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In this research a novel model was proposed for calculation of the phase behavior in polymer solutions. The proposed model consists of modified Freed-FV, non-randomness factor and the new expression derived volume-based group contribution local composition model activity coefficients. Firstly the proposed model was considered without pseudo chemical part to obtain the interaction parameters of functional groups (This is for the use of interaction parameters of functional groups in various systems). The binary interaction parameters of the functional groups of new local composition model have been calculated by correlation of the experimental vapor-liquid equilibria (VLE) data with different molecular weights (MW) and temperatures of several polymers. The interaction parameters of functional groups were reported and the deviations of new local composition model were compared with UNIFAC and Entropic-FV models and proved the proposed model has an acceptable advantage over the mentioned models. By obtaining the practical interaction parameters of functional groups, the proposed model was applied for modeling of liquid-liquid equilibria (LLE) of polymer-polymer aqueous two-phase systems. Also, it was compared with UNIQUAC and UNIQUAC-NRF models. The suggested model consists of three adjustable parameters. Moreover, the coordination number was developed based on molar fraction and molecular size of solution components. The results revealed that the proposed model can predict aqueous multicomponent polymer systems with great precision.

In recent years, risk-adjusted control charts that account for the preoperative risk of patients have been widely used for monitoring of surgical outcomes. Generally, risk-adjusted control ...

In some application, quality of product or performance of a process described by some functional relationships between some variables known as multivariate linear profile in the literature. In this paper, we propose Max-MEWMA and Max-MCUSUM control charts for simultaneous monitoring of mean vector and covariance matrix in multivariate multiple linear regression profiles in Phase II. The proposed control charts also have ability to diagnose either the location or variation of the process is responsible for out-of-control signal. The performance of the proposed control charts is compared with existing method through Monte-Carlo simulations. Finally, the applicability of the proposed control charts is illustrated using a real case of calibration application in the automotive industry.

The problem of axisymmetric vibration of a flat thin rigid circular plate located inside a vertically exponentially graded, transversely isotropic material of infinite extent is addressed by means of a displacement potential method. The contact condition on one side of the foundation is assumed to be the perfect adhesion with the media but known to be faced by a penny-shaped crack at the other side as it occurs in anchors. The mixed boundary value problem is formulated with the aid of Hankel integral transforms and is written in the form of a set of singular integral equations. The analytical procedure for the special case of vertical movement of the rigid plate results in a closed form solution. The solution is pursued numerically for the general elastodynamic case. The physical quantities, such as contact stress on the plate and the stress and displacement fields in the non-homogeneous medium are obtained for different materials.

Purpose The purpose of this paper is to develop some robust approaches to estimate the logistic regression profile parameters in order to decrease the effects of outliers on the performance of T2 control chart. In addition, the performance of the non-robust and the proposed robust control charts is evaluated in Phase II. Design/methodology/approach In this paper some, robust approaches including weighted maximum likelihood estimation, redescending M-estimator and a combination of these two approaches (WRM) are used to decrease the effects of outliers on estimating the logistic regression parameters as well as the performance of the T2 control chart. Findings The results of the simulation studies in both Phases I and II show the better performance of the proposed robust control charts rather than the non-robust control chart for estimating the logistic regression profile parameters and monitoring the logistic regression profiles. Practical implications In many practical applications, there are outliers in processes which may affect the estimation of parameters in Phase I and as a result of deteriorate the statistical performance of control charts in Phase II. The methods developed in this paper are effective for decreasing the effect of outliers in both Phases I and II. Originality/value This paper considers monitoring the logistic regression profile in Phase I under the presence of outliers. Also, three robust approaches are developed to decrease the effects of outliers on the parameter estimation and monitoring the logistic regression profiles in both Phases I and II.

The general form of the one- and two-point correlation tensor of a homogeneous and \((K,\theta )\)-isotropic random field and the spectral expansion of such a field in terms of stochastic integrals with respect to certain random measures depend on the choice of a basis in the linear space where the field takes its values. We choose a basis for 11 different fields. It turns out that the basis depends only on the crystal system of the group K.

