a.h. amiri

In some statistical quality control applications, the process outcome is better expressed by a functional relationship among several correlated response variables and one independent variable called multivariate simple linear prole. Monitoring such proles without taking the correlation structure among the response variables into account leads to misleading interpretations. Specically, monitoring each prole by a separate chart increases the probability of Type I error. With increasing customer expectations, detecting small and moderate changes has become important in today's competitive markets. In this regard, some monitoring schemes including memorytype charts, adaptive charts, and progressive mean (PM) charts have been proposed to enhance the chart sensitivity in reacting to small and moderate disturbances. In this paper, three PM based monitoring schemes including MPMa, MPMe and MPMae charts are developed for Phase II monitoring of multivariate simple linear proles. Extensive simulations in terms of average run length (ARL) metric are carried out to probe the capability of the proposed charts in detecting separate and simultaneous changes in regression model parameters (intercept, slope and standard deviation). Moreover, the sensitivity of the proposed PM based charts is compared with competing ones in the literature including MEWMA, MEWMA/x2 and MEWMA-3 schemes. The results conrm that under dierent correlation coe cient values, when the intercept parameter of one pro- le changes from its nominal value, the proposed charts work better than the competing ones. Under the mentioned shift structure, the sensitivity of all charts improves by increasing the value of correlation coecient. Concerning the sustained shifts in slope parameter, it is observed that by increasing the correlation coecient and shift magnitude, the MPMa and MPMae charts perform better than the other ones. Besides, under standard deviation disturbances, the proposed charts have almost the same sensitivity to react to small and moderate changes. The results indicate that under simultaneous shifts in model parameters of both proles, the proposed PM based schemes have better detectability than their competing ones. Finally, the applicability of the best proposed chart is illustrated using a real life example from automotive industry.

Most Shewhart control charts are designed to monitor changes in the mean or variance of the process. There are some situations when the process mean fluctuates from time to time, but is still considered as in-control and the process standard deviation is a linear function of the process mean. In addition, in some cases, the mean and the variance of the process are actually dependent on each other. Also, in many processes, monitoring the mean or variance of the process is unreasonable due to the nature of the process, and it is recommended that the coefficient of variation be used to monitor the process. Although monitoring multivariate coefficient of variation was studied at both Phases I and II, the design of chart for monitoring multivariate CV considering measurement errors was not thoroughly studied in previous studies; hence, it has been considered in this research. In this paper, a run sum control chart is developed for monitoring multivariate coefficient of variation in the presence of measurement errors at Phase II and the performance of the proposed chart with and without the assumption of measurement errors was compared through Average Run Length (ARL) criterion based on Markov chain approach. The results show that the presence of measurement errors has a negative effect on the performance of the run sum control chart. In other words, ARL of the run sum chart in the presence of measurement errors gets far away from the corresponding value without measurement errors as the magnitude of measurement errors increases. This research considers multiple measurements approach to reduce the effect of measurement errors on the performance of control charts in monitoring the multivariate coefficient of variation at Phase II. The results of the proposed chart's performance show that ARL decreases in the presence of measurement errors due to increasing the effect of measurement errors on the performance of control chart. The results show that by using the multiple measurements approach, the results become closer to the case without measurement errors.

One of the most important goals of organizations and manufacturing companies is to provide suitable products and services to customers, requiring high-quality processes and keeping them at a desired quality level. In many cases, product quality is low due to equipment deterioration; however, it cannot be figured out until the equipment breaks down. On the other hand, control charts can be used to identify the condition of the process, where the out-of-control state for a quality characteristic means deterioration in the equipment, which is used for the manufacturing purpose. Hence, the statistical process control and maintenance decisions can be combined to form an integrated model that enjoys higher efficiency in reducing costs of quality and maintenance. Furthermore, using delayed monitoring policy to monitor processes is one of the newest research fields in this regard. Delayed monitoring means that processes are in control at the beginning of the process and sampling can be delayed until the pre-specified scheduled time. With a delayed monitoring policy, the total cost of production per unit is expected to be more affordable as the sampling rate decreases; however, it may be lead to an increase in the quality and maintenance costs. Therefore, determining efficient decision variables is important in the model. In this paper, an integrated statistical process control and maintenance model based on delayed monitoring is designed for a two-stage process. By using this procedure, 28 different scenarios are created in which variations in quality and different break-down states are considered. barX residual mean control charts have been used for monitoring purposes. In order to integrate statistical process control and maintenance, a model is proposed such that the expected cost per time unit of manufacturing is minimized by using a genetic algorithm. To evaluate the performance of the proposed method, an illustrative example is presented. In addition, sensitivity analysis of some parameters of the proposed model is carried out. The results show the appropriate performance of the proposed model.