Journal of Quality Engineering and Management

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 Abstract: One of the basic issues in Ultrahigh-dimensional data analysis is fitting the optimal model and estimating its unknown quality parameters in such a way that it can correctly interpret the structure of the investigated data. In this article, we compare two non-local hyper priors: hyper product moment and hyper product inverse moment priors in determining the optimal model at the same time as estimating the parameters in variable selection using Bayesian Shrinkage in ultrahigh-dimensional generalized linear models. In order to compute the posterior probabilities, the Laplace approximation method was used, and to select the optimal model in the model space of posterior probabilities, Simplified shotgun stochastic search algorithm with screening (S5) for GLMs was used along with screening. Finally, through the study of simulation and real data analysis, the effectiveness of the above Bayesian Shrinkage methods has been evaluated with the ISIS-LASSO and ISIS-SCAD method. The advantage of the model is shown.

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.