Healthcare processes comprise multiple stages in practice. Also, few researchers have addressed Phase I monitoring of healthcare outcomes. Hence, the purpose of the proposed method is Phase I monitoring by two risk adjusted control charts in multistage healthcare processes. The proposed control charts are based on the Bernoulli state space model and consider other categorical covariates in addition to patient’s risk. To estimate the model parameters, an expectation-maximization algorithm is applied in a Kalman filter and smoother framework. The performance of the proposed monitoring schemes is compared in two and three stages. The simulation results show that the standardized likelihood ratio test method has competitive performance relative to Hotelling’s chart under different step shifts and drift. Also, Hotelling’s chart is superior to the standardized likelihood ratio test method in for outlier patients. Finally, a real case is utilized to show the applicability of the proposed risk adjusted charts.

Following the motivation of this work, this chapter introduces the basic concepts of continuum mechanics and electromagnetism. Attention is then focused on linear piezoelectricity, elaborating two ways of writing the governing equations: the displacement approach and the stress approach. This leads to variational principles. The final section provides a basis for generalising piezoelectricity—and, by mathematical analogy, piezomagnetism—to random media whose description necessitates tensor-valued random fields.

Background: In the healthcare area of cancer patients, the diagnosis procedure of cancerous tumors and metastases is a valuable and popular research subject in magnetic resonance imaging. A highly accurate diagnosis procedure can be support for doctors in interpreting and diagnosing medical data. Methods: To address this subject, we used a two-dimensional discrete wavelet transform. First, some features of the image texture were extracted by statistical and transform methods. Then, a genetic algorithm was used for data reduction and feature selection. Afterward, to diagnose bone marrow metastatic patients, we used two methods including a fuzzy c-Means clustering algorithm and a multivariate Hotelling’s T2 control chart. In this paper, we employed ADC and T1-weighted images of the pelvic region. From 204 bone marrow samples, 76 features were extracted, six of which were selected and a 204 × 6 feature vector matrix was generated. Finally, the performance of the two proposed methods was compared in terms of diagnosis and accuracy measures. Results: The results showed that the diagnosis (100%) and accuracy (100%) of the multivariate Hotelling’s T2 control chart were better than those of the other method, with a diagnosis of 99.49% and accuracy of 99.51%. Conclusion: In this paper, instead of classification and clustering methods, for the first time, we used a multivariate control chart with the Hotelling’s T2 statistic for the diagnosis of patients suspected of bone marrow metastasis. Then, using some patient samples, the performance of this phase I control chart was evaluated, and the results showed the validity of the proposed method. The validation results revealed that the accuracy and specificity metrics were better for the multivariate Hotelling’s T2 control chart than for the fuzzy clustering method.

The effect of measurement errors on adaptive Shewhart charts have been investigated by several researchers. However, the effect of measurement errors on the performance of variable sample size EWMA control charts has not so far been investigated. In this paper, the performance of the VSS EWMA chart in the presence of measurement errors is investigated using a linear covariate error model and a Markov chain method. It is shown that the performance of the VSS EWMA chart is significantly affected by the presence of measurement errors. The effect of taking multiple measurements for each item in a subgroup on the performance of the VSS EWMA chart is also investigated. Moreover, the performance of the VSS EWMA control chart is compared with several other control charts in the presence of measurement errors. At last, an illustrative example is presented to show the application of the VSS EWMA control chart with measurement errors.

The manufacturing operations often involve multistage processes where the process capability of each stage is affected by the process capability of its precedent processes. This property is known as the cascade property. The purpose of this paper is to estimate the process capability of the second stage of two-stage process while the cascade property impact is removed using residuals analysis. To this end, a method is proposed to determine the specification limits of the residuals based on the specification limits of the quality characteristics in the first and second stages. The C p, C pk and S pk indices are used to calculate the capability of the second stage in the two-stage process. The results of simulation study show the satisfactory performance of the proposed method in estimating the pure process capability of the second stage.

