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It is proved that adaptive control charts have better performance than classical control charts due to adaptability of some or all of their parameters to the previous process information. Fuzzy classical control charts have been occasionally considered by many researchers in the last two decades; however, fuzzy adaptive control charts have not been investigated. In this paper, we introduce a new adaptive X − R fuzzy control chart that allows all of the charts' parameters to adapt based on the process state in the previous sample. Also, the warning limits are redefined in the fuzzy environments. We utilise fuzzy mode defuzzification technique to design the decision procedure in the proposed fuzzy adaptive control chart. Finally, an illustrative example is used to present the application of the proposed control chart.

In most statistical process control (SPC) applications, quality of a process or product is monitored by univariate or multivariate control charts. However, sometimes a functional relationship between a response variable and one or more explanatory variables is established and monitored over time. This relationship is called “profile” in SPC literature. In this paper, we specifically consider processes with compositional data responses, including multivariate positive observations summing to one. The relationship between compositional data responses and explanatory variables is modeled by a Dirichlet regression profile. We develop a monitoring procedure based on likelihood ratio test (lrt) for Phase I monitoring of Dirichlet regression profiles. Then, we compare the performance of the proposed method with the best method in the literature in terms of probability of signal. The results of simulation studies show that the proposed control chart has better performance in Phase I monitoring than the competing control chart. Moreover, the proposed method is able to estimate the real time of a change as well. The performance of this feature is also investigated through simulation runs which show the satisfactory performance. Finally, the application of the proposed method is illustrated based on a real case in comparison with the existing method.

In most statistical process control applications, the quality of a process or product is characterized by univariate or multivariate quality characteristics and monitored by the corresponding univariate and multivariate control charts, respectively. However, sometimes, the quality of a process or a product is better characterized by a relationship between a response variable and one or more explanatory variables. This relationship, which can be linear, nonlinear, or even a complicated model, is referred to as a profile. So far, several methods have been proposed for monitoring simple linear profiles. In this paper, a new method based on cumulative sum statistics is proposed to enhance monitoring of linear profiles in phase II. The performance of the proposed method is evaluated by average run length criterion. A comprehensive comparison is also conducted between the performance of the proposed method and the existing methods for monitoring simple linear profiles. The results show that the proposed method performs satisfactorily. In addition, the effects of reference value, sample size, and corrected sum of squares of explanatory variables on the performance of the proposed method are investigated.

In some statistical process control applications, quality of a process or product is characterized by a relationship between two or more variables which is referred to as profile. Sometimes, this relationship can be characterized by a polynomial profile. There are some methods in the literature which can be easily extended and used for monitoring polynomial profiles. In this paper, a new method is proposed for monitoring kth order polynomial profiles in phase II. In the proposed method, the polynomial profiles are transformed to orthogonal polynomial profiles, and the parameters of the transformed model are monitored by separate exponentially weighted moving average control charts. Based on the relationship between the parameters of the main and transformed model, the step shifts in the parameters of main model lead to larger step shifts in the parameters of the transformed model. Hence, this transformation leads to quicker detection in phase II. The performance of the proposed method is compared with the existing methods using numerical simulation runs in terms of average run length criterion.

In some statistical process control applications, quality of a process or product is characterized by a relationship between two or more variables which is referred to as profile. In many practical situations, a profile can be modeled as a polynomial regression. In this article, three methods are developed for monitoring polynomial profiles in Phase I. Their performance is evaluated using power criterion. Furthermore, a method based on likelihood ratio test is developed to identify the location of shifts. Numerical simulation is used to evaluate the performance of the developed method.

Control charts are commonly used to monitor quality of a process or product characterized by a quality characteristic or a vector of quality characteristics. However, in many practical situations the quality of a process or product can be characterized by a function or profile. Here we consider a linear function and investigate the violation of common independence assumption implicitly considered in most control charting applications. We specifically consider the case when profiles are not independent from each other over time. In this article, the effect of autocorrelation between profiles is investigated using average run length (ARL) criterion. Simulation results indicate significant impact on the ARL values when autocorrelation is overlooked. In addition, three methods based on time series approach are used to eliminate the effect of autocorrelation. Their performances are compared using ARL criterion.

