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All Journal Statistika JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA) BAREKENG: Jurnal Ilmu Matematika dan Terapan ESTIMASI: Journal of Statistics and Its Application MATHunesa: Jurnal Ilmiah Matematika STATISTIKA
Herdiani, Erna Tri
Department Of Statistics, Faculty Of Mathematics And Natural Science, Hasanuddin University, Indonesia
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Energy Engineering Environmental Science Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Medicine & Pharmacology Physics Transportation

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COMPARISON OF EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHART WITH HOMOGENEOUSLY WEIGHTED MOVING AVERAGE CONTROL CHARTS AND ITS APPLICATION Herdiani, Erna Tri; Mustabsyirah, Mustabsyirah
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp2243-2262

Abstract

The Exponentially Weighted Moving Average (EWMA) control chart is a widely used memory-type control chart known for detecting small shifts in process means. The recently developed Homogeneously Weighted Moving Average (HWMA) control chart modifies the weighting scheme of EWMA, giving more weight to the latest data and distributing smaller weights evenly to past data to further improve sensitivity. This paper compares the performance of EWMA and HWMA control charts on an iron pipe production process dataset. The methodology involves a two-phase analysis: Phase I for establishing in-control process limits (with normality testing, parameter estimation, and determination of optimal smoothing weights) and Phase II for monitoring new data using the established charts. The performance of each chart is evaluated using the Average Run Length (ARL) metric – specifically, the ability to quickly detect small shifts (ARL₁) while maintaining a low false alarm rate (ARL₀). The results indicate that the HWMA chart consistently achieves a smaller ARL₁ than the EWMA chart for small mean shifts without sacrificing in-control ARL, implying higher sensitivity to subtle process changes. Consequently, the HWMA control chart can detect small deviations in the iron pipe length more rapidly than the EWMA chart. These findings align with recent literature and demonstrate practical significance for quality control: the HWMA chart would enable earlier detection of process issues, allowing for quicker corrective actions in manufacturing. We conclude that the HWMA control chart outperforms the EWMA chart in this application, and we recommend its use for processes where small shifts in the mean are of critical concern. Additionally, we suggest further validation through Monte Carlo simulation and comparisons with other control chart methods (such as CUSUM or extended EWMA variants) to reinforce these conclusions for broader contexts.
Model Robust Geographically Weighted Regression pada Data Kemiskinan di Sulawesi Selatan Tahun 2019 Rahman, Aqilah Salsabila; Tinungki, Georgina Maria; Herdiani, Erna Tri
ESTIMASI: Journal of Statistics and Its Application Vol. 6, No. 2, Juli, 2025 : Estimasi
Publisher : Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/ejsa.v6i2.18046

Abstract

Geographically Weighted Regression (GWR) is a method of spatial analysis that can be used to perform analysis by assigning weights based on the geographical distance of each observation location and the assumption of having spatial heterogenity. The result of this analysis is an equation model whose parameter values apply only to each observation location and are different from other observation locations. However, when there are outliers at the observation location, a more robust estimation method is needed. One of the robust methods that can be applied to the GWR model is the Least Absolute Deviation method. In this study, model estimation was carried out on the factors that affect poverty in South Sulawesi in 2019 using Robust Geographically Weighted Regression (RGWR) with the Least Absolute Deviation (LAD) method. Determination of weighting is done by using the adaptive kernel bisquare weighting function. The results obtained are RGWR models which are different and apply only to each district/city in South Sulawesi. In addition, it was also found that the RGWR model with the LAD method was the best model for data that experienced spatial heterogenity and contained outliers.
THE APPLICATION OF GUMBEL COPULA TO ESTIMATE VALUE AT RISK WITH BACKTESTING IN TELECOMMUNICATION STOCK Najiha, Alimatun; Herdiani, Erna Tri; Tinungki, Georgina Maria
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 1 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (384.546 KB) | DOI: 10.30598/barekengvol17iss1pp0245-0252

Abstract

The Value at Risk (VaR) method refers to a statistical risk measurement tool used to determine the maximum loss of an investment, while the distribution that must be met is the normal distribution. This is not in line with the actual situation, because the distribution of the return value is found to be not normally distributed but depends on market conditions that occurred at that time, thus invalidating the VaR estimate and resulting in greater portfolio risk. Therefore, in this study, the estimation of risk value will be carried out using the Gumbel Copula method which can model the dependency structure between stocks and is flexible enough to model financial return data from https://finance.yahoo.com/. The parameter estimates produced by the Gumbel Copula method are then used to calculate the VaR at 90%, and 99% confidence levels. The resulting VaR values ​​are 0,076 and 0.231. To test the feasibility of the VaR model, backtesting was carried out and concluded that the VaR value obtained was valid and suitable for use in the risk assessment of PT. XL Axiata Tbk and PT. Telkomunikasi Indonesia Tbk.
VALUE AT RISK ESTIMATION USING EXTREME VALUE THEORY APPROACH IN INDONESIA STOCK EXCHANGE Najamuddin, Fadhila Febriyanti; Herdiani, Erna Tri; Jaya, Andi Kresna
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0695-0706

Abstract

Extreme Value Theory (EVT) is a method used to identify extreme cases in heavy tail data such as financial time series data. This research aimed to obtain an estimate of stock risk through the EVT approach and compare the accuracy of the two EVT approaches, Block Maxima (BM) and Peaks Over Threshold (POT). The method used to estimate stock risk is VaR with the BM and POT approaches, and the Z statistic is used to compare the accuracy. The data used, and the limitation in this research is daily closing price data for non-cyclical consumer stocks included in LQ45 for the period February 01, 2017, to January 31, 2023. Other research limitations are using weekly blocks or 5 working days in dividing BM blocks, using the percentage method in determining threshold values in the POT approach, and using Maximum Likelihood Estimation (MLE) to estimate EVT parameter estimates. The results of the VaR analysis show that the risk level generated by the POT method is greater than the risk level from BM. The results of backtesting between the two EVT approaches in estimating VaR values show that the POT approach is more accurate than the BM approach.
COMPARISON OF CONTROL CHART X ̅ BASED ON MEDIAN ABSOLUTE DEVIATION WITH S Mayashari, Mayashari; Herdiani, Erna Tri; Anisa, Anisa
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0737-0750

Abstract

A stable and controlled process will produce products of good quality following predetermined specifications. A control chart is one of the statistical tools that can be used to measure the stability of a product process in a controlled state. Control charts commonly used to evaluate the statistical control process are Shewhart control charts ( and ). The control chart is used to control the process, as seen from the average and variability of the process. If the data used is not normally distributed or there are outliers, then an alternative control chart, namely the Median Absolute Deviation (MAD), can be used. MAD is used to monitor the process mean and process standard deviation because it has properties that are robust or resistant to deviations. This research aims to form a control chart based on MAD, apply it to data on fat content in animal feed products, and compare control charts based on with the control chart based on control chart based on MAD. The limitations in this study are the quality characteristics used consist of only one variable and the data is not normally distributed, only limited to the mean process, and the data used in this study are observation data on the fat content contained in animal feed products at PT Japfa Comfeed Indonesia Tbk Makassar Unit from December 2021 to January 2022. The results of this study show that the control chart based on MAD detects more out-of-control points than the control based on . The performance of the control chart based on MAD is better at detecting changes in the process than the control chart based on because it has a relatively smaller ARL value.
RESIDUAL-BASED MEWMA CONTROL CHART FOR DRINKING WATER QUALITY MONITORING AT PDAM TIRTA Takdir, Agung Muhammad; Herdiani, Erna Tri; Sunusi, Nurtiti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp1513-1526

Abstract

Ensuring the consistent quality of drinking water remains a major challenge in Indonesia, particularly due to natural variability and operational limitations in regional water companies (PDAMs). Statistical quality control methods such as the Multivariate Exponentially Weighted Moving Average (MEWMA) chart, are widely applied for monitoring; however, their assumption of independent and identically distributed observations reduces their effectiveness when applied to autocorrelated time-series data. This study proposes a Vector Autoregressive (VAR)-based MEWMA control chart for monitoring water quality parameters, turbidity, and residual chlorine at PDAM Tirta. Daily observations from 2023 (n = 365) were analyzed. The VAR(3) model was selected using the Akaike Information Criterion (AIC), and residuals were validated to be free from autocorrelation. These residuals were then incorporated into the MEWMA framework with a smoothing parameter λ = 0.03. A comparative analysis was conducted between the standard MEWMA and the VAR-based MEWMA through Monte Carlo simulations (5,000 replications) across three shift scenarios. Results showed that both methods achieved comparable ARL₀ values (≈3), confirming stability under in-control conditions. However, the VAR-based MEWMA consistently demonstrated lower ARL₁ values in detecting small shifts, especially in turbidity, with improvements of up to 22% compared to the standard MEWMA. These findings highlight the VAR-based MEWMA as a more sensitive and reliable monitoring tool, offering water utilities an early-warning system that enables timely corrective actions and ensures compliance with drinking water quality standards.
MODELING THE GROSS ENROLLMENT RATIO BASED ON DETERMINING FACTORS THROUGH A MIXED-EFFECTS MODEL APPROACH IN INDONESIA: PEMODELAN ANGKA PARTISIPASI KASAR BERDASARKAN FAKTOR-FAKTOR PENENTU MELALUI PENDEKATAN MIXED-EFFECTS MODEL DI INDONESIA Zhulmuhqsith Busrah; Anna Islamiyati; Erna Tri Herdiani; Danu Raihan Muhammad Faisal
MATHunesa: Jurnal Ilmiah Matematika Vol. 14 No. 1 (2026)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v14n1.p56-63