In most researches in the area of profile monitoring, it is assumed that observations are independent of each other. Whereas, this assumption is usually violated in practice and observations are autocorrelated. The control charts are the most important tools of the statistical process control which are used to monitor the processes over time. The control charts usually signal the out-of-control status of the process with a time delay. Whereas knowing real-time of the change (change point), one can achieve great savings on time and expenses. In this paper, the estimation of the change point in the simple linear profiles with AR (1) autocorrelation structure within each profile is considered. In the proposed method, by acquiring the joint probability density function of the autocorrelated observations, the maximum likelihood estimation method is applied to estimate the step change point. Here, we specifically focus on Phase II and compare the performance of the proposed estimator with the existing estimators in the literature through simulation studies. In addition, the application of the proposed estimator in comparison with the two estimators is illustrated through a real case. The results show the better performance of the proposed estimator.

In some applications, the quality of a process or product is characterized by correlated multivariate linear and generalized linear model (GLM) regression profiles. Monitoring these profiles separately leads to misleading results because the correlation structure among the multivariate linear and GLM profiles is neglected. In this paper, we specifically concentrate on Phase II and propose some procedures for monitoring multivariate linear and GLM regression profiles. Simulation studies are used to compare the performance of the proposed methods under different magnitudes of shifts in the regression parameters in terms of the average run length criterion. The results of simulation studies show the superior performance of the proposed methods compared to monitoring multivariate linear and GLM profiles separately. In addition, the performance of the proposed monitoring schemes is illustrated by a numerical example. Finally, the application of the proposed methods is shown by a real-world case.

In this study, we propose a control chart for monitoring two-stage processes whose quality characteristic to be monitored in the second stage follows a binomial distribution. The proposed control chart is based on the deviance residual in which essentially the generalized log-likelihood ratio statistic is obtained from the generalized linear model. To establish the relationship between the first- and second-stage quality characteristics, we propose using a new link function in a generalized linear model framework. The performance of the proposed control chart with the new link function is compared with that under the traditional logit link function in terms of the average run length criterion. In addition, the performance of the proposed control chart is compared with the chart designed based on the original residuals under the new link function as well as the traditional np-chart applied for monitoring the binomial quality characteristic in the second stage.

Profile monitoring is a useful technique in statistical process control used when the product or process quality is represented by a function over a time period. This function represents the relationship between a response variable and one or more explanatory variables. Most existing control charts for monitoring profiles are based on the assumption that the observations within each profile are independent of each other which is often violated in practice. Sometimes there are one or more outliers in each profile, which leads to poor statistical performance of the control chart. This paper focuses on Phase II monitoring of a simple linear profile with autocorrelation within profile data in the presence of outliers. In this paper, we propose a new combined control chart based on the robust Holt-Winter model to decrease the effect of outliers. We first evaluate the effect of outliers on the performance of the proposed combined control chart. Then, we apply robust Holt-Winter and design a robust combined control chart to overcome the effect of outliers. The performance of the proposed robust Holt-Winter control chart is evaluated through extensive simulation studies. The results show that the proposed robust control chart performs well.

Different control charts are proposed by many researchers for the aim of detecting process shifts in the mean and assuring quality of the product. Exponentially weighted moving average (EWMA) control charts is one of the famous charts which performs well in detecting small shifts in the process mean. In this paper, a new statistic based on different smoothing parameters is proposed to improve the performance of the exponentially weighted moving average (EWMA) control chart in detecting large shifts as well as small and medium shifts. The performance of the developed scheme based on the proposed smoothing parameter is evaluated in terms of average run length criterion in comparison with the traditional EWMA control chart. The results show the better performance of the proposed scheme rather than the traditional EWMA control charts in most cases.

The effect of measurement errors on the performance of adaptive control charts has rarely been investigated in the univariate case and, as far as we know, it has not been investigated at all in the...

The effect of parameters estimation on profile monitoring methods has only been studied by a few researchers and only the assumption of a normal response variable has been tackled. However,...