The manufacturing processes often involve multistage processes where the process capability of each stage is affected by the process capability of its previous stages. This property is known as cascade property. Therefore, the measured process capability indices in each stage represent the total capability of that stage. In the multistage processes two kinds of process capability index are defined in each stage of the multistage processes as follows: total process capability index and specific process capability index. The process capability indices are proposed under the assumption that there are no measurement errors. However, sometimes in the real application, this assumption is violated. The measurement errors affect the process capability indices significantly. In this paper, the effect of measurement errors on the total process capability index in the second stage of two-stage processes is statistically analyzed.

The present study suggests a novel model for simulating electromagnetic characteristics of spheroidal nanofillers. The electromagnetic interference shielding efficiency of prolate and oblate ellipsoids in the X-band frequency range is studied. Different multilayered nanocomposite configurations incorporating carbon nanotubes, graphene nanoplatelets, and carbon blacks are fabricated and tested. The best performance for a specific thickness is observed for the multilayered composite with a gradual increase in the thickness and electrical conductivity of layers. The simulation results based on the proposed model are shown to be in good agreement with the experimental data. The effect of filler alignment on shielding efficiency is also studied by using the nematic order parameter. The ability of a nanocomposite to shield the incident power is found to decrease by increasing alignment especially for high volume fractions of prolate fillers. The interaction of the electromagnetic wave and the fillers is mainly ...

A horizontally multilayered Green elastic transversely isotropic half-space is considered as the domain of the boundary value problem involved in this paper, such that the axes of material symmetry of different layers are parallel to the axis of material symmetry of the lowest half-space, which is depthwise. The domain is assumed to be affected by an arbitrary time-harmonic forced vibration due to a rigid rectangular surface foundation. With the use of a potential function method and the Hankel integral transforms, the displacements and stresses Green's functions are determined in each layer. The unknown functions due to integrations in each layer are transformed to the unknown functions of the surface layer with the use of the concept of propagator matrix and the continuity conditions. The mixed boundary conditions at the surface of the whole domain are numerically satisfied with the assumption of piecewise constant distribution of tractions in the contact area. It is numerically shown that the surface displacement and stress boundary conditions are satisfied very well. The vertical and horizontal impedance functions of the rectangular foundation are determined, which may be used as lumped parameters in time-harmonic soil-structure interaction with transversely isotropic horizontally layered domain as the soil. It is shown that the impedance functions determined in this paper coincide with the same functions for the simpler case of isotropic homogeneous half-space as degenerations of this study.

Control charts are the most important tools of statistical process control used to discriminate between assignable and common causes of variation and to improve the quality of a process. To design a control chart, three parameters including sample size, sampling interval, and control limits should be determined. The objectives are hourly expected cost, in-control average run length, power of the control chart, and average time to signal. Different approaches such as statistical design, economic design, and economic-statistical design of control charts have been considered by many researchers. Recently, multi-objective design of control chart has been investigated in the literature. In this paper we propose a multi-objective economic-statistical design of np control chart (np-MOESD). To solve the multi-objective model, a method is used to find the Pareto optimal solution and then a combined method based on Data Envelopment Analysis (DEA) is proposed to determine the most efficient design parameters. A numerical example of Duncan [1] illustrates the proposed approach. Sensitivity analysis is performed to evaluate the proposed model. In addition, the proposed model is compared with pure economic design (Duncan’s model) as well as another model in the literature. Results show that the proposed np-MOESD model improves statistical properties of np control charts.

