Journal of Quality Engineering and Management

Abstract In shock models, the system will fail as soon as the amount of damages caused by shocks exceeds its failure threshold. In this research, the design of control chart for reliability monitoring of systems with random failure threshold subjected to cumulative random shocks is discussed. In the cumulative shock model, the system fails when the cumulative amount of damage caused by the shocks exceeds the failure threshold of the system. For the analytical solution of the model related to the control chart, there are some complexities such as the existence of unknown distributions, obtaining the convolutions of the distributions and integral calculations. To overcome these problems, phase-type distribution is used for modeling. By presenting a numerical example, the results of the presented analytical model are evaluated and compared with the Monte Carlo simulation method. Also, the performance of the proposed control chart using the average run length and average time to out of control signal criteria is evaluated.

Abstract The economic design of control charts depends on the process shock model distribution and due to difficulties from both theoretical and practical aspects. This paper pursues to develop the economic design of X ̅ control chart for monitoring continuous flow processes under Bur XII shock model. The Burr XII distribution is flexible and its hazard rate can take many forms like as fixed, increasing, decreasing, and single mode or even U-shaped. Continuous flow processes are used in batch processes such as those meet to filtering, chemical processing and etc. A sensitivity analysis is executed and numeric examples are given to illustrate the effects of changing the parameters of the shock model distribution on the optimum values of the economic design models as discussed in this paper. In addition, we use uniform and non-uniform sampling schema and comparison between them. This comparison show that for non-constant hazard rate, non-uniform sampling scheme is better.

Abstract In this paper, an economic statistical design of control chart is presented for individual qualitative characteristics that have an exponential distribution. For this purpose, we first convert the exponential distribution of individual observations to the normal distribution using the approximation proposed by Nelson. Then, using Costa and Rahim economic model, we have obtained an economic statistical design for the transformed observations. In order to optimize the model parameters that are calculated based on the design parameters, we have obtained the optimal values of the design parameters using the honey bee algorithm. Finally, the results of the economic statistical design of the control chart are compared with the economic design and the positive performance of the economic statistical design compared to the economic design is shown. Also, by simulated data from the exponential distribution, the efficiency and performance of the introduced control chart in comparison with the case that the distribution of the qualitative characteristics is normal, has been investigated. 
 
 

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 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 Traditional control diagrams are based on the basic assumption that process data are sequentially independent of each other and have a normal distribution. However, in many cases in the real world, including in chemical and continuous processes, this assumption does not exist and there is a kind of autocorrelation between the data collected from the process. The use of traditional control charts in self-correlated processes is unreliable and increases erroneous warnings. One of the methods developed to control autocorrelation processes is to identify the structure of process time series and use residual values ​​to control process. In this paper, a model based on adaptive neural-fuzzy systems to identify time series structure and predict design use. May be. Is in AR (2). Also, the residual control diagrams based on this system for the self-return data of degree 2 and for (EWMA) finally using the simulated data, the efficiency of the proposed method in the moving average diagram are evaluated. Different degrees of correlation are evaluated.

Abstract As is well known, data obtained from real-world processes are typically autocorrelated, and monitoring such processes requires accounting for this autocorrelation. The control charts developed so far for monitoring the defective proportion (p) are generally based on the assumption that binary observations are independent, which ignores the inherent correlation in the data.
In this paper, a cumulative sum (CUSUM) control chart is proposed that incorporates the autocorrelation between binary observations using a first-order two-state Markov chain model. Furthermore, using the Average Number of Observations to Signal (ANOS) index, it is shown that under 100% inspection conditions, the proposed chart performs better than the Bernoulli CUSUM chart—which assumes independent observations—and, in other words, detects increases in p more quickly.