In this study, drought characteristics of Arak, Bandar Anzali, Tabriz, Tehran, Rasht, Zahedan, Shiraz and Kerman stations during the statistical period of 1956 to 2015 were studied by Reconnaissance Drought Index (RDI) and Standardized Precipitation Index. Precipitation and temperature data were needed to calculate RDI. Precipitation data was also required to estimate SPI. In this study, Drinc software was used to calculate RDI, SPI and potential evapotranspiration (PET). The software calculated PET by the Thornthwaite method. One of the main challenges in drought monitoring is to determine the indicator that has a high reliability based on its monitoring purpose. Therefore, in this research, two methods used for selecting the appropriate index based on the minimum rainfall and normal distribution were evaluated. The results of the evaluation of the minimum rainfall method for selecting the appropriate index showed that most drought indices with the occurrence of minimum rainfall level indicated severe or very severe drought situations; in most cases, it could not lead to selecting an exact and unique index. Based on the results of the normal distribution method for the stations of Arak, Tabriz, Rasht, Zahedan, Shiraz and Kerman, SPI index, and for the stations of Bandar Anzali and Tehran, RDI index were selected as the most appropriate ones.

In certain statistical process control applications, quality of a process or product can be characterized by a function between response variable and one or more independent variables. This function commonly referred to as profile. Response variable can be continuous or discrete. All of the research assumes that the response variable is continuous. Whereas, some of the potential applications of profile monitoring are cases where the output can be modeled using polytomous (especially multinomial) or binary logistic regression models. Polytomous response variables, especially multinomial variables, can have various applications especially in service industry. In this paper, we propose some methods for monitoring a profile when the process output is a multinomial response variable. Multinomial logistic regression (OLR) provides the basis for our profile model. Performances of the proposed methods in terms of the signal probability for different out-of-control scenarios are compared based on simulation studies.

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.

Statistical variables are divided into two categories: nominal and ordinal, both of which have many uses. In some statistical process monitoring applications, the quality of a process or product is described by multiple ordinal quality characteristics, which is called ordinal Multivariate process. An ordinal contingency table is used to show the relationships between these variables and is modeled on an ordinal log-linear model. In our manuscript, two new statistics including simple ordinal categorical and Generalized-p are developed for Phase II monitoring the ordinal log-linear model-based processes. The performance of the proposed statistics will be evaluated using some simulation studies and real-world numerical examples. The results show the advantages of a simple ordinal category control card. In addition, the performance of these statistics is accessed through sensitivity analysis of the row and column sizes of the contingency table. Meanwhile, a sensitivity analysis with three and four categorical factors is performed and similar results are obtained.

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 linear profiles. Indeed, monitoring correlated Multivariate profiles is a new subject in the filled of statistical process control. In this paper, we investigate the effect of autocorrelations 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.

When there is a serious cause manifested in a process and it makes the process departs to an out-of-control condition, an effective root cause analysis could lead the process management to identify and eliminate the serious cause. When a change takes place in a Multivariate process, while several correlated variables exist, the root-cause analysis of the process relatively is more challenging compared to the case of a univariate process. Considering an out-of-control Multivariate process, one can experience an effective root-cause analysis if only a comprehensive scheme allows detecting the out-of-control condition, identifying the change point, diagnosing the variable(s) contributing to the unnatural condition and distinguishing the shift direction all simultaneously. Although statistical approach has provided effective solution for the univariate process, the approach has not provided a comprehensive solution in which a p-variate process is considered. The Multivariate literature indicates that the solution based on the soft computing is illustrated more effectively in comparison with the statistical approach. This research approached practically shows only one of the scheme among the several schemes proposed in the Multivariate literature is able to trigger simultaneously all the required signals leading to an effective root-cause analysis. The extensive literature review on the Multivariate environment led the authors to represent the comprehensive scheme. The out-of-control ARL criterion is used to evaluate the performance of the scheme compared to the performance of a traditional scheme when the monitoring of the correlated quality specifications in a real car body manufacturing process has been investigated.