Design Of Control Charts Research Articles

Designing economic-statistical Hotelling’s T 2 control charts for monitoring linear profiles under uncertainty of parameters

This paper proposes a robust economic-statistical design for Hotelling’s T 2 control chart to monitor linear profiles, accounting for uncertain parameters. Unlike previous studies assuming fixed inputs, this work applies an uncertainty interval approach to address parameter uncertainty when investigating the T 2 chart design. In this way the challenge of parameter uncertainty's adverse impact on the effectiveness of quality control models in practice is addressed. The key contribution of this study is formulating a T 2 control chart that maintains accuracy despite uncertainty. Results demonstrate the value of increased costs to mitigate uncertainty risks. The proposed approach also facilitates selecting appropriate protection levels against uncertainty. The paper examines practical challenges and applications of implementing the T 2 chart under real-world conditions affected by uncertainty. Overall, the proposed robust T 2 control chart design incorporates parameter ranges for monitoring linear profiles, contrasting with previous models assuming fixed parameters.

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.

The multi-objective economic statistical design of the p-chart: NSGA II approach

A control chart is a crucially important tool in statistical process control that is essentially used to differentiate between assignable and chance causes of variation. With the advent of Six Sigma in the parlance of quality management, the control chart assumes more significance to hold the gain in the control phase after attaining process improvement in the improve phase. The sample size, sampling interval, and control limits’ multiplier are three important parameters required to design an effective as well as efficient control chart. Many approaches like economic design, statistical design, and economic statistical design of control charts have been studied by several researchers. All these approaches consider a single objective function. In this paper, we have proposed a multi-objective design of the p-chart, where we are minimizing both out-of-control Average Run Length ( ARL δ ) and the expected cost per cycle ( C E ). Non-dominated Sorting Genetic Algorithm II (NSGA II) is used to solve the proposed multi-objective model. The proposed approach is demonstrated with the help of two numerical examples and the corresponding results are found to be quite encouraging for minimizing both objectives in comparison to another pertinent model given in the literature. Sensitivity analysis has been carried out to give credence to the worth of the proposed approach.

A-202 Quality control design survey reveals 399 ways to do it wrong

Abstract Background The effectiveness of statistical quality control processes to detect unacceptable patient risk depends on the choices that laboratory professionals make for the design of quality control charts and acceptable patient risk. Recommended best practice consists of putting a meaningful recent mean and SD on the QC chart, selecting rules based on the method’s margin for error to unacceptable risk or Sigma value, and basing acceptable risk on clinical need. Methods A survey was circulated through LinkedIn and Labvine. Forty respondents who included their credentials were included in the final analysis. Respondents were asked to select the one most correct answer four questions regarding the parameters that govern the effectiveness of quality control processes. 1. The best source of the mean on the QC chart? (Four choices) 2. Best source of the SD on the QC chart? (Five choices) 3. Best way to select QC rules for each QC sample? (Six choices) 4. If an analytical process “fails,” we should stop reporting before [errors are reported.] (Five choices) A total of 400 potential patterns of QC selections were chosen. (4 * 5 * 5 * 4). Results When asked acceptable error rate if an analytical process “fails,” responses were More than 5% errors are reported - 11%. Any errors are reported - 66% It varies with clinical use of the test - 16% It varies with capabilities of our method - 8% While most respondents chose at least one of the recommended answers for QC chart design and rules, only three chose the best choice for all parameters. Conclusions Despite decades of recommendations of best practice for quality control, typical practice throughout the laboratory community in general does not reflect this. It is time to consider a new approach to teaching, validating and certifying competency in medical laboratory quality control.

A new control chart based on proportional hazards and frailty regression models for monitoring high‐quality processes with censored observations

AbstractImproving quality and reducing defects in various processes have led to the design of numerous control charts for monitoring count data. These charts are characterized by a large number of zero defects and are modeled with zero‐inflated distributions. Besides, it is important to consider the influence of key factors on the number of defects in some processes. This paper presents three monitoring scenarios that utilize cumulative sum (CUSUM) control charts in Phase II. These scenarios are valuable for monitoring high‐quality processes, particularly with censored observations. The first scenario uses a zero‐inflated Poisson (ZIP) distribution while the second one employs a proportional hazards regression model to account for observed variables. The third scenario combines the proportional hazards and frailty regression models to consider both observed and unobserved variables. The performance of all three control charts is evaluated by applying shifts to both parameters of the ZIP distribution separately and simultaneously. Extensive simulation studies are conducted and the effects of low, moderate, and high censoring rates are thoroughly studied. The results highlight the importance of considering influential variables for detecting early shifts, as neglecting them significantly impairs the control chart performance. Finally, a real case study, involving defect counts in printed rolls at a label printing factory, has been provided and discussed to show the application of the monitoring procedures.

