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All Journal BIMASTER Desimal: Jurnal Matematika Jurnal SOLMA BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Matematika UNAND Jurnal Sintak STATISTIKA Limits: Journal of Mathematics and Its Applications
Nahrul Hayati
Batam Institute Of Technology
Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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THE APPLICATION OF DISCRETE HIDDEN MARKOV MODEL ON CROSSES OF DIPLOID PLANT Hayati, Nahrul; Setiawaty, Berlian; Purnaba, I Gusti Putu
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 3 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss3pp1449-1462

Abstract

The hidden Markov model consists of a pair of an unobserved Markov chain {Xk} and an observation process {Yk}. In this research, the crosses of diploid plant apply the model. The Markov chain {Xk} represents genetic structure, which is genotype of the kth generation of an organism. The observation process represents the appearance or the observed trait, which is the phenotype of the generation of an organism. Since it is unlikely to observe the genetic structure directly, the Hidden Markov model can be used to model pairs of events and unobservable their causes. Forming the model requires the use of the theory of heredity from Mendel. This model can be used to explain the characteristic of true breeding on crosses of diploid plants. The more traits crossed, the smaller probability of plants having a dominant phenotype in that period. Monohybrid, dihybrid, and trihybrid crosses have a dominant phenotype probability of 99% in the seventh, eighth, and ninth generations, with the condition of previous generations having a dominant phenotype. But in seventh generation, monohybrid crosses only have the probability of an optimal genotype of 50%, dihybrid crosses have a probability of an optimal genotype of 25% in the eighth generation, and trihybrid crosses have a probability of an optimal genotype of 12.5% in the ninth generation
Correlation Analysis between Manhour and Manpower in The Aircraft Structure Repair Division at Batam Aero Technic Hangar Auwalia, Farda; Hayati, Nahrul
JURNAL SINTAK Vol. 4 No. 1 (2025): SEPTEMBER 2025
Publisher : LPPM-ITEBA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62375/jsintak.v4i1.585

Abstract

This study aims to analyze the correlation between manhours (working time) and manpower (labor) in the Aircraft Structure Repair Division at Batam Aero Technic Hangar, specifically for aircraft maintenance work on PK-LJQ 2024 with lightning strike damage. Using a quantitative approach with correlational analysis, secondary data in the form of historical operational records from 2024 were analyzed to measure the interdependence between these two variables. Pearson correlation test results showed a very strong positive relationship (r = 0,980; p < 0,05), with a coefficient of determination (r²) of 96,04%, indicating that 96.04% of manhour variation can be explained by manpower variation. Descriptive analysis revealed a proportional resource allocation pattern, where 180-minute jobs required 1 technician, 360–480-minute jobs required 2 technicians, and 720-minute jobs required 3 technicians. These findings prove that repair time efficiency is highly influenced by optimal labor allocation. This research provides practical implications for the aviation Maintenance, Repair, and Overhaul (MRO) industry in enhancing productivity by adjusting personnel numbers based on job complexity. The results can also serve as a basis for managerial decision-making in more efficient resource planning.
Analysis of Fabrication Work Progress Based on Time Duration and Component Weight at PT. DIP Engineering Oktavia, Rantini Dwi; Hayati, Nahrul
JURNAL SINTAK Vol. 4 No. 1 (2025): SEPTEMBER 2025
Publisher : LPPM-ITEBA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62375/jsintak.v4i1.719

Abstract

This study aims to analyze the progress of fabrication work at PT. DIP Engineering based on time parameters and component weight. The research method used is descriptive quantitative by analyzing secondary data of daily production output and inter-stage durations. The results show that peak activity occurred at the end of May, followed by a decline in early June due to design revisions and stage transitions. Duration analysis identified the waiting time from fit-up to welding as the main bottleneck, with an average of 5.42 days (73% of the total 7.42-day cycle). Pearson correlation test showed a strong and significant positive relationship between weight and quantity of item in the welding and visual inspection stages, although the coefficient of determination indicates that other factors such as item complexity also have a major influence. The study concludes that monitoring based on weight and time data provides objective insights for production planning, and optimization efforts should be focused on reducing queues at the welding stage to accelerate the overall production cycle.
Markov Chain Analysis of Bank Customer Migration: Implication for Financial Inclusion in Maritime Economies Hayati, Nahrul; Sulistyono, Eko; Gusrita, Rani
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.32121

Abstract

Objectives: This study analyzes customer migration patterns among five major banks (BCA, BNI, BRI, BSI, and Bank Mandiri) in Batam’s strategic maritime economic zone using a Markov Chain model to assess long-term market dynamics and financial inclusion implications. The research aims to quantify interbank transition probabilities, to identify key switching drivers, and to develop targeted policy recommendations. Methods: Using a quantitative descriptive-analytical approach, we collected structured questionnaires from 250 Batam Institute of Technology academic members, capturing historical bank transitions and 5-point Likert-scale evaluations of eight switching factors. These factors included ATM/branch proximity, administrative fees, mobile/internet banking service, salary/ scholarship payment linkages, promotions/rewards, interest rates, family/friend recommendations, and Sharia compliance. Data were analyzed via Markov Chain modeling to project steady-state distributions. Results: The transition matrix revealed BCA’s superior retention (85.1%) compared to peers, with steady-state projections showing market dominance (32.44%), followed by Bank Mandiri (26.51%) and BSI (26.39%). Salary linkages (mean score: 3.45) and ATM accessibility (3.16) emerged as primary retention drivers, while BCA’s digital services (3.40) and low fee perception (3.67) explained its competitive edge. Paradoxically, BSI capitalizes on institutional salary systems (4.27) despite moderate Sharia compliance ratings (2.87). Implications: Three key policy directions emerge: hybrid digital-physical banking for coastal communities, Islamic financial ecosystem development, and fee transparency regulations. The study advances Markov Chain applications in behavioral finance while providing SEZ-specific insights for inclusive banking strategies.
Correlation Analysis Between Material Thickness and Welding Length on The Completion Time of Vessel Product in The Static Mixer Project Bahri, Salsabila; Hayati, Nahrul
JURNAL SINTAK Vol. 4 No. 2 (2026): MARET 2026
Publisher : LPPM-ITEBA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62375/jsintak.v4i2.801

Abstract

This study aims to analyze the relationship between fabrication technical parameters (material thickness and welding length) and the completion time of static mixer vessel products. The research sample consisted of 30 product units, with data collected retrospectively from the project documentation of PT. NOV Profab for the period December 2024 until July 2025. The method used was quantitative correlational. The Shