Journal of Quality Engineering and Management

Abstract Purpose: The main goal of this study is to propose a realistic and practical model for the economic-statistical design of control charts in the presence of multiple independent assignable causes under the Burr Type XII shock model. The model aims to minimize the underestimation of the actual cost per unit time of the quality cycle.
Methodology: This research utilizes the Burr Type XII distribution as a shock model to develop the RED model for optimal design of control charts. The Lorenz and Van cost function is also extended to account for multiple assignable causes, and a numerical example is provided to demonstrate the solution approach.
Findings: Numerical results reveal that the proposed model outperforms existing models in accurately estimating the real cost per unit time of the quality cycle. Furthermore, an increase in the shock probability leads to a non-decreasing trend in the average cost, underscoring the importance of accounting for this probability in E(A) calculations.
Originality/Value: This is the first study to employ the Burr Type XII distribution as a shock model in the economic-statistical design of control charts. By extending existing cost models, the paper introduces a novel and realistic approach to designing control charts in the presence of multiple independent shocks.

Abstract In many control charts, the assumption of normality is a fundamental premise. However, in real-world applications, this assumption is often violated, leading to reduced efficiency in parametric control charts. When process data follow an unknown or non-normal distribution, parametric methods may yield unreliable results, making nonparametric control charts a more effective alternative. Among these, the sign control chart is a widely used technique for monitoring the location parameter of a process without requiring distributional assumptions. This study focuses on the economic design of the sign control chart in the presence of multiple independent assignable causes. A modified cost model, adapted from Duncan’s economic model, is developed to optimize the chart’s parameters. The analysis balances inspection costs and process performance to determine the most cost-effective monitoring strategy. Results indicate that the proposed model significantly enhances economic efficiency and detection performance under non-normal data conditions, making it a valuable tool for practical applications.

Abstract Control charts are one of the most effective tools used in quality control to monitor various quality characteristics in a process with the aim to improve quality of the product. Usually, in Shewhart control charts, the normality assumption met for the data, but sometimes there is lack of information regarding the statistical distribution of the observations. For this reason, non-parametric control charts are used in this situation. In this research, non-parametric sign charts are introduced to deal with the lack of information regarding observations’ statistical distribution. Nonparametric Generalized Weighted Moving Average Sign Control Chart (NS GWMA) designed using statistical design and average run length (ARL) and its statistical performance was studied. But statistical design is not enough to ensure the performance of a control chart, so in the next steps, economic design (ED) and economic-statistical design (ESD) were applied using cost model of Lorenzen and Vance, in order to optimize both statistical and economical characteristics of the control chart.

Abstract Control charts are widely used to identify changes in the production process, and when it comes to identifying small changes in the process, non-Shewhart control charts such as exponential weighted moving average (EWMA) and generalized weighted moving average (GWMA) are better alternatives to control charts than Shewhart ¯X control chart. In this context, nonparametric control charts are used when the distribution of quality characteristic of the process is unknown, in which the Sign control chart is one of the most popular nonparametric control charts. In this paper, for the first time, a generalized weighted moving average sign control chart using a ranked set sampling (RSS) design is introduced. The performance of the proposed control chart is evaluated using simulated data according to the average run length evaluation criterion, and simulation studies showed that the GWMA sign control chart under the RSS design is better at detecting small process changes than the EWMA sign control chart under the RSS design.

Abstract In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process is introduced. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carrited out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations.
Statistical quality control charts were introduced in the early work of Shewhart (1926) and since then several variations of them have been proposed for monitoring continuous characteristics. Most of the control charts are distribution-based procedures in the sense that the process output is assumed to follow a specified probability distribution (usually normal); see, for example, Albers et al. (2004).

Abstract We introduce a method for the statistical design of a depth-based control chart, using the percentile-based approach. The proposed control chart is affine invariant and is asymptotically distribution-free. Generally, the performance of a control chart is evaluated with the average run length metric. The average run length metric has a geometric distribution skewed to the right with a large standard deviation and may not be a proper measure for evaluating the control chart. Therefore, we use the statistical design method of control charts with the PL approach, which is an improvement and development on classical statistical design. By employing constraints on average run length, the length of in-control and out-of-control performances are guaranteed with predetermined probabilities and we can ensure that the in-control run length exceeds the desired value and the out-of-control run length is less than the desired value. Simulation studies show that the proposed control chart is more efficient than the average run length approach.

Abstract Abstract: One of the most widely used tools in the rapid detection of assignable causes is control charts. Given the importance of economic costs, Duncan proposed the first economic model in the presence of multiple assignable causes in order to reduce the economic costs of the quality cycle. In his model and all the economic designs derived from that, assumed that after the occurrence of an assignable  cause, process is free from the occurrence of other assignable causes. In this paper, after criticizing previous models for incorrect and unrealistic use of this assumption to calculate the average cost per unit of quality cycle time, a realistic economic-statistical design in the presence of multiple assignable causes for economic-statistical design of  X-bar control chart is presented. The numerical results of our model show well that in the previous models; the average cost per unit time of the quality cycle is severely underestimated compared to the actual value and with increasing the Weibull distribution shape parameter, the probability of this assumption is greatly reduced. Therefore, it is suggested that in order to eliminate the shortcomings of the economic design of various types of control charts with multiple assignable causes in future research, they should be redesigned based on our model.

Abstract Any statistical method designed to detect process changes over time is within the scope of statistical process control. Among the most widely used tools for statistical process control, the control chart is the most important and powerful tool for statistical process control. Here it is important to understand that statistical process control charts are not complete in relation to process control in two respects. They do not have non-random causes and their elimination. In this paper, we introduce robust control diagrams for time-series data to detect reasoned deviations. We collect daily diagrams and draw solid control charts and standard control charts for time series data. Statistical analysis of this design was performed using SPSS16 software and finally by comparing Solid control diagram With standard control diagram for time series data, we conclude that the stable control diagram has a better performance than the standard control diagram. 

Abstract Extensive research has been done in the field of statistical process control. Also recently, control charts based on the Bayesian predictive distribution idea have been proposed in statistical process control texts. This idea was first proposed by Menzefricke and its parameters were considered unknown. In this paper, for the first time, statistical-economic design of control charts for monitoring the process mean with known standard deviation based on Bayesian predictive distribution is presented. According to the results presented in the article, regarding the superiority of statistical-economic design over economic design and also the superiority of Bayesian approach over the classical approach in designing control charts, it is suggested to use Bayesian control chart with statistical-economic design in controlling the process mean. 

Abstract   One of the most important control charts is Shewhart  ̅ chart. This sampling technique has proven to be very effective in situations where measurments are difficult or expensive, but could inexpensively be ordered. This article investigated economic design and economic-statistical design of  ̅X control chart based on RSS. The numerical results are shown economic statistical design is better than economic design based on RSS. Since economic-statistical design is more reasonable than economic design based on RSS. The result is shown the cost of  economic-statistical design has been increased a bit more than economic design based on RSS .So, It is suggested to use economic- statistical design  ̅X    control chart for controling of services and industrial processes mean based on economic and statistical optimization features of  ̅X  control chart and the results paper.   

Abstract Abstract: The chart is commonly used for monitoring processes where each produced items is characterized by its number of nonconformities. Recent studies have approved the advantages of using adaptive schemes rather than static one in monitoring such processes. In this paper, we develop a full adaptive model for control charts in which all design parameters (sample size, sampling interval, control limit) switch between two values, according to the most recent process information. The proposed scheme is investigated from the economic statistical viewpoint. The cost model is developed by using the Markov chain approach. Using numerical examples, we illustrate the performance of the proposed models and compare their efficiency with the other schemes. A sensitivity analysis is also carried out to investigate the effects of model parameters on the solution of the economic statistical design by using the design of experiments and regression analysis techniques.

Abstract Control charts are one of the most important tools for evaluating process performance and monitoring. In the classic design of a control chart, the cost of quality depends on whether the quality characteristic is inside or outside the control. The use of loss function in the design of control charts, as an estimator of the cost of production of defective products, contributes to a more comprehensive assessment and better management decisions. Therefore, in this article, the combination of loss function and economic statistical design of control charts. The loss functions used so far in this field have been symmetric functions, but in many cases overestimating or underestimating the ideal value for a quality characteristic does not produce the same losses. Therefore, for the first time in the literature on the design of control charts, this paper uses the asymmetric loss function of Linux. Using a practical example, the performance of quadratic, linear, exponential and linear loss functions are compared. The result of these comparisons showed that the Linex loss function has the lowest cost in statistical-economic design of the control chart compared to other loss functions.

Abstract The main function of a control chart is to help manage the detection of various sources of variability in a production process. Control charts are also widely used in the industry as a tool to monitor a production process to improve product quality. The most common control chart with one characteristic in mind is the control chart. In this paper, we propose and present an economic design model and statistical-economic design in order to optimally design control charts by considering the new generalized two-parameter Weibull distribution as a process failure mechanism. . From the comparison, we conclude that the statistical-economic model is better but more expensive than the economic model in terms of achieving the statistical properties of the desired control chart.

Abstract Multi-response optimization performed by the response procedure method is very common. Before optimization, we need to select and fit the appropriate model for each response. A major problem that may occur due to incorrect fitting of models and failure to reach optimal solutions is model misidentification. The solid regression model method, which is a semi-parametric method for estimating d, can have a better performance than both parametric and non-parametric estimation methods against model misclassification. In this research, the use of a robust regression model method is proposed to improve the model estimation and the appropriate fit of each of the answers will be investigated by one of the multivariate optimization methods, namely the utility function. In the following, an applied study is presented to compare parametric, nonparametric and semi-parametric methods. The results of this study show that the performance of the stable regression model is more appropriate in many situations as well as in the modeling stage than the other two methods. Therefore, the optimization results with a stable regression model are much more reliable.

Abstract Control chart is one of the basic tools of statistical quality control and monitoring during production of production and service processes. The cost of quality in the classical approach to control chart design depends on whether the quality characteristic is inside or outside the control range. Since the integration of the loss function approach into in-production monitoring activities such as control charts, which is derived from Taguchi's concept of social quality loss, in which the cost of quality depends on the amount of deviation of the quality characteristic from the target value, is a more comprehensive evaluation process. It is better guided in the management strategy. This paper combines the Taguchi loss function and the economic design of the X نمودار control chart. In addition, since the output data of the process may not follow the normal distribution or the assumptions of the central limit theorem may not be true of it, it is necessary to study the integrated model in these situations, in addition to the normal distribution mode. In this regard, the economic design parameters of the integrated model will be compared in the presence of normal and abnormal data, in which, due to the extent of incremental failure rate in production systems, from non-uniform sampling design for sample inspection and Weibull shock model for failure mechanism. The process is used.