Many processes contain several dependent steps. If a change happens in a stage it will affect the successive quality characteristics which referred to as cascade property. Hence, to monitor the quality characteristics in each stage we have to use a procedure to omit the effect of preceding stages. Therefore, cause selecting control charts are suggested for this purpose. To the best of our knowledge, in all of the papers in the area of monitoring multistage processes with control charts, it is assumed that the quality characteristics are crisp. However, in some applications, the quality characteristics may be imprecise and they can be expressed by fuzzy numbers. In this paper, we specifically assume that there is a two-stage process with fuzzy quality characteristic in the second stage. Note that the fuzzy quality characteristic represents two kinds of uncertainty including randomness and fuzziness. Then, we propose a fuzzy cause selecting control chart to monitor the process in phase I. The performance of the proposed method is evaluated using simulation studies in terms of power. The use of the proposed method is shown step by step through a numerical example. The results show the satisfactory performance of the proposed control chart.

When a control chart signals, it shows the process parameters have changed due to assignable cause(s). However, control chart signal is not the real time of a change in the process. Knowing the real time of change would simplify the detection and elimination of the assignable causes of variation. In this paper, a two-stage process is considered when the mean values of quality characteristics are changed under step shift and linear drift. First, a control chart based on the discriminant analysis (DA) is utilized to monitor the process. Then, when the out-of-control signal is received, the maximum likelihood estimator (MLE) based on the DA statistics, and clustering approach based on Mahalanobis distance of residuals are developed to estimate the real time of the change. The performances of the proposed estimators under different shifts are evaluated through numerical examples and a real case. The results indicate the better performance of the clustering approach rather than the MLE in most cases under both step shift and drift.

In this paper a new method in multi response experimental design is proposed to determine the optimal settings for controllable factors, where the responses are uncorrelated. This method leads to improving the quality characteristic with the lower process capability index (PCI) with more priority. Due to the application of this study in a batch manufacturing and existing of some parts in each treatment, PCI has been computed for each treatment for every initial response. Then an aggregated index (c i ) has been computed by TOPSIS based on the calculated signal to noise ratios of PCI's. Finally the optimal controllable factors have been determined by optimizing a fitted linear regression to the aggregated index and values of controllable factors. The proposed method is illustrated by a real case study in a plastic molding factory. The results show the effectiveness of the proposed method in improving the quality characteristic with the lowest c pk .

In some real case problems, the relationship between a response variable and one or more explanatory variables called as profile should be monitored over time instead of the quality characteristic itself. Profile monitoring is used in such instances. Many researches have been done in the area of profile monitoring but in most of them it is assumed that the response variable follows normal distribution. In recent years Yeh et al. (2009) proposed 5 T2 based methods for monitoring logistic profiles in which response variable is binary. In this paper we evaluate two of the best T2 methods for Poisson response profiles monitoring in Phase I.

There are many researches in the area of profile monitoring and most of them have two basic assumptions including the normality of response variable as well as independency of observations within each profile. In recent years there are some researches investigating the violation of the assumptions. This paper shows the effect of ignoring autocorrelation on the performance of T2 control chart when the response variable follows a binomial distribution. Besides, a simple method is proposed to account for this effect in the T2 control chart. At the end, the performance of the proposed method is evaluated using simulation studies.

Recently, Profile monitoring in which the quality of a process or product can be characterized by a relationship between two or more variables has been considered by a lot of researchers. In different applications, the profiles can be linear or nonlinear in nature. Several methods have been proposed for monitoring simple linear profiles in Phase II. Some of these methods either have been developed to detect increasing step shifts or their performance is just evaluated under this type of shift. However, sometimes, a decreasing step shift can be occurred leading to poor performance of the process. In this paper, we modify the methods including T2, EWMA-3, and CUSUM-3 to improve their performance in detecting decreasing step shifts in Phase II. The performance of the modified methods as well as other existing methods including EWMA/R, MEWMA and LRT has been evaluated under decreasing step shifts by using simulation studies via Average Run length criterion.

In this paper, a control chart is proposed to detect changes in the covariance matrix of a multivariate normal process, when sample size is one. The proposed chart statistic is constructed based on the exponentially weighted form of sample covariance matrix given by individual observation over time. Distance between the values of variance and covariance components in this multivariate exponentially weighted moving sample covariance matrix and, the in-control corresponding elements of process variance-covariance matrix provides a basis for process variability monitoring. The statistical performance of the proposed method is evaluated through the use of a Monte Carlo simulation. The results show the superiority of the proposed control chart performance especially in the case of incremental changes in covariance matrix.

