Journal of Quality Engineering and Management

Abstract Purpose: In many industrial processes, there are situations where simultaneous monitoring and control of two or more dependent variables are necessary. In such cases, univariate control of quality characteristics can be misleading when considered independently. In the classical approach, when a quality characteristic falls outside the specified technical limits, the quality loss is regarded as a cost. All products within the technical limits of the quality characteristic are assumed to have similar quality, regardless of the deviation of the quality characteristic from its target value. However, it is essential to distinguish between products that fall within the technical limits of the quality characteristic, as any deviation from the target value incurs a proportional loss.
Methodology: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated. In summary, this study focuses on the statistical-economic design of a multivariate T²-Hotelling control chart with multivariate variable sampling intervals in the presence of a reflected normal multivariate loss function (RNLMVSIT²). Additionally, a sensitivity analysis is conducted to examine the effects of time and cost parameters on the design parameters and the average cost.
Findings: The results demonstrate the satisfactory performance of the proposed models.
Originality/Value: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated.

Abstract  
 If the identification of small changes in the production process is intended, the Moving Averaging Control Chart (EWMA) is a good alternative to the X control chart. In situations where a large sample of the population cannot be extracted due to economic constraints, the Simple Random Sampling Scheme (SRS) may not be accurate enough, in which case the RSS can be used. Appeared. In this paper, for the first time, the economic and statistical-economic design of the EWMA control chart under the RSS design is reviewed. By presenting numerical results, the advantages of statistical-economic design over economic design are shown. The results show that costs in statistical-economic design have increased slightly compared to economic design, but due to the low false alarm rate are in line with statistical quality control objectives and at the same time reduce costs. , Controls the quality of the product at the desired level of error and high power. Keywords: Statistical-economic design, ranking set sampling, shock model. 

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 One of the most important tools for statistical process control is the control chart. The construction of control diagrams is achieved by determining the design parameters of the sample size, sampling distance and coefficient of control limits. Statistical-economic design is the best way to determine these parameters by considering statistical properties and cost. Statistical design - Economics Control charts require a distribution for the process failure mechanism. The most popular distributions in the analysis of the failure mechanism of the exponential distribution process are gamma and Weibull. Recently, a new distribution called generalized exponential distribution has been added to conventional distributions in data life analysis and process failure mechanisms. If the failure mechanism data follows this distribution, the use of other distributions will give users misleading and inaccurate results. On the other hand, a fundamental assumption in most control charts is the independence of process-related observations; But in practice we have situations with correlated data. As a result, it is of particular importance to identify control charts that can be used to control such data.In this paper, statistical-economic design of control charts with correlated data under generalized shockwave and Weibull models and by providing a numerical example , We show their application. We have applied a sensitivity analysis to investigate the effect of changing the controlled properties of the first type error rate, power and correlation coefficient. The results show that this type of control charts have undesirable statistical properties and the limitation on the first type of error has a significant effect on determining the average cost per unit time and design parameters. Also, the correlation coefficient is indirectly related to the sample size and sampling distance and is directly related to the average cost per unit time.

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.