In this article, we investigate the effect of measurement errors on the performance of the VP (Variable Parameters) X, ¯, , , , , control chart. After introducing the VP scheme for the X, ¯, , , , , chart with measurement errors, we evaluate the chart performance by using the average time to signal criterion, and we investigate the effect of measurement errors on the chart’s performance through extensive numerical studies. In addition, we investigate the effect of multiple measurements and the value of the linearly covariate error model’s parameters on the performance of VP X, ¯, , , , , control chart. We also consider the overall performance of the VP X, ¯, , , , , control chart and the optimal design parameters. Finally, the application of the proposed scheme is shown through an illustrative example.

Sometimes the quality of a process is best expressed by a relationship between response variables and explanatory variables. Checking over the time the stability of such functional relationships using statistical methods is called “profile monitoring”. Since 2007, when a detailed review paper in the field of profile monitoring was presented, an increasing number of papers have been published in this area. In this paper, we present a conceptual classification scheme and classify the papers in this area since 2008 up to 2018. The relevant papers are categorized and analyzed under different metrics and directions for future studies are recommended.

Profile monitoring is one of the new research areas in statistical process control. Most of the control charts in this area are designed with fixed sampling rate which makes the control chart slow in detecting small to moderate shifts. In order to improve the performance of the conventional fixed control charts, adaptive features are proposed in which, one or more design parameters vary during the process. In this paper the variable sample size feature of EWMA3 and MEWMA schemes are proposed for monitoring simple linear profiles. The EWMA3 method is based on the combination of three exponentially weighted moving average (EWMA) charts for monitoring three parameters of a simple linear profile separately and the Multivariate EWMA (MEWMA) chart is based on the using a single chart to monitor the coefficients and variance of a general linear profile. Also a two-sided control chart is proposed for monitoring the standard deviation in the EWMA3 method. The performance of the proposed charts is compared ...

In some statistical process control applications, the combination of both variable and attribute quality characteristics which are correlated represents the quality of the product or the process. In such processes, identification the time of manifesting the out-of-control states can help the quality engineers to eliminate the assignable causes through proper corrective actions. In this paper, first we use an artificial neural network (ANN)-based method in the literature for detecting the variance shifts as well as diagnosing the sources of variation in the multivariate-attribute processes. Then, based on the quality characteristics responsible for the out-of-control state, we propose a modular model based on the ANN for estimating the time of step change in the multivariate-attribute process variability. We also compare the performance of the ANN-based estimator with the estimator based on maximum likelihood method (MLE). A numerical example based on simulation study is used to evaluate the performance of the estimators in terms of the accuracy and precision criteria. The results of the simulation study show that the proposed ANN-based estimator outperforms the MLE estimator under different out-of-control scenarios where different shift magnitudes in the covariance matrix of multivariate-attribute quality characteristics are manifested.

The objective of this paper is to study the Phase I monitoring and change point estimation of autocorrelated Poisson profiles where the response values within each profile are autocorrelated. Two c...

In some profile monitoring applications, the independency assumption of consecutive binary response values within each profile is violated. To the best of our knowledge, estimating the time of a change in the parameters of an autocorrelated binary profile is neglected in the literature. In this paper, two maximum likelihood estimators are proposed to estimate the real time of step changes and drift in Phase II monitoring of binary profiles in the case of within-profile autocorrelation, respectively. Our proposed estimators, not only identify the change point in the autocorrelated logistic regression parameters, but also in autocorrelation coefficient. The performance of the proposed estimators to identify the time of change points either in regression parameters or autocorrelation coefficient is evaluated through simulation studies. The results in terms of the accuracy and precision criteria show the satisfactory performance of the proposed estimators under both step changes and drift. Moreover, a numerical example is given to illustrate the application of the proposed estimators.