Profile monitoring is effectively used in a case where the response variable is measured along with the corresponding value of an explanatory variable(s). Profile monitoring allows quality engineers to monitor performance of a process statistically considering a functional relationship at a given time. Although several papers can be found in the literature approached nonlinear profile monitoring, to the best of the authors' knowledge, there is not any researches in monitoring Allan variance nonlinear profile approaching artificial neural network (ANN). ANN capabilities help quality engineers to monitor complex nonlinear profiles in real cases effectively. In this paper an ANN model is proposed to monitor the nonlinear profile of Allan variance. Allan variance is a measure of stability of tools such as oscillator and amplifier. The proposed ANN model not only is capable to identify an out-of-control condition, but also the model is capable to diagnose the parameter(s) responsible to the out-of-control condition. A numerical example is considered to evaluate the performance of the proposed ANN when the process experiences different shift sizes. The evaluation of the performance is investigated using average run length (ARL) and correct classification criteria.

In this paper, the EWMA-3 control chart for monitoring simple linear profile is economic-statistically designed. Average run length criterion of the EWMA-3 control chart is computed by using a Markov chain approach. In the proposed model, the Lorenzen and Vance cost function is applied and the parameters of non-conforming production cost are computed based on the Taguchi cost function. The proposed model is solved by a genetic algorithm. Finally, a sensitivity analysis is done on the parameters of the proposed model.

While most of the methods developed for computing process capability indices (PCI) concentrate on cases with normally or continuous non-normally distributed quality characteristics, computing this measure for processes with mixed distributed data has not been investigated so far. In this paper, a new method is proposed for computing (PCI) for mixed binary-normal quality characteristics. In the proposed method, first a mixed binary-normal distribution is considered to be fitted on the available data. Having estimated the unknown parameters of the fitted distribution using maximum likelihood estimation and genetic algorithm, the proportion of the conforming items of the corresponding distribution is estimated by Monte Carlo simulation runs. Finally, the PCI is computed based on the relationship of PCI and proportion of conforming items. The performance of the proposed method is evaluated using simulation studies as well as a case study in a plastic injection moulding process.

Identifying the real time change in a process, when an out-of-control signal is given by a control chart is crucial and leads to cost and time savings significantly. There are processes or products whose quality is described by a relationship between a response variable and one or more explanatory variable. This relationship is known as profile in the literature of statistical process control and is modelled by different regression types including logistic regression. This type of profile is used where the response variable follows a binomial distribution. In this paper, a maximum likelihood estimator (MLE) based on regression parameters is developed to find the real time of a step change in logistic regression profiles. Simulation studies are provided to evaluate the performance of the proposed change point estimator under both single step change and linear trend change.

Estimating the real time of shifts in process would ease the identification of special causes and leads to saving in time and cost, so it is very important for process improvement. On the other hand, in many applications of statistical process control, quality of a process or product is summarised by a functional relationship referred to as profile. Although there are many real cases with gamma responses in profiles, little studies have been devoted to the estimation of the change point of this type of profiles. The main contribution of the paper is deriving a maximum likelihood estimator for change point estimation in gamma regression profiles with a linear trend disturbance. Also, a T2 control chart is used to detect the out-of-control signal in monitoring gamma regression profiles. The performance of the proposed estimator is evaluated through simulation studies. The results show the accurate and precise estimates of the change point by the proposed estimator. Afterwards, a confidence set estimator for the process change point based on the logarithm of the likelihood function is presented. Finally, the performance of the estimator is illustrated through a numerical example.

