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In most modern manufacturing systems, products are often the output of some multistage processes. In these processes, the stages are dependent on each other, where the output quality of each stage depends also on the output quality of the previous stages. This property is called the cascade property. Although there are many studies in multistage process monitoring, there are fewer works on profile monitoring in multistage processes, especially on the variability monitoring of a multistage profile in Phase-I for which no research is found in the literature. In this paper, a new methodology is proposed to monitor the standard deviation involved in a simple linear profile designed in Phase I to... 

In most modern manufacturing systems, products are often the output of several correlated stages. Nevertheless, quality of a product or process in both single and multistage processes is usually expressed by a single quality characteristic, two or more characteristics, or profiles. Although there are many studies in univariate and multivariate-multistage process monitoring, fewer works focus on profile monitoring of multistage processes. This paper addresses the problem of monitoring a simple linear profile that is going through a multistage process in phase II. Using a first-order autoregressive correlation model, the relationship between the stages is first modeled. Then, the cascade... 

Today's competitive market has witnessed a growing interest in improving the reliability of products in both service and industrial operations. A large number of monitoring schemes have been introduced to effectively control the reliability-related quality characteristics. These methods have focused on single-stage processes or considered quality variables which are independent. However, the main feature of multistage processes is the cascade property which needs to be justified for the sake of optimal process monitoring. The problem becomes complicated when the presence of censored observations is pronounced. Therefore, both the effects of influential covariates and censored data must be... 

This paper addresses the problem of robust parameter estimation of simple linear profiles in multistage processes in the presence of outliers in Phase I. In this regard, two robust approaches, namely the Huber’s M-estimator and the MM estimator, are proposed to estimate the parameters of the process in Phase I in the presence of outliers in historical data. In addition, the U statistic is applied to the robust parameter estimates to remove the effect of the cascade property in multistage processes and as a result, to obtain adjusted robust estimates of the parameters of simple linear profiles. The performance of the proposed methods is evaluated under weak and strong autocorrelations... 

This paper addresses the problem of robust parameter estimation of simple linear profiles in multistage processes in the presence of outliers in Phase I. In this regard, two robust approaches, namely the Huber’s M-estimator and the MM estimator, are proposed to estimate the parameters of the process in Phase I in the presence of outliers in historical data. In addition, the U statistic is applied to the robust parameter estimates to remove the effect of the cascade property in multistage processes and as a result, to obtain adjusted robust estimates of the parameters of simple linear profiles. The performance of the proposed methods is evaluated under weak and strong autocorrelations... 

This paper addresses the problem of robust parameter estimation of simple linear profiles in multistage processes in the presence of outliers in Phase I. In this regard, two robust approaches, namely the Huber’s M-estimator and the MM estimator, are proposed to estimate the parameters of the process in Phase I in the presence of outliers in historical data. In addition, the U statistic is applied to the robust parameter estimates to remove the effect of the cascade property in multistage processes and as a result, to obtain adjusted robust estimates of the parameters of simple linear profiles. The performance of the proposed methods is evaluated under weak and strong autocorrelations... 

When a multistage manufacturing process is monitored statistically, the cascade property results in a more complicated condition compared to the case when a single-stage process is controlled. The cascade property usually exists in different stages of a multistage process, where the quality of a stage influences the performance of the next stage. Moreover, sometimes the quality of a product/process is best characterized by a functional relationship. This relationship is referred to as a profile. In this paper, phase I monitoring of simple linear profile is addressed for a multistage process involving the cascade property. To aim this, the capabilities of the methods that may be used to... 

When a multistage manufacturing process is monitored statistically, the cascade property results in a more complicated condition compared to the case when a single-stage process is controlled. The cascade property usually exists in different stages of a multistage process, where the quality of a stage influences the performance of the next stage. Moreover, sometimes the quality of a product/process is best characterized by a functional relationship. This relationship is referred to as a profile. In this paper, phase I monitoring of simple linear profile is addressed for a multistage process involving the cascade property. To aim this, the capabilities of the methods that may be used to... 

Monitoring industrial and service processes with the purpose of improving the product reliability has been largely addressed in the literature. The surveillance procedures have been proposed with the concentration on single-stage processes with independent quality characteristics. However, the cascade property in multistage processes entails specific monitoring methods which take into account the dependency structure among quality variables in successive stages of a process. This is referred to as regression-adjustment that justifies the heterogeneity in the study population and thus leads to optimal monitoring of multistage processes. In general, it is not straightforward to adjust a... 

In this paper, a new control scheme is proposed for Phase-II monitoring of simple linear profiles in multistage processes. In this scheme, an approach based on the U transformation is first applied to remove the effect of the cascade property involved in multistage processes. Then, a single max-EWMA-3 control statistic is derived based on the adjusted parameter estimates for simultaneous monitoring of all the parameters of a simple linear profile in each stage. Not only is the proposed scheme able to detect both increasing and decreasing shifts but it also has the feature of identifying the out-of-control parameter responsible for the source of process shift. Using extensive simulation... 

In this article, the general linear profile-monitoring problem in multistage processes is addressed. An approach based on the U statistic is first proposed to remove the effect of the cascade property in multistage processes. Then, the T2 chart and a likelihood ratio test (LRT)-based scheme on the adjusted parameters are constructed for Phase-I monitoring of the parameters of general linear profiles in each stage. Using simulation experiments, the performance of the proposed methods is evaluated and compared in terms of the signal probability for both weak and strong autocorrelations, for processes with two and three stages, as well as for two sample sizes. According to the results, the... 

In some quality control applications, processes consist of multiple components, stations or stages to finish the final products or the services. Some quality characteristics in each stage of these processes (called multistage processes) can be represented by a relationship between a response and one or more explanatory variables which is named as profile. In this paper, a general model is proposed for monitoring multivariate profiles in multistage processes. To this aim, the multivariate form of the U transformation approach is first used to remove the effect of the cascade property between the stages. Then, three control schemes are employed to monitor the parameters of multivariate simple... 

In some quality control applications, processes consist of multiple components, stations or stages to finish the final products or the services. Some quality characteristics in each stage of these processes (called multistage processes) can be represented by a relationship between a response and one or more explanatory variables which is named as profile. In this paper, a general model is proposed for monitoring multivariate profiles in multistage processes. To this aim, the multivariate form of the U transformation approach is first used to remove the effect of the cascade property between the stages. Then, three control schemes are employed to monitor the parameters of multivariate simple...