In some processes, quality of a product should be characterized by functional relationships between response variables and a signal factor. Hence the traditional methods cannot be used to find the optimum solution. In this paper, we propose a method which considers two different dispersion effects, i.e. in domain and between replicates variations in the functional responses. Besides, we propose an integral based measure to find the deviation from t

Quality of final production multi-stage processes depends on several quality characteristics in the previous stages, which is referred to as cascade property. Sometimes, the quality of a process or product is characterized by a functional relationship known as profile. In some applications, this relationship is a Poisson regression profile. In this paper, Phase II monitoring of Poisson regression profile in multi-stage processes is investigated. Then, four methods are proposed and their performances are compared through simulation studies in terms of the average run length (ARL) criterion. In order to investigate the method performance, an illustrative example and a real example are also presented.

Uncertainty in the cost and process parameters is very common in practice. In this paper, we develop a scenario-based robust economic and economic-statistical design of exponentially weighted moving average control chart to account for economic and statistical criteria as well as the uncertainty. For this purpose, we use Lorenzen and Vance cost function for economic and economic-statistical design of an exponentially weighted moving average control chart in the real applications. Absolute robustness criterion which minimizes the worst-case scenario and also robust deviation which minimizes the deviation from the optimal solutions are applied to explore the robust approach for robust design of the exponentially weighted moving average control chart. The optimization models are solved by using the genetic algorithm. The performance of the proposed methods is illustrated through two numerical examples. Finally, the application of the proposed methods is illustrated in a real manufacturing case in the tile production industry.

Control charts are one of the most applicable tools in statistical process control. The time in which the control chart signals an out-of-control alarm is not the actual time in which the change has occurred. In other words, control chart detects the change with some delay. The actual time of the change taking place is referred to as change point. Change point estimation facilitates the identification of cause(s) of change and reduces the corresponding time and cost. There are many processes in which the control of two correlated attributes is necessary. Multiattribute control charts are used in such cases due to correlation between attributes. In this paper, two methods including maximum likelihood estimation (MLE) and clustering are proposed for estimating change point in nonconformity ratio vector of a process with bivariate binomial distribution. Also, the performances of these methods are evaluated and compared by Monte Carlo simulations.

In some industrial applications, the quality of a process or product is characterized by a relationship between the response variable and one or more independent variables which is called as profile. There are many approaches for monitoring different types of profiles in the literature. Most researchers assume that the response variable follows a normal distribution. However, this assumption may be violated in many cases. The most likely situation is when the response variable follows a distribution from generalized linear models (GLMs). For example, when the response variable is the number of defects in a certain area of a product, the observations follow Poisson distribution and ignoring this fact will cause misleading results. In this paper, three methods including a T2-based method, likelihood ratio test (LRT) method and F method are developed and modified in order to be applied in monitoring GLM regression profiles in Phase I. The performance of the proposed methods is analysed and compared for the s...

Diagnosis aids in addition to detecting the out-of-control state is an important issue in multivariate multiple linear regression profiles monitoring; because a large number of parameters and profiles in this structure are involved. In this paper, we specifically concentrate on identification of profile(s) and parameter(s) which have changed during the process in multivariate multiple linear regression profiles structure in Phase II. We demonstrate the effectiveness of our proposed approaches through Monte Carlo simulations and a real case study in terms of accuracy percent.

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 monitor standardized residuals. Finally, two examples and a case study with a Poisson response variable are investigated, and the performance of the charts is evaluated by using average run length (ARL) criterion in comparison with the best literature method.

Time-harmonic response of a vertically graded transversely isotropic, linearly elastic half-space is analytically determined by introducing a new set of potential functions. The potential functions are set in such a way that the governing equations be simple and with physical meaning as well. In addition, the potential functions introduced in this paper are degenerated to a complete set of potential functions used frequently for wave propagations in homogeneous transversely isotropic media. Utilizing Fourier series and Hankel integral transforms, the governing equations for the potential functions are solved, after which the displacements and stresses are presented in the form of line integrals. Both the displacements and stresses determined here are collapsed on the solution previously reported for the constant profile transversely isotropic material. Because of complicated integrand functions, the integrals are evaluated numerically and presented graphically, where the effect of degree of change of material properties plays a major role, which may be recognized easily.

