arXiv subjects

Seyedeh Azadeh Fallah Mortezanejad

Publications and source records attributed to Seyedeh Azadeh Fallah Mortezanejad.

6 recordsLinked to original sources

arXiv2025

Signed Rank Chart For Tied Observations: An Application of Deep Learning Models

Shewhart Control Charts (SCC)s are constructed under the assumption of normality and are widely recognized in statistical quality control by numerous researchers. Problems arise when the distribution of process data does not conform to a typical Normal Distribution (ND) or when there is insufficient evidence to confirm that the data has approximately ND. Additionally, in some processes, Tied Observations (TO)s are present. The resolution of the measurement device used to assess a quality characteristic can lead to rounding errors, as well as TOs. In many cases, SCCs prove inadequate. In this paper, we address the challenges of non-normal observations and rounding errors by developing a Shewhart Signed-Rank Control Chart (SS-RCC) based on the Wilcoxon statistic. We define a random variable for TOs and another for Untied Observations (UO)s. Subsequently, we approximate their distributions using a Scaled-Normal Distribution (SND) and apply a Deep Learning (DL) model to estimate the scale parameters of the SND for the Control Chart (CC). In practice, we calculate the Average Run Length ($ARL$) for specific cases using Johnson-type distribution benchmarks to illustrate the effects of ties and shifts in manufacturing processes.

stat.AP↗

arXiv2025

Physics-Informed Neural Networks with Unknown Partial Differential Equations: an Application in Multivariate Time Series

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles to enhance predictions when dealing with sparse, noisy, or incomplete data? Physics-Informed Neural Networks (PINNs) put this idea into practice by incorporating physical equations, such as Partial Differential Equations (PDEs), as soft constraints. This guidance helps the networks find solutions that align with established laws. Recently, researchers have expanded this framework to include Bayesian NNs (BNNs), which allow for uncertainty quantification while still adhering to physical principles. But what happens when the governing equations of a system are not known? In this work, we introduce methods to automatically extract PDEs from historical data. We then integrate these learned equations into three different modeling approaches: PINNs, Bayesian-PINNs (B-PINNs), and Bayesian Linear Regression (BLR). To assess these frameworks, we evaluate them on a real-world Multivariate Time Series (MTS) dataset. We compare their effectiveness in forecasting future states under different scenarios: with and without PDE constraints and accuracy considerations. This research aims to bridge the gap between data-driven discovery and physics-guided learning, providing valuable insights for practical applications.

cs.LG↗

arXiv2025

Addressing Challenges in Time Series Forecasting: A Comprehensive Comparison of Machine Learning Techniques

The explosion of Time Series (TS) data, driven by advancements in technology, necessitates sophisticated analytical methods. Modern management systems increasingly rely on analyzing this data, highlighting the importance of effcient processing techniques. State-of-the-art Machine Learning (ML) approaches for TS analysis and forecasting are becoming prevalent. This paper briefly describes and compiles suitable algorithms for TS regression task. We compare these algorithms against each other and the classic ARIMA method using diverse datasets: complete data, data with outliers, and data with missing values. The focus is on forecasting accuracy, particularly for long-term predictions. This research aids in selecting the most appropriate algorithm based on forecasting needs and data characteristics.

cs.LG↗

arXiv2024

Dependence control chart using maximum copula entropy

Statistical quality control methods are noteworthy to producing standard production in manufacturing processes. In this regard, there are many classical manners to control the process. Many of them have a global assumption around the distributions of the process data. They are supposed to be Normal, but it is clear that it is not always valid for all processes. Such control charts made some wrong decisions that waste funds. So, the main question while working with multivariate data set is how to find the multivariate distribution of the data set, which saves the original dependency between variables. To our knowledge, a copula function guarantees dependence on the result function. It is not enough when there is no other fundamental information about the statistical society, and we have just a data set. Therefore, we apply the maximum entropy concept to deal with this situation. In this paper, first of all, we get the joint distribution of a data set from a manufacturing process that needs to be in-control while running the production process. Then, we get an elliptical control limit via the maximum copula entropy. Finally, we represent a practical example using the method. Average run lengths are calculated for some means and shifts to show the ability of the maximum copula entropy. In the end, two practical data examples are presented, and the results of our method are compared with the traditional way based on Fisher distribution.

stat.AP↗

arXiv2023

Profile control chart based on maximum entropy

Monitoring a process over time is so important in manufacturing processes to reduce the waste of money and time. Some charts as Shewhart, CUSUM, and EWMA are common to monitor a process with a single intended attribute which is used in different kinds of processes with various ranges of shifts. In some cases, the process quality is characterized by different types of profiles. The purpose of this article is to monitor profile coefficients instead of a process mean. In this paper, two methods are proposed for monitoring the intercept and slope of the simple linear profile, simultaneously. In this regard, two methods are compared here. The first one is the linear regression, and the one is the maximum entropy principle. The T2 Hotelling statistics is used to transfer two coefficients to a scalar. A simulation study is applied to compare the two methods in terms of the second type of error and average run length. Finally, two real examples are presented to demonstrate the applicability of the proposed chart. The first one is about semiconductors, and the second one is about pharmaceutical production processes. The performance of the methods is relatively similar. The maximum entropy plays an important role in correctly identifying differences in the pharmaceutical example, while linear regression did not correctly detect these changes.

stat.AP↗

arXiv2023

A historical view on the maximum entropy

How to find unknown distributions is questioned in many pieces of research. There are several ways to figure them out, but the main question is which acts more reasonably than others. In this paper, we focus on the maximum entropy principle as a suitable method of discovering the unknown distribution, which recommends some prior information based on the available data set. We explain its features by reviewing some papers. Furthermore, we recommend some articles to study around the generalized maximum entropy issue, which is more suitable when autocorrelation data exists. Then, we list the beneficial features of the maximum entropy as a result. Finally, some disadvantages of entropy are expressed to have a complete look at the maximum entropy principle, and we list its drawbacks as the final step.

stat.OT↗