Abstract

The Gross Enrollment Ratio (GER) is a key indicator of access to formal education, yet substantial disparities across Indonesian provinces reflect variations in regional socio-economic conditions. This study analyzes the effects of Average Years of Schooling (AYS), Open Unemployment Rate (OUR), and Gross Regional Domestic Product (GRDP) per capita on GER using a Linear Mixed-Effects Model (LMM) based on provincial-level data. The results indicate that OUR has a positive and significant effect on GER (p < 0.001), suggesting that higher unemployment encourages individuals to pursue further education to improve labor market competitiveness. AYS shows a negative but statistically insignificant effect (p > 0.05), implying that educational attainment does not directly translate into increased new participation. GRDP per capita exhibits a positive and significant influence on GER (p < 0.05), highlighting the role of economic capacity in expanding educational access. The Intraclass Correlation Coefficient (ICC) of 0.63 indicates that 63% of the total variation in GER is attributable to provincial-level differences, supporting the appropriateness of the mixed-effects approach. Overall, the findings demonstrate that economic conditions and labor market dynamics are key determinants of educational participation and highlight the need for region-specific policies to address disparities in educational access.
Meramalkan Curah Hujan di Kabupaten Maros dengan Menggunakan Metode Adaptive Neuro Fuzzy Inference System Tandirerung, Rael Hofni; Herdiani, Erna Tri; Sahriman, Sitti
ESTIMASI: Journal of Statistics and Its Application Vol. 7, No. 1, Januari, 2026 : Estimasi
Publisher : Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/ejsa.v7i1.26433

Abstract

The adaptive neuro-fuzzy inference system or ANFIS method is a hybrid of the fuzzy time series method and artificial neural networks. This algorithm maps the input data in the input layer to the target in the output layer via neurons in the hidden layer using time series data. The working principle of ANFIS has layers that function as input and output. This study aims to obtain the results of rainfall forecasting using the ANFIS method in Maros Regency, South Sulawesi. This research is divided into training data and testing data with details of 292 training data and 73 test data. Then the forecasting results were obtained using 73 test data, namely the period October 20 - October 31, which obtained a value of 0.384% from the calculation of MAPE (Mean Absolute Percentage Error) in the very good forecasting category. The correlation coefficient was obtained by 0.99 with a strong correlation category. So, it can be concluded that the ANFIS method can predict rainfall in Maros Regency with a good degree of accuracy.
Co-Authors ada, Nuralyatussa’ Aidawayati Rangkuti Andi Fitri Ayu Andi Kresna Jaya Andi waru A. Paluseri Anisa Anisa Anisa Anisa Anna Islamiyati Arifin, Samsul Arwini Arisandi Danu Raihan Muhammad Faisal Fathanah, Nur Fitriani Fitriani Georgina Maria Tinungki Ika Fitriana Irawaty Irawaty Maria Tinungki, Georgina Mayashari, Mayashari Mustabsyirah, Mustabsyirah Najamuddin, Fadhila Febriyanti Nasrah Sirajang Nasruddin, Nurmasyita Nirwan Ilyas Nuravia Nuravia Nurhidaya L NURTITI SUNUSI Puji Puspa Sari Rahman, Aqilah Salsabila Rasyid, Riska Ratmila Mammi Rizki Adiputra Sahriman, Sitti Saleh AF Sirajang, Nasrah Sitti Sahriman Sitti Sahriman Sonya, Sonya Sri Astuti Thamrin Suci Barlian Sari Takdir, Agung Muhammad Tandirerung, Rael Hofni Zhulmuhqsith Busrah