Control charts are widely used in monitoring the quality of a product or a process. In most of the cases, quality of a product or a process can be characterized by two or more correlated quality characteristics. Many control charts have been proposed for monitoring multivariate or multi-attribute quality characteristics, separately, but sometimes the correlated variables and attribute quality characteristics represents the quality of a process. In this paper, the use of four transformation methods is proposed to monitor the multivariate–attribute processes. In the first one, the distribution of correlated variables and attribute quality characteristics are transformed to approximate multivariate normal distribution, and then the transformed data are monitored by multivariate control charts including T 2 and MEWMA. Based on the second transformation method, the correlated variables and attribute quality characteristics are transformed, such that the correlation between the quality characteristics approaches to zero, then univariate control charts are used in monitoring the transformed data. In the third and fourth proposed methods, a combination of two transformation methods is used to make the quality characteristics independent and to transform them to normal distribution. The difference between the third and fourth method is the order of using the transformation techniques. The performance of the proposed methods is evaluated by using simulation studies in terms of average run length criterion. Finally, the proposed approach is applied to a real dataset.

When a control chart sounds the alarm that the process is out of control (OC), the process will be paused and specialists will start the procedure of finding the root cause(s) that made the process out of control. Knowing the time of change will substantially aid the process engineer to figure out the assignable causes and solve the problem sooner, so the time, energy, and costs spent to implement corrective actions will be considerably reduced. Maximum likelihood estimator (MLE) as one of the statistical technique is frequently used for estimating the change point time. In this paper, an MLE is derived to estimate the time of first change in the mean vector of a multivariate normal process when the type of change is monotonic. The performance of the proposed change point estimator is evaluated in terms of accuracy and precision in comparison with the change point estimators developed under the assumptions of a step shift and drift. Finally, a numerical example is presented to show the application of the proposed change point estimator.

An overview on the effect of measurement errors on different areas of SPM.Providing a comprehensive classification of articles in this area.Presenting an analytical overview on the researches in this area.Introducing research gaps in this area to motivate future studies. In most industrial applications, the measures performed on inspected units are often strongly contaminated by either the inspector or the measuring device leading to measurement errors. It is recognized that the measurement errors affect the performance of control charts in various statistical process monitoring applications. In this paper, we present a conceptual classification scheme based on content analysis method to analyze and categorize the researches which have explored the effect of measurement errors on different aspects of statistical process monitoring (SPM). Moreover, based on 60 relevant papers in this field, the research gaps are mentioned and some directions to motivate the future studies are provided.

When a signal is detected by control charts, a search begins to identify and eliminate the sources of this signal. Knowing when a process has changed is very helpful for this purpose. The unknown special point that the process changed for the first time is referred to as change point. In this paper, we propose a maximum-likelihood estimator for the behavior model of the process fraction nonconforming in a high-quality process monitored with a cumulative count of conforming (CCC) control chart. We estimate the time of change without requiring the prior knowledge of the change type rather than we assume the type of change present belongs to a family of monotonic changes. Then, we compare the performance of the proposed change point estimator relative to estimators for the process fraction nonconforming change point derived under a single step and a linear trend change assumption. We do this for a number of monotonic change types following a signal from a CCC control chart. Finally, the application of the proposed change point estimator is shown through a real case.

Sometimes, quality of a process can be described by a functional relationship between response variables and explanatory variables which called profile. In some situations, there is an autocorrelation structure within a profile. Most of the times in real practice there is no enough data to estimate the process parameters. In this case, we can use a self-starting control chart which does not need preliminary data to start monitoring in start-up stages. In this paper, we consider a simple linear profile in the presence of a first order autoregressive (AR(1)) autocorrelation structure within profile and propose a self-starting control chart to monitor mean and variance of a simple linear profile simultaneously.

