribution, is introduced. The new modified sine-Weibull distribution is flexible enough to capture symmetrical and asymmetrical behaviors of its density function. An industrial application is considered to show the importance and implacability of the proposed distribution in quality control. Based on the proposed model, an attribute control chart is developed under a truncated life test. The control chart limits (ARLs) are also computed for the proposed model. The ARLs of the proposed control chart are compared with the attribute control chart of the Weibull distribution. The results show that the developed chart is more efficient than the existing attribute control chart for the Weibull distribution.

A change-point–based control chart for detecting sparse mean changes in high-dimensional heteroscedastic data

Because of the “curse of dimensionality,” high-dimensional processes present challenges to traditional multivariate statistical process monitoring (SPM) techniques. In addition, the unknown underlying distribution of and complicated dependency among variables such as heteroscedasticity increase the uncertainty of estimated parameters and decrease the effectiveness of control charts. In addition, the requirement of sufficient reference samples limits the application of traditional charts in high-dimension, low-sample-size scenarios (small n, large p). More difficulties appear when detecting and diagnosing abnormal behaviors caused by a small set of variables (i.e., sparse changes). In this article, we propose two change-point–based control charts to detect sparse shifts in the mean vector of high-dimensional heteroscedastic processes. Our proposed methods can start monitoring when the number of observations is a lot smaller than the dimensionality. The simulation results show that the proposed methods are robust to nonnormality and heteroscedasticity. Two real data examples are used to illustrate the effectiveness of the proposed control charts in high-dimensional applications. The R codes are provided online.

Efficient Monitoring of a Parameter of Non-Normal Process Using a Robust Efficient Control Chart: A Comparative Study

The control chart is a fundamental tool in statistical process control (SPC), widely employed in manufacturing and construction industries for process monitoring with the primary objective of maintaining quality standards and improving operational efficiency. Control charts play a crucial role in identifying special cause variations and guiding the process back to statistical control. While Shewhart control charts excel at detecting significant shifts, EWMA and CUSUM charts are better suited for detecting smaller to moderate shifts. However, the effectiveness of all these control charts is compromised when the underlying distribution deviates from normality. In response to this challenge, this study introduces a robust mixed EWMA-CUSUM control chart tailored for monitoring processes characterized via symmetric but non-normal distributions. The key innovation of the proposed approach lies in the integration of a robust estimator, based on order statistics, that leverages the generalized least square (GLS) technique developed by Lloyd. This integration enhances the chart’s robustness and minimizes estimator variance, even in the presence of non-normality. To demonstrate the effectiveness of the proposed control chart, a comprehensive comparison is conducted with several well-known control charts. Results of the study clearly show that the proposed chart exhibits superior sensitivity to small and moderate shifts in process parameters when compared to its predecessors. Through a compelling illustrative example, a real-life application of the enhanced performance of the proposed control chart is provided in comparison to existing alternatives.