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.

The ability to monitor supplier performance is a critical capability to maintain a strong organization-supplier relationship, especially for organizations where the supplier plays a significant role in their end product and market retention. In this article, a multi-variable multi-PROFILE MONITORING model is presented, taking into account the risk conditions in two stages for MONITORING the quality of parts and supplier products. In the first step, the criteria and indicators for evaluating the quality process as well as the risk function are extracted according to the library resources and the opinion of experts and elites of the relevant industry. In the next phase, in the first phase of MONITORING, using the Hotelling’s  Statistic Based on the Successive Differences, the parameters of the model are calculated and monitored, and in the second phase, the likelihood ratio method is used to monitor the supplier's quality process over time, so that if the presence of a warning will show the control chart in the shortest possible time. This model has been implemented in the automotive industry of Iran Khodro Company and the supplier of gearbox parts by Niro Travezah Company.

The ability to monitor supplier performance is a critical capability to maintain a strong organization-supplier relationship, especially for organizations where supplier quality plays a significant role in their final product and market retention. In this article, a PROFILE MONITORING model in two phases is presented for MONITORING the quality of products and supplier processes. In the first step, criteria and indicators for quality assessment are extracted according to library resources and the opinion of experts and elites of the industry. In the next phase, in the first phase of MONITORING, the parameters of the model are calculated and monitored using the Kong Albain T^2 method, and in the second phase, the Hotling T^2 method is used to monitor the quality of the supplier over time, so that if there is a warning in the shortest time The control chart may show it. This model has been implemented in the automotive industry of Iran Khodro Company and the supplier of gearbox parts by Niromoharkeh Company.