In statistical process control, an important issue in phase I is to identify the time of a change in process parameters. Control charts monitor the process over time, but the time an alarm is signaled by a control chart is not necessarily the real time of change in the process. Finding the real time of change, called as change point, is important because it leads to saving cost and time in detecting the assignable cause. Recently, profile monitoring in which a response variable and one or more explanatory variables are modeled by a regression function is attracted by many researchers. One type of profiles considered in the literature is a logistic profile where the distribution of the response variable is binary. In this paper, we develop two methods including likelihood ratio test and clustering to estimate the real time of a step change in phase I monitoring of the logistic profiles. The performance of the proposed methods is evaluated and compared through simulation studies. The results show the efficiency of both estimator methods. A real case is also studied to show the applicability of the proposed methods in practice.

In some situations, the quality of a process or product is characterized by a linear regression model between two or more variables which is called a linear regression profile. Moreover, in some cases, several correlated quality characteristics can be modeled as a set of linear functions of one explanatory variable which is typically referred to as multivariate simple linear profiles structure. On the other hand, process capability index is an important concept in statistical process control and measures the ability of the process to provide products that meet certain specifications. Little work, however, is done to evaluate the capability of a process with profile quality characteristic. This paper proposes three new methods for measuring process capability in multivariate simple linear profiles. Performance of the proposed methods is evaluated through simulation studies. In addition, the applicability of the proposed methods is illustrated using a real case of calibration application.

In profile monitoring, a relationship between a response variable and one or more explanatory variables is monitored. Different methods were developed for phase II monitoring of simple linear profiles. While some of the methods can be used to detect both increasing and decreasing shifts in the regression parameters, others need to be modified to enable detection of decreasing shifts in a process. In this paper, necessary modifications of the phase II methods for simple linear profile monitoring are proposed to improve their performance in detecting decreasing shifts. The paper also presents a performance comparison of several phase II methods.

Profile monitoring is used to monitor the regression relationship between a response variable and one or more explanatory variables over time. Many researches have been done in this area, but in most of them, the distribution of the response variable is assumed to be normal. However, this assumption is violated in many real case problems. In these instances, classic methods cannot be used for monitoring the profiles. For example, when the response variable is binary, logistic regression methods should be used rather than ordinary least square or other classic regression methods. There are some methods for monitoring logistic profiles in the literature, but the basic assumption of these methods is the independency of the consecutive observations, while this assumption is violated in some instances for example when the successive samples are taken in short intervals. This paper considers the effect of autocorrelation presence between the observations in different levels of the independent variable in a logistic regression profile on the monitoring procedure (T2 control chart) and proposes two remedies to account for the autocorrelation within logistic profiles. In one of the remedies, upper control limit of the traditional T2 control chart is modified. In the second one, we use a generalized linear mixed model (GLMM) to estimate the regression parameters and then use the T2 control chart for monitoring autocorrelated logistic regression profiles. Simulation studies show the better performance of T2 control chart when the regression parameters are estimated by the GLMM method under both step shifts and drifts.

Control charts are intended to aid quality practitioners in monitoring whether a change has occurred in a process. When a control chart indicates an out-of-control signal, it means that the process has changed. However, control chart signals do not indicate the real time of process changes; so estimators are applied to indicate the time when a change in the process takes place, which is referred to as the change point. This paper provides a maximum likelihood estimator to identify the real time of a step change in phase II monitoring of binary profiles, in which the quality of a process is characterized by a logistic regression between the response and predictor variables. Simulation studies are provided to evaluate the effectiveness of the change point estimator.

In certain applications of statistical process control, it is possible to model quality of a product or process using a multiple linear regression profile. Some methods exist in the literature which could be used for monitoring multiple linear regression profiles. However, the performance of most of these methods deteriorates as the number of regression parameters increases. In this paper, we specifically concentrate on phase II monitoring of multiple linear regression profiles and propose a new dimension reduction method to overcome the dimensionality problem of some of the existing methods. The robustness, effectiveness, and limitations of the proposed method are also discussed. Simulation results show that in term of average run length criterion, the proposed method outperforms the traditional methods and has comparable performance with another dimension reduction method in the literature.