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ANALISIS KUANTITATIF KECELAKAAN LALU LINTAS DI AMERIKA SERIKAT PADA TAHUN 2000-2023 MENGGUNAKAN STATISTICAL QUALITY CONTROL IDA AYU OKTAVIANTI; ZAKIA ALYA ALYA ROSYDA; KEZIA BRILLIANT NAZARENA; NI WAYAN RUSNIATI; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 14 No. 4 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i04.p493

Abstract

Traffic accidents are a critical issue in road safety and public health in the United States. This study examines the patterns and statistical stability of annual traffic accidents from 2000 to 2023 using a Statistical Quality Control (SQC) approach. Secondary data were obtained from official publications of the National Highway Traffic Safety Administration (NHTSA), including accident severity, numbers of fatalities and injuries, population size, and risk indicators. The analysis employed five of the seven basic SQC tools, namely check sheets, histograms, Pareto diagrams, control charts (p-charts and u-charts), and cause-and-effect diagrams. The results show that property damage only accidents dominate total crash occurrences, while fatal crashes represent a small proportion but lead to significant loss of life. Control chart analysis indicates statistical instability in the proportion of fatal crashes and fatality rates, suggesting the presence of special causes rather than random variation. Overall, the findings highlight the usefulness of SQC as an effective tool for monitoring traffic safety performance and identifying critical variations requiring targeted interventions.
ANALISIS PENGENDALIAN CACAT PRODUK TELUR AYAM MENGGUNAKAN STATISTICAL QUALITY CONTROL DI BRAM FARM EVA KOSASIH; ALEN VIKTORIA BRIA; NI NYOMAN AYU NIRMALA LUKITA; NI PUTU SINTYA ARTA DEWI; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 14 No. 4 (2025)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2025.v14.i04.p492

Abstract

This study aims to analyze the quality control of chicken egg production at Bram Farm by applying Statistical Quality Control (SQC) tools to identify the level and types of defects that occur during the production process. Quantitative data were obtained from primary documentation through daily records collected over a 14-day observation period, consisting of the total number of eggs produced and the number of defective eggs categorized into specific defect types. Qualitative data were collected through direct observations and unstructured interviews with the farm owner to validate statistical findings and explore operational factors causing defects. The analysis employs three main SQC tools: the check sheet to record defect occurrences, the Pareto diagram to identify dominant defect categories, and the p-chart to evaluate the statistical stability of the production process. The results show that cracked eggs, thin-shelled eggs, and broken eggs are the dominant defects contributing to the overall defect rate. The p-chart indicates that all daily defect proportions fall within the control limits, demonstrating that the production process was statistically stable. These findings suggest that quality control at Bram Farm is effective, although improvement efforts should focus on the dominant defect categories to enhance production quality further.
PENERAPAN MODEL PROSES RENEWAL DALAM MANAJEMEN PERSEDIAAN BAHAN PANGAN DI HOTEL MERCURE RESORT SANUR, BALI DIVA FELIZIA BAGINDO; MADE IREINA DWIANDRA DIVAYANTI; NARISKA DESWITA WINANDI; CHRISTIAN MELANIA LEU; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 15 No. 2 (2026)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2026.v15.i02.p503

Abstract

The daily operation of a hotel kitchen relies heavily on the consistent availability of staple goods. This study analyzes the inventory management of key staples such as rice, cooking oil, milk, and eggs at Mercure Resort Sanur Bali. The research aims to determine optimal safety stock levels and reorder points to handle uncertain demand and market fluctuations. Using a renewal process model, the study analyzes the hotel’s inventory patterns based on usage and restocking data. The results show that Rice C4 should be reordered when stock reaches 40 kg, with a safety stock of 7 kg. Cooking Oil (18 LT) should be replenished at 2 jars, with 1 jar as safety stock. Milk UHT full cream should be reordered at 43 liters remaining, with an 8 liters safety stock. Chicken Eggs should be reordered at 30 kg, with a 6 kg safety stock. These findings demonstrate that applying a renewal process helps maintain the availability of essential food items and supports smooth, continuous kitchen operations at the resort.
ESTIMASI KEDATANGAN PELANGGAN DAN TRANSAKSI PESANAN RUMAH MAKAN MAHIRA MENGGUNAKAN RENEWAL-REWARD PROCESS PIONITA MARETTI BR AMBARITA; KETUT GITA SEKARINI; TASSYA MURNI PASARIBU; WIRA PRANATA T. TAMBUN; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 15 No. 1 (2026)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2026.v15.i01.p499