The exponentially weighted moving average (EWMA) control charts are useful for detecting small shifts in the process mean. In this paper, we investigate multi-objective economic-statistical design of the EWMA control charts and propose two evolutionary algorithms including non-dominated sorting genetic algorithm (NSGA-II) and multi-objective genetic algorithm (MOGA) to determine the optimal chart parameters. The cost function used in this paper is Lorenzen and Vance cost function. We also used quadratic Taguchi loss function to determine the costs of producing non-conforming items under both in-control and out-of-control situations. The average run length values in both in-control and out-of-control states are computed by using Markov chain approach. A numerical example is applied to compare the results of proposed algorithms in finding the Pareto optimal solution of the multi-objective economic-statistical model. Finally, a sensitivity analysis on the economic and the statistical criteria of the EWMA control chart under both proposed algorithms is conducted.

The various advantages of MEWMA control chart such as the ability to detect small shifts in the process with multiple quality characteristics have motivated users to apply this chart for process monitoring. Considering the high costs of implementing MEWMA control chart, the economic-statistical design of this chart has been increasingly investigated. In most of the previous studies the cost function has been considered as the objective function while the statistical properties have been modelled as constraints in a mathematical programming. According to the dependency of the cost function on statistical properties in the constraints, the results of these methods are not efficient enough. In this paper, two multi-objective approaches, an aggregative and a non-aggregative approach are applied and optimised using a genetic algorithm. The proposed approaches are evaluated through a numerical example from the literature and the efficiency of the multi-objective approaches are verified in comparison with the previous methods.

In a high quality process, the fraction of nonconforming is very low. In this area, standard Shewhart control charts are no longer useful. The Cumulative Count of Conforming (CCC) control charts, which enumerates the number of conforming items between the occurrences of two nonconforming ones, have been shown to be effective in the monitoring of high quality processes. When the CCC control chart signals an out-of-control condition, the process engineers should search for the source of the assignable causes. Knowing the exact time of the process change would help them to reduce the time for identification of the assignable causes. This paper provides a maximum likelihood estimator for the change point of the nonconforming level of the high quality process with a linear trend. Then, a Monte Carlo simulation is applied to evaluate the performance of the proposed estimator. In addition, the proposed estimator is compared with the MLE of the process fraction nonconforming, derived under a single step change. The results show that the proposed estimator outperforms the MLE designed for step change, when a linear trend disturbance is present in the process.

In this paper, we focus specifically on a two stage process with multivariate-attribute quality characteristics in the second stage. The main purpose of this study is extending discriminant analysis (DA) based control charts to monitor a two stage process. We propose three methods including EWMA (DA), integrated EWMA (DA) and P-value (DA), and integrated multivariate exponentially weighted moving average (MEWMA) and T2 charts based on the DA approach to monitor the multivariate-attribute quality characteristic in a two stage process. The performance of the proposed methods is evaluated through simulation studies as well as a real case.

In this study, we develop a neural network with a time shifting approach to forecast time series patterns. We investigate the impact of different layer-weight configurations to capture the trends in the forms of seasonal, chaotic, etc. We also hypothesize the combined effect of the delayed inputs and the forward connections to introduce a dynamical structure. The effect of overfitting issue is procedurally monitored to gain the resistance property from the early stoppage of training process and to reduce the predictions' error. Finally, the performance of the proposed network is challenged by six well-known deterministic and non-deterministic time series and compared by the autoregression (AR), artificial neural network (ANN), adaptive k-nearest neighbors (AKN), and adaptive neural network (ADNN) models. The results show that the proposed network outperforms the conventional models, particularly in forecasting the chaotic and seasonal time series.

Chapter 8 In the SPC-related literature, there are various cases in which we are interested in monitoring geometric specifications of products. Roundness, flatness, straightness, or cylindricity of products could be examples of such quality characteristics. It is obvious that under such circumstances, one would be interested in detecting any departure from the baseline shape of the product. Figure 1.17 shows various types of nonconforming shapes for a machined cylinder discussed by Henke et al. (1999) and Zhang et al. (2005). Detailed discussions on the methods for monitoring quality characteristics related to the geometric specifications of manufactured products are presented in this chapter.