multiple assignable causes

The main goal of this study is to propose a realistic and practical model for the economic-statistical design of X ̄control charts in the presence of multiple independent assignable causes under the Burr Type XII shock model. The model aims to minimize underestimation of the actual cost per unit time of the quality cycle.

This research utilizes the Burr Type XII distribution as a shock model to develop the RED model for optimal design of X ̄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.

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, emphasizing the importance of considering this probability in E(A) calculations.

 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.

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.

Statistical Process Monitoring (SPM),maintenance are two major concepts todecrease the number of non-conforming products. In this regard,an integratedmodel of SPM,maintenance for imperfect high-quality processes is presented.Furthermore,in studies that consider these two concepts simultaneously,it is assumed that there is only one assignable cause in the production process. This simplifying assumption is unlikely to occur in real production processes due tothe usual complexity of manufacturing systems. It may lead to a poor performance in both economic,statistical criteria if the assignable cause originating the shift is different from the one anticipated at the design of the chart. To make the model more adapted to real manufacturing situations,the process under consideration can turn into an out-of-control state due to several types of assignable causes. The particle swarm optimization algorithm is used to maximize the expected profit per time unit,subject to statistical quality constraints. Then,the effects of parameters lambda,in (the event occurrence rate when the process is in the in-control state),A,in(the false alarm cost),A,out(the search,repair cost),V,in (the profitper time unit when the process is in-control state),V,out (the profit per time unit when the process is out-of-control state),and C,e (the cost incurred by the occurrence of the event) on the profit per time unit are investigated. Finally,to show the effectiveness of the suggested approach,two comparative studies are presented. In the first comparative study,the integrated model is compared to a similar model without maintenance activities. The results confirm that implementation of maintenance activities leads to a significant increasein the manufacturer's profit. In the second comparative study,the presented model is compared to a similar model in which statistical constraints are eliminated. The results indicate that the proposed model extremely improves average time to signal in both in-control,out-of-control states while the profit per time unit decreases slightly.