Abstract

Random fluctuations in customer arrivals at restaurants often result in suboptimal operational planning based on subjective estimates. This study aims to estimate customer arrival patterns and transaction values at Mahira Jimbaran Restaurant using the renewal-reward process approach, as well as to calculate long-term revenue rates. The methods used include collecting primary data for 4 hours on Saturday, November 8, 2025 (1:00 p.m. to 5:00 p.m. Wita) by recording the time between arrivals and the transaction value per customer. The analysis was conducted by calculating the expected transaction value (E[R]), expected inter-arrival time (E[X]), and long-term reward rate using the Wald Equation. The results show an average transaction of IDR 23,808.99 per customer, an average inter-arrival time of 2.013 minutes, and a revenue rate of IDR 11,828.67 per minute. These quantitative estimates can be used as a basis for operational decision-making related to workforce scheduling, queue management, and raw material planning.
ANALISIS SISTEM ANTREAN PADA SPBU 54.803.16 ULUWATU UNTUK MENGUKUR EFISIENSI PELAYANAN RAGAH NIHAN RAZANDO; NOVIA NURROHMAH; NI MADE ARI PUAN KAMINI; I GEDE DARMA YUDA UDAYANA; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 15 No. 1 (2026)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2026.v15.i01.p501

Abstract

This study aims to analyze the queuing characteristics of motorcycles refueling pertalite at SPBU 54.803.16 Uluwatu and to determine the most appropriate queueing model to represent the performance of its service system. Data were collected through direct observation on Monday and Saturday to examine the patterns of vehicle arrivals and service times. The analysis was carried out using queueing theory, applying the M/G/1 and G/G/1 models along with distribution tests to identify the suitability of arrival and service patterns. The results indicate that the distribution of arrivals on both observation days is not entirely uniform, with noticeable variations at specific time intervals. Based on the data analysis, the G/G/1 model provides a more accurate representation of the queueing conditions, as both arrival and service processes exhibit randomness without following a specific theoretical distribution. System performance evaluation shows that the server utilization rate is relatively high, leading to increased waiting times and longer queues during peak hours. These findings suggest the need for operational adjustments, particularly during high-demand periods, to improve service efficiency and reduce traffic congestion around the fuel station.
PENERAPAN BIRTH-AND-DEATH PROCESS PADA KASUS TERINFEKSI DAN KEMATIAN COVID-19 KALIMANTAN TIMUR JANUARI 2021 WINA CHRISTIANI PARHUSIP; NI KOMANG KHARINA GAYATRI; DEWA AYU RATIH ISAKA PUTRI; GINA CORNELIA BR TARIGAN; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 15 No. 2 (2026)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2026.v15.i02.p504

Abstract

The birth and death process is a powerful Markov process for modeling population changes due to two events: births and deaths. In this study, the birth and death events are described as the number of new infections and deaths due to the Covid-19 virus in East Kalimantan for the period 1–31 January 2021. In this study, the birth and death processes are used to analyze the data with a focus on estimating the parameters of the birth rate and death rate and observing the ratio between the two parameters. The results show that the estimated parameter values ​​for the birth (λ) and death (µ) are 0.0139132 and 0.00024230, respectively, and the ratio of the two parameters is 57.42. This indicates that the birth and death rates in this case are still in the supercritical category. This means that without significant external interventions such as emergency PPKM (restrictions on community activities), mass vaccination, or drastic increases in testing and tracing capacity, the number of active cases is likely to increase indefinitely in the long term.
MODEL SISTEM ANTREAN PADA KEDATANGAN DAN KEPERGIAN PELANGGAN DI CIRCLE K SURAPATI DENPASAR DESAK MADE NIRMALA YONI; NI LUH MEILIANA; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 15 No. 3 (2026)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2026.v15.i03.p516

