International Journal of Industrial Engineering & Production Research

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  In an increasing number of practical situations, the quality of a process or product can be effectively characterized and summarized by a profile. A profile is usually a functional relationship between a response variable and one or more explanatory variables which can be modeled frequently using linear or nonlinear regression models. In this paper, we study the effect of non-normality on profile monitoring in Phase II when within or between autocorrelation is present. Different levels of autocorrelation and skewed and heavy-tailed symmetric non-normal distributions are used in our study to evaluate the performance of three existing monitoring schemes numerically. Simulation results indicate that the non-normality and autocorrelation can have a significant effect on the in-control performances of the considered schemes. Results also indicate that the out-of-control performances of the schemes are not very sensitive to low and moderate levels of autocorrelation in moderate and large shifts .

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Abstract Profile monitoring in statistical quality control has attracted attention of many researchers recently. A profile is a function between response variables and one or more independent variables. There have been only a limited number of researches on monitoring multivariate profiles. Indeed, monitoring correlated multivariate profiles is a new subject in the fileld of statistical process control. In this paper, we investigate the effect of autocorrlation in monitoring multivariate linear profiles in phase II. The effect of three main models namely AR(1), MA(1), and ARMA(1,1) on the methods of multivariate linear profile monitoring is evaluated and compared by using simulation study and average run length criteria. Results indicate that autocorrelation affects performance of the existing methods significantly.

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In many industrial and non-industrial applications the quality of a process or product is characterized by a relationship between a response variable and one or more explanatory variables. This relationship is referred to as profile. In the past decade, profile monitoring has been extensively studied under the normal response variable, but it has paid a little attention to the profile with the non-normal response variable. In this paper, the focus is especially on the binary response followed by the bernoulli distribution due to its application in many fields of science and engineering. Some methods have been suggested to monitor such profiles in phase I, the modeling phase however, no method has been proposed for monitoring them in phase II, the detecting phase. In this paper, two methods are proposed for phase II logistic profile monitoring. The first method is a combination of two exponentially weighted moving average (EWMA) control charts for mean and variance monitoring of the residuals defined in logistic regression models and the second method is a multivariate T2 chart to monitor model parameters. The simulation study is done to investigate the performance of the methods.

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In certain statistical process control applications, quality of a process or product can be characterized by a function commonly referred to as profile. Some of the potential applications of profile monitoring are cases where quality characteristic of interest is modelled using binary,multinomial or ordinal variables. In this paper, profiles with multinomial response are studied. For this purpose, multinomial logit regression (MLR) is considered as the basis.Then, the MLR is converted to Poisson GLM with log link. Two methods including Multivariate exponentially weighted moving average (MEWMA) statistics, and Likelihood ratio test (LRT) statistics are proposed to monitor MLR profiles in phase II. Performances of these three methods are evaluated by average run length criterion (ARL). A case study from alloy fasteners manufacturing process is used to illustrate the implementation of the proposed approach. Results indicate satisfactory performance for the proposed method.

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In many manufacturing processes, the quality of a product is characterized by a non-linear relationship between a dependent variable and one or more independent variables. Using nonlinear regression for monitoring nonlinear profiles have been proposed in the literature of profile monitoring which is faced with two problems 1) the distribution of regression coefficients in small samples is unknown and 2) with the increasing complexity of process, regression parameters will increase and thereby the efficiency of control charts decreases. In this paper, wavelet transform is used in Phase II for monitoring nonlinear profiles. In wavelets transform, two parameters specify the smoothing level, the first one is threshold and the second one is decomposition level of regression function form. First, using the adjusted coefficient of determination, decomposition level is specified and then process performance is monitored using the mean of wavelet coefficients and profile variance. The efficiency of the proposed control charts based on the average run length (ARL) criterion for real data is compared with the existing control charts for monitoring nonlinear profiles in Phase II

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Change point estimation is as an effective method for identifying the time of a change in production and service processes. In most of the statistical quality control literature, it is usually assumed that the quality characteristic of interest is independently and identically distributed over time. It is obvious that this assumption could be easily violated in practice. In this paper, we use maximum likelihood estimation method to estimate when a step change has occurred in a high yield process by allowing a serial correlation between observations. Monte Carlo simulation is used as a vehicle to evaluate performance of the proposed method. Results indicate satisfactory performance for the proposed method.

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Laser marking is an advanced technology in material processing that has a permanent effect on materials. With the use of laser engraving, the material is removed, layer by layer, in the laser path through melting displacement, ablation, and evaporation. Al-SiC is a metal matrix composite, widely used in aerospace, automobile manufacturing, and electronic packaging. Accumulative roll bonding (ARB) is one of the newest manufacturing processes of metal matrix composites, which leads to the production of materials with high strength, low weight, and great environmental compatibility. In this paper, we present the laser engraving of Al-SiC composite samples, which are produced through ARB process, using Q-switched Nd:YAG laser. A 2^k factorial design is used to analyze the effect of factors, including assistant gas flow, distance of sample from beam focus location (distance), pulse repetition frequency, and pumping current on the qualitative characteristics of engraved zone (width, depth and contrast of engraved zone). Desirability function is used for optimization. Results based on experimental data indicate the optimal setting of input factors which leads to pre-specified target values of responses.
 

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In the last few decades, profile monitoring in univariate and multivariate environment has drawn a considerable attention in the area of statistical process control. In multivariate profile monitoring, it is required to relate more than one response variable to one or more explanatory variables. In this paper, the multivariate multiple linear profile monitoring problem is addressed under the assumption of existing autocorrelation among observations. Multivariate linear mixed model (MLMM) is proposed to account for the autocorrelation between profiles. Then two control charts in addition to a combined method are applied to monitor the profiles in phase II. Finally, the performance of the presented method is assessed in terms of average run length (ARL). The simulation results demonstrate that the proposed control charts have appropriate performance in signaling out-of-control conditions.
 

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Organizations have used Customer Lifetime Value (CLV) as an appropriate pattern to classify their customers. Data mining techniques have enabled organizations to analyze their customers’ behaviors more quantitatively. This research has been carried out to cluster customers based on factors of CLV model including length, recency, frequency, and monetary (LRFM) through data mining. Based on LRFM, transaction data of 1865 customers in a software company has been analyzed through Crisp-DM method and the research roadmap. Four CLV factors have been developed based on feature selection algorithm. They also have been prepared for clustering using quintile method. To determine the optimum number of clusters, silhouette and SSE indexes have been evaluated. Additionally, k-means algorithm has been applied to cluster the customers. Then, CLV amounts have been evaluated and the clusters have been ranked. The results show that customers have been clustered in 4 groups namely high value loyal customers, uncertain lost customers, uncertain new customers, and high consumption cost customers. The first cluster customers with the highest number and the highest CLV are the most valuable customers and the fourth, third, and second cluster customers are in the second, third, and fourth positions respectively. The attributes of customers in each cluster have been analyzed and the marketing strategies have been proposed for each group.