Implementing Statistical Distribution for Control Chart Design in Higher Education Institutions

Implementing Statistical Distribution for Control Chart Design in Higher Education Institutions

Design of Control Charts Using Repetitive Sampling: A Comparative Study of Conditional Expected Delay

Design of Control Charts Using Repetitive Sampling: A Comparative Study of Conditional Expected Delay

Assessing the economic-statistical performance of an attribute SVSSI-np control chart based on genetic algorithms

The SVSSI scheme, featuring three variable sample sizes and two variable sampling intervals, considerably enhances the performance of control charts in detecting shifts. As a novel contribution, this study proposes an optimized design of the SVSSI-np control chart using genetic algorithms, illustrating its superior performance over other sampling schemes by considering economic and statistical perspectives in a unified model. The outcomes of implementing the SVSSI alongside other sampling schemes are assessed via a numerical example, demonstrating the influence of varying parameters such as process failure rate, shift value, and proportion of nonconforming items. Based on the obtained results, the SVSSI scheme outperforms other schemes by achieving over a 10% reduction in costs and over a 30% improvement in reducing time to signal and false alarm rates in most runs. The impact of inaccurately estimating the shift size is also investigated, revealing that incorrect estimates can lead to ineffective adjustments and improvements. Finally, optimal SVSSI designs are explored through comprehensive sensitivity analysis and robust optimization to address uncertainty, and the results of applying fractional factorial design are statistically analyzed. In summary, the SVSSI-np control chart demonstrates potential for enhanced cost reduction, process monitoring, and efficiency gains.

The Mixed MEWMA and MCUSUM Control Chart Design of Efficiency Series Data of Production Quality Process Monitoring

The Mixed MEWMA and MCUSUM Control Chart Design of Efficiency Series Data of Production Quality Process Monitoring

A nonparametric adaptive EWMA control chart for monitoring multivariate time-between-events-and-amplitude data

Multivariate time-between-events-and-amplitude (TBEA) data, which includes the time interval between two consecutive occurrences of the event as well as their amplitudes, is a common data type in manufacturing and service operations. Designing control charts to monitor TBEA data is of great significance to improve product quality. However, most TBEA control charts are typically constructed under the assumption that the data distribution is known. The monitoring performance of these parametric TBEA control charts may become less reliable when the assumed data distribution is unknown. To address this issue, we propose a nonparametric adaptive TBEA (NATBEA) control chart based on the antirank method and adaptive strategy. Firstly, a nonparametric monitoring statistic is constructed by using the antirank method. With using the adaptive strategy, a nonparametric adaptive EWMA control chart is designed to monitor TBEA data, and the monitoring performance of various shifts is improved. Then, we compare the monitoring performance of the NATBEA control chart and other eight control charts, and the numerical simulation results show that the NATBEA control chart has superior monitoring performance for various mean shifts with different data distributions. Finally, an example of a company’s production failure demonstrates that the developed NATBEA control chart outperforms various conventional control charts by providing rapid alarms when the process is out of control.

The economic production quantity model for an imperfect production process by control chart design

The Economic Production Quantity (EPQ) plays a crucial role in the manufacturing process. The traditional EPQ model operates under the assumption that Non-Conforming (NC) items are not produced, and the process remains under control. However, real-world scenarios often involve the production of NC products, leading to process deviations. This study introduces a model that optimizes the design of a control chart to incorporate NC products into the EPQ model. The model integrates inventory and quality-related costs to minimize the expected total cost by determining EPQ, sample size, and control limit. The solution methodology employs direct search techniques to solve this problem. The sensitivity analysis results demonstrate the significant cost reduction achieved by the proposed model compared to the classical EPQ model. The numerical examples presented in the study show an average cost reduction of approximately 21 percent, highlighting the potential effectiveness of the model in cost reduction efforts.