Abstract

This study aims to analyze the queueing model based on the customer arrival and departure dynamics at Circle K Surapati, Denpasar. The study uses primary data obtained by recording customer arrival and departure times during a single observation period from 15:00 to 17:30 WITA. The results show that the arrival rate increases from 1.6 customers per 10 minutes at state 0 to 18 customers per 10 minutes at state 3, while the departure rate decreases from 4.4 customers per 10 minutes at state 1 to 1.5 customers per 10 minutes at state 4. The highest steady-state probability occurs at state 4 (0.8279), indicating that this condition most frequently appears in the long run. Furthermore, the Chi-Square goodness-of-fit test reveals that both interarrival and service time do not follow exponential distributions. Consequently, the system is best represented by a general distribution queueing model. The system is identified as a :  queueing model, utilizing two active service facilities under a first come-first served discipline
ANALISIS PEMILIHAN MODA TRANSPORTASI MAHASISWA FAKULTAS MIPA UNIVERSITAS UDAYANA MENGGUNAKAN RANTAI MARKOV WIRYA CHANDRA ADIWIJAYA; NI PUTU AMAYLIA PRADNYANDARI; FAUZIAH NURHASNA NINGSIH; MARULI SIMATUPANG; MADE AYU DWI OCTAVANNY
E-Jurnal Matematika Vol. 15 No. 3 (2026)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2026.v15.i03.p514

Abstract

Student mobility on university campuses often depends on multiple transportation options that may shift over time. This study analyzes the dynamics of transportation mode choices among undergraduate students of the Faculty of Mathematics and Natural Sciences at Udayana University using a discrete-time Markov chain approach. The research aims to identify weekly transition patterns among four transportation modes, namely private vehicles, public transportation, online transportation, and walking, and to estimate their long-term usage probabilities. Primary data were obtained through a structured questionnaire distributed to 114 students selected using proportional simple random sampling. The observed transition frequencies were used to construct a one-step transition matrix, whose stochastic properties were then assessed to ensure ergodicity before computing the steady-state distribution to identify the long-run behavioral tendencies. The results indicate that private vehicles remain the dominant mode of transportation both in the current period and in long-term projections, with a steady-state probability of 77.05 percent, while the other modes contribute relatively small proportions. These findings suggest a strong reliance on private transportation among students and highlight the need for improved mobility planning, strengthened alternative transportation options, and the development of more sustainable mobility strategies within the campus environment.
Co-Authors ALEN VIKTORIA BRIA CHRISTIAN MELANIA LEU DESAK MADE NIRMALA YONI DEWA AYU RATIH ISAKA PUTRI DIVA FELIZIA BAGINDO EVA KOSASIH FAUZIAH NURHASNA NINGSIH GINA CORNELIA BR TARIGAN I GEDE DARMA YUDA UDAYANA IDA AYU OKTAVIANTI KETUT GITA SEKARINI KEZIA BRILLIANT NAZARENA MADE IREINA DWIANDRA DIVAYANTI MARULI SIMATUPANG NARISKA DESWITA WINANDI NI KOMANG KHARINA GAYATRI NI LUH MEILIANA NI MADE ARI PUAN KAMINI NI NYOMAN AYU NIRMALA LUKITA NI PUTU AMAYLIA PRADNYANDARI NI PUTU SINTYA ARTA DEWI NI WAYAN RUSNIATI NOVIA NURROHMAH PIONITA MARETTI BR AMBARITA RAGAH NIHAN RAZANDO TASSYA MURNI PASARIBU WINA CHRISTIANI PARHUSIP WIRA PRANATA T. TAMBUN WIRYA CHANDRA ADIWIJAYA ZAKIA ALYA ALYA ROSYDA