In many circumstances, the quality of a process or product is best characterized by a given mathematical function between a response variable and one or more explanatory variables that is typically referred to as profile. There are some investigations to monitor auto correlated Linear and nonLinear profiles in recent years. In the present paper, we use the Linear mixed models to account autocorrelation within observations which is gathered on phase II of the monitoring process. We undertake that the structure of correlated Linear profiles simultaneously has both random and fixed effects. The work enhanced a Hotelling’s T2 statistic, a multivariate exponential weighted moving average (MEWMA), and a multivariate cumulative sum (MCUSUM) control charts to monitor process. We also compared their performances, in terms of average run length criterion, and designated that the proposed control charts schemes could effectively act in detecting shifts in process parameters. Finally, the results are applied on a real case study in an agricultural field.

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.

In most statistical quality control (SQC) applications, quality of a process or product is characterized by a univariate quality characteristic or a vector of quality characteristics, which is controlled by a univariate or multivariate quality control chart, respectively. However, in many practical situations, the quality of a process or product is characterized by a relationship between two or more variables. This relationship, which is referred to as profile can be Linear or nonLinear in nature. So far, several methods have been proposed for monitoring Linear profiles in phase H. In this paper, two other methods are proposed for improving the performance of Linear profiles in phase H. Average run length criterion is used as a vehicle to evaluate the performance of the proposed methods.

In this paper a new method for the design of a Linear phase distributed amplifier in 180nm CMOS technology is presented. The method is based on analogy between transversal filters and distributed amplifiers topologies. In the proposed method the Linearity of the phase at frequency range of 0-50 GHz is obtained by using proper weighting factors for each gain stage in cascaded amplifier topology. These weighting factors have been extracted using MATLAB software. Finally, by plotting the frequency response of the amplifier resulted from MATLAB code and also simulation from ADS, the phase Linearity of the designed amplifier is shown.

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 monitor multistage processes with the cascade property. To this aim, an autoregressive correlation model between the stages is considered first.Then, the effect of the cascade property on the performances of three types ofT2 control charts in phase I with shifts in standard deviation is investigated. As we show that this effect is significant, aU statistic is next used to remove the cascade effect, based on which the investigated control charts are modified. Simulation studies reveal good performances of the modified control charts.

In some quality control applications, the quality of a process or a product is described by the relationship between a response variable and one or more explanatory variables, called a profile. Moreover, in most practical applications, the qualitative characteristic of a product/service is vague, uncertain and linguistic and cannot be precisely stated. The purpose of this paper is to propose a method for monitoring simple Linear profiles with a fuzzy and ambiguous response. To this end, fuzzy EWMA and fuzzy Hotelling' sT2 statistics are developed using the extension principle. To monitor phase II of fuzzy Linear profiles, two methods using fuzzy hypothesis testing, are presented based on these statistics. A case study in ceramic and tile industry, is provided. A simulation study to evaluate the performance of the proposed methods in terms of average run length (ARL) criterion showed that the proposed methods are very efficient in detecting various sized shifts in process profiles.

In some applications of statistical process monitoring, a quality characteristic can be characterized by Linear regression relationships between several response variables and one explanatory variable, which is referred to as a “ multivariate simple Linear profile. ” It is usually assumed that the process parameters are known in phase II. However, in most applications, this assumption is violated; the parameters are unknown and should be estimated based on historical data sets in phase I. This study aims to compare the effect of parameter estimation on the performance of three phase II approaches for monitoring multivariate simple Linear profiles, designated as MEWMA, MEWMA_3 and MEWMA∕  2. Three metrics are used to accomplish this objective: AARL, SDARL and CVARL. The superior method may be different in terms of the AARL and SDARL metrics. Using the CVARL metric helps practitioners make reliable decisions. The comparisons are carried out under both in-control and out-of-control conditions for all competing approaches. The corrected limits are also obtained by a Monte Carlo simulation in order to decrease the required number of phase I samples for parameter estimation. The results reveal that parameter estimation strongly affects the in-control and out-of-control performance of monitoring approaches, and a large number of phase I samples are needed to achieve a parameter estimation that is close to the known parameters. The simulation results show that the MEWMA and MEWMA∕  2 methods perform better than the MEWMA_3 method in terms of the CVARL metric. However, the superior approach is different in terms of AARL and SDARL.

An integer Linear programming model for university courses timetabling is proposed here. In order to reduce the number of decisive variables, a combination of a course, a professor schedule and the students ‘group was defined as an activity. In this context, the two integer programming models namely the activity-based model and a two-phase activity-based model were proposed. In the first model, all activities were scheduled based on the number of required weekly sessions in the weekdays intervals; however, in the second model, classes and training courses were determined according to the planned sessions considering their special restrictions. These models were formulated based on the process of assigning the university courses within specific intervals throughout the week considering fierce constraints for a given semester in the department of Economics at University of Isfahan. All regulation concerning the courses timetable of a semester were formulated in GAMS software. Then, 239 courses were successfully scheduled using the two-phase activity-based model in only 9 minutes and 16 seconds.