On moving average based location charts under modified successive sampling

Ceramics are made up of water, clay, and powders. These are categorized as non-metallic and inorganic materials. It is revealed in the literature that Longquan celadon glaze had irregular cracks in glaze layers due to the relatively high content of $Na_{2}O$. Therefore, it is necessary to monitor the influence of $Na_{2}O$ in the ceramic process. Control charts are a possible tool to monitor the changes in the ceramic process. For single event issues, simple random sampling strategy is utilized; however, modified successive sampling is preferred as the favored sampling strategy at regular intervals of time when the quality of any product is evaluated. Hence, this paper is designed to propose moving average $M{A_{MSS\left( S \right)}}$ and double moving average $DM{A_{MSS\left( S \right)}}$ based control charts to detect small to moderate location shifts using the modified successive sampling technique. We have highlighted the performance evaluations of designed control charts with respect to run-length metrics, and their comparison has been made with the existing $Shewhar{t_{MSS\left( S \right)}}\;$control chart. The results revealed that the $DM{A_{MSS\left( S \right)}}$ performs more efficiently as compared to the $Shewhar{t_{MSS\left( S \right)}}$ and $M{A_{MSS\left( S \right)}}\;$control charts. Further, to demonstrate the application of the designed charts, a dataset of the chemical composition of the ceramic is also utilized.

CPV Monitoring - Optimization of Control Chart Design by Reducing the False Alarm Rate and Nuisance Signal

The Food and Drug Administration’s 2011 Process Validation Guidance and International Council for Harmonization Quality Guidelines recommend continued process verification (CPV) as a mandatory requirement for pharmaceutical, biopharmaceutical, and other regulated industries. As a part of product life cycle management, after process characterization in stage 1 and process qualification and validation in stage-2, CPV is performed as stage-3 validation during commercial manufacturing. CPV ensures that the process continues to remain within a validated state. CPV requires the collection and analysis of data related to critical quality attributes, critical material attributes, and critical process parameters on a minimum basis. Data is then used to elucidate process control regarding the capability to meet predefined specifications and stability via statistical process control (SPC) tools. In SPC, the control charts and Nelson rules are commonly used throughout the industry to monitor and trend data to ensure that a process remains in control. However, basic control charts are susceptible to false alarms and nuisance alarms. Therefore, it is imperative to understand the assumptions behind control charts and the inherent false alarm rates for different Nelson rules. In this article, the authors have detailed the assumptions behind the usage of control charts, the rate of false alarms for different Nelson rules, the impact of skewness and kurtosis of a data distribution on the false alarm rate, and methods for optimizing control chart design by reducing false alarm rates and nuisance signals.

Economic and Economic-Statistical Designs of the Synthetic Bayesian Control Chart

Economic and Economic-Statistical Designs of the Synthetic Bayesian Control Chart

A hybrid design for jointly optimizing production scheduling, control chart design and maintenance in continuous flow manufacturing

Integrating the three crucial functions of quality control, economic production quantity (EPQ) and maintenance leads to cost savings and increased efficiency for manufacturing processes. While in the literature, they have typically been studied separately. Moreover, most of the existing integration models are designed for the discrete piece-part manufacturing environment. This study, nevertheless, focuses wholly on continuous flow manufacturing (CFM), which is distinctly different from piece-part manufacturing, as the sampling unit is described in light of laboratory requirements instead of the production unit. Based on this fact, this paper proposes an integrated EPQ scheme jointly designed with control-chart design and maintenance planning for the CFM process. A developed genetic algorithm is employed to minimize the expected total production cost under constraints on the economic-statistical quality. Of the costs considered, quality-related costs are quantified via an approximate formula derived from the quality loss curve depending on Taguchi’s quality loss function. A sensitivity analysis is performed on the expected total production cost and variations in the chosen system parameter values to offer insights into the issue. Finally, a comparative investigation of the suggested model and two similar models that contributed to this field is conducted.

Control Charts for Exponentially Distributed Characteristics: SD, ED, ESD with Taguchi’s Loss Function

ABSTRACT This paper addresses the challenge of quality characteristics that follow an exponential distribution, which can significantly impact decision-making in various fields. Existing approaches rely on approximations to convert exponential distributions to normal distributions, upon which control charts are constructed. However, such conversions introduce errors that can lead to incorrect outcomes, particularly for highly sensitive characteristics. To address this limitation, we propose the development of control charts specifically designed for exponential characteristics, without relying on approximations. Our objective is to introduce four different schemes for constructing these control charts: a statistical scheme, an economic scheme, an economic-statistical scheme combined with Taguchi’s loss function, and an economic-statistical scheme without the application of a loss function. To determine optimal design parameter values for each scheme, we employ the artificial bee colony algorithm. Additionally, we conduct a sensitivity analysis to investigate the impact of design parameters on each proposed design. To illustrate the practical implementation of these control charts, we provide a numerical example that demonstrates their effectiveness. By addressing the limitations of existing approaches and offering novel control chart designs, this paper contributes to enhancing decision-making accuracy and reliability in scenarios involving exponentially distributed quality characteristics.

The Development and Evaluation of Homogenously Weighted Moving Average Control Chart based on an Autoregressive Process

This research aims to investigate a Homogenously Weighted Moving Average (HWMA) control chart for detecting minor and moderate shifts in the process mean. A mathematical model for the explicit formulae of the average run length (ARL) of the HWMA control chart based on the autoregressive (AR) process is presented. The efficacy of the HWMA control chart is evaluated based on the average run length, the standard deviation of run length (SDRL), and the median run length (MRL). As illustrations of the design and implementation of the HWMA control chart, numerical examples are provided. In numerous instances, a comparative analysis of the HWMA control chart relative to the Extended Exponentially Weighted Moving Average (Extended EWMA) and cumulative sum (CUSUM) control charts with mean process shifts is performed in detail. Additionally, the relative mean index (RMI), the average extra quadratic loss (AEQL), and the performance comparison index (PCI) are utilized to evaluate the performance of control charts. For various shift sizes, the HWMA control chart is superior to the Extended EWMA and CUSUM control charts. This study applies empirical data from the area of economics to validate the explicit formula of ARL values for the HWMA control chart. Doi: 10.28991/HIJ-2024-05-01-02 Full Text: PDF

Optimal constrained design of control charts using stochastic approximations

In statistical process monitoring, control charts typically depend on a set of tuning parameters besides its control limit(s). Proper selection of these tuning parameters is crucial to their performance. In a specific application, a control chart is often designed for detecting a target process distributional shift. In such cases, the tuning parameters should be chosen such that some characteristic of the out-of-control (OC) run length of the chart, such as its average, is minimized for detecting the target shift, while the control limit is set to maintain a desired in-control (IC) performance. However, explicit solutions for such a design are unavailable for most control charts, and thus numerical optimization methods are needed. In such cases, Monte Carlo-based methods are often a viable alternative for finding suitable design constants. The computational cost associated with such scenarios is often substantial, and thus computational efficiency is a key requirement. To address this problem, a two-step design based on stochastic approximations is presented in this paper, which is shown to be much more computationally efficient than some representative existing methods. A detailed discussion about the new algorithm’s implementation along with some examples are provided to demonstrate the broad applicability of the proposed methodology for the optimal design of univariate and multivariate control charts. Computer codes in the Julia programming language are also provided in the supplemental material.

Optimization design of control charts: A systematic review

AbstractIn today's competitive landscape, fulfilling customer expectations and achieving a competitive edge are crucial for business success. These objectives can be attained by effective monitoring in both manufacturing and service sectors to enhance quality, reduce variation, and augment productivity. The control chart, a widely used tool for this purpose, has attracted significant attention from researchers for its ability to detect anomalies and manage out‐of‐control situations. The optimization of control charts, a central focus of this review, not only enhances the detection effectiveness but also maintains the desired false alarm rate, thus ensuring efficient process control without additional cost, complexity, or operational challenges for shop floor personnel. The optimization process involves adjusting charting parameters like the sample size, sampling interval, and control limits within a hypothesis testing framework, thereby achieving optimal system performance. Numerous optimization models have been developed to enhance control chart performance. This paper introduces a classification scheme to analyze and categorize the existing research on control chart optimization. By conducting a thorough review of more than 240 articles, the study pinpoints research gaps and offers valuable insights, thereby advancing the future research in this domain.

Patient‐based real‐time quality control in medical laboratories: On the design and robustness of the moving average control chart with truncation limits

AbstractQuality is an indispensable requirement in medical laboratories, where controls are performed at different phases of the laboratory processes. In the following, we consider the internal quality control activities during the analytical phase of medical laboratories for verifying the test results prior to their release. To monitor the measurement process for errors in the test results, one approach that is considerably attracting the health professionals is patient‐based real‐time quality control. In this respect, real‐time patient test results are monitored, commonly by implementing the Moving Average (MA) control chart with truncation limits. A usual practice is the use of truncation limits to exclude abnormal patient test results from the MA calculations. However, an open issue in the literature is how to determine the width of the truncation limits and the window size in the MA calculations. Furthermore, the distributions of the test results are often nonnormal and difficult to model by personnel having insufficient training in statistics. Consequently, robustness of the performance of the MA control chart to non‐normal distributions of test results is another open topic in the literature. In this study, a detailed robustness analysis is performed by considering various distributions having different shapes. Performance of several MA control chart designs constructed by altering the truncation limits and window sizes are investigated. Based on our simulation results with selected distributions, we conclude that the truncation limits should not be used and a window size of 20 is recommended. Under such a setting, the MA control chart performs similar to its intended performance in terms of false alarms and in detecting systematic errors, hence being robust to non‐normality of the test results.