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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... 

In this study, we introduce a multivariate gamma distribution, then, by defining a new statistic, three control charts called the MG charts, are proposed for this distribution. The first control chart is based on the exact distribution of this statistic, the second control chart is based on the Satterthwaite approximation, and the last is based on the normal approximation. The efficiency of the proposed control charts is evaluated by the average run length (ARL) criterion. The results show that whenever the magnitude of the parameter shifts c<1, the control chart based on the exact distribution has smaller ARL1s, while for c>1, the control chart based on Satterthwaite approximation show... 

In economic design of profiles, parameters of a profile are determined such that the total implementation cost is minimized. These parameters consist of the number of set points, n, the interval between two successive sampling, h, and the parameters of a control chart used for monitoring. In this paper, the Lorenzen-Vance cost function is extended to model the costs associated with implementing profiles. The in-control and the out-of-control average run lengths, ARL0 and ARL1, respectively, are used as two statistical measures to evaluate the statistical performances of the proposed model. A genetic algorithm (GA) is developed for solving both the economic and the economic-statistical... 

A new approach is developed in this paper to detect general mean shifts of multivariate quality control systems and to determine the quality characteristic(s) responsible for the shift. This approach takes advantage of both a decomposition method and an EWMA-based control statistics that are employed for multivariate normal distributions. In order to evaluate the performance of the proposed methodology, simulation studies are provided to estimate the in- and out-of-control average run lengths under different mean and variance shift scenarios. Simulation experiments are also given to compare the performances of the proposed procedure with the ones of the well-known MEWMA and MCUSUM methods.... 

The usual key assumptions in designing quality control charts are the normality and independency of serial samples. While the normality assumption holds in most cases, in many continuous-flow processes such as the chemical processes, serial samples have some degrees of autocorrelation associated with them. Ignoring the autocorrelation structure in constructing control charts, results in decreasing the in-control run length, and so increasing the false alarms. Moreover, when the object is to detect small shifts in the mean vector of a process, the performance of Cumulative Sum (CUSUM) control charts is dramatically better than Schewhart control charts. One of the methods, which have been... 

Recently, many researchers and practitioners have shown interest on profile monitoring as a relatively new subarea of statistical process control. One main reason for this interest, and perhaps a key factor for the contributions of many researchers to this field, is the various applications of profile monitoring in real life. Although one can easily encounter many univariate applications of profile monitoring in service and manufacturing environments, there exist situations where quality of a product or process needs to be modeled in multivariate terms. In this paper, we investigate monitoring of multivariate simple linear profiles in phase II when independence assumption of observations... 

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 this paper, a new procedure is developed to monitor a two-stage process with a second stage Poisson quality characteristic. In the proposed method, log and square root link functions are first combined to introduce a new link function that establishes a relationship between the Poisson variable of the second stage and the quality characteristic of the first stage. Then, the standardized residual statistic, which is independent of the quality characteristic in the previous stage and follows approximately standardized normal distribution, is computed based on the proposed link function. Then, Shewhart and exponentially weighted moving average (EWMA) cause-selecting charts are utilized to... 

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 paper, an approach based on the U statistic is first proposed to eliminate the effect of between-profile autocorrelation of error terms in Phase-II monitoring of general linear profiles. Then, a control chart based on the adjusted parameter estimates is designed to monitor the parameters of the model. The performance of the proposed method is compared with the ones of some existing methods in terms of average run length for weak, moderate, and strong autocorrelation coefficients under different shift scenarios. The results show that the proposed method provides significantly better results than the competing methods to detect shifts in the regression parameters, while the competing... 

A new methodology is proposed in this paper to both monitor an overall mean shift and classify the states of a multivariate quality control system. Based on the Bayesian rule (Montgomery, Introduction to statistical quality control, 5th edn. Wiley, New York, USA, 2005), the belief that each quality characteristic is in an out-of-control state is first updated in an iterative approach and the proof of its convergence is given. Next, the decision-making process of the detection and classification the process mean shift is modeled. Numerical examples by simulation are provided in order to understand the proposed methodology and to evaluate its performance. Moreover, the in-control and... 

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... 

In this research, an iterative approach is employed to analyze and classify the states of uni-variate quality control systems. To do this, a measure (called the belief that process is in-control) is first defined and then an equation is developed to update the belief recursively by taking new observations on the quality characteristic under consideration. Finally, the upper and the lower control limits on the belief are derived such that when the updated belief falls outside the control limits an out-of-control alarm is received. In order to understand the proposed methodology and to evaluate its performance, some numerical examples are provided by means of simulation. In these examples, the... 

Although multivariate statistical process control has been receiving a well-deserved attention in the literature, little work has been done to deal with multi-attribute processes. While by the NORTA algorithm one can generate an arbitrary multi-dimensional random vector by transforming a multi-dimensional standard normal vector, in this article, using inverse transformation method, we initially transform a multi-attribute random vector so that the marginal probability distributions associated with the transformed random variables are approximately normal. Then, we estimate the covariance matrix of the transformed vector via simulation. Finally, we apply the well-known T2 control chart to the... 

In this research, the main parameters of the multivariate cumulative sum (CUSUM) control chart (the reference value k, the control limit H, the sample size n and the sampling interval h) are determined by minimising the Lorenzen-Vance cost function [Lorenzen, T.J., and Vance, L.C. (1986), The Economic Design of Control Charts: A Unified Approach, Technometrics, 28, 3-10], in which the external costs of employing the chart are added. In addition, the model is statistically constrained to achieve desired in-control and out-of-control average run lengths. The Taguchi loss approach is used to model the problem and a genetic algorithm, for which its main parameters are tuned using the response... 

In most real-world manufacturing systems, the production of goods comprises several autocorrelated stages and the quality characteristics of the goods at each stage are correlated random variables. This paper addresses the problem of monitoring a multivariate-multistage manufacturing process and diagnoses the possible causes of out-of-control signals. To achieve this purpose using multivariate time series models, first a model for the autocorrelated data coming from multivariate-multistage processes is developed. Then, a single neural network is designed, trained and employed to control and classify mean shifts in quality characteristics of all stages. In-control and out-of-control average...