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.

The removal of the most prevalent heavy metal ions [cadmium(II), lead(II), copper(II), and zinc(II)] by adsorption on Scots pine (Pinus sylvestris L.) biochar and Silver birch (Betula pendula) biochar has been investigated, following the determination of physical and chemical adsorption properties of biochar. The efficiency of adsorption of heavy metal ions [cadmium(II), lead(II), copper(II), and zinc(II)] on biochar was studied at different concentrations of heavy metals [onefold maximum contaminant level, twofold maximum contaminant level, fivefold maximum contaminant level (in accordance with the requirements set out in the Water Framework Directive 2000/60/EC), dosages of biochar (1.6-140 g), and biochar types (Scots pine (P. sylvestris L.) biochar and Silver birch (B. pendula) biochar produced at slow and fast pyrolysis) at constant pH of leaching solution, temperature, and contact time. Adsorption capacity of Scots pine (P. sylvestris L.) biochar and Silver birch (B. pendula) biochar was assessed by the application of extended Freundlich isotherm. In this study, biochar was evaluated as a potential adsorbent to efficiently reduce concentration of heavy metal ions in metal-contaminated water. The maximum adsorption capacity were reached of copper(II) on Silver birch (B. pendula) biochar (128.7 mg g-1) and of zinc(II) on Scots pine (P. sylvestris L.) biochar (107.0 mg g-1). Adsorption capacity of lead (II) on Silver birch (B. pendula) and Scots pine (P. sylvestris L.) biochar varied from 1.29 to 3.77 and from 2.37 to 4.49 mg g-1, respectively.

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.

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.

This article presents a new multivariate non-parametric control chart in PHASE II based on depth functions. The proposed statistic is an affine invariant and asymptotically free distribution. Indeed, the asymptotic distribution of the proposed statistic is derived under the in-control process. Based on simulation studies, the performance of the proposed statistic, using several depth functions, has been evaluated and compared with three competing statistics. The results show that the introduced statistic performs adequately and, in some cases, outperforms the competing statistics. A real dataset has been analyzed based on the proposed chart.

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 [1] a feasible timetable generator stochastic simulation modeling framework for the train scheduling problem was developed to obtain a train timetable which includes train arrival and departure times at all visited stations and calculated average train travel time for all trains in the system. In this study, the framework is integrated with a genetic algorithm (GA) in order to get an optimal or suboptimal feasible train timetable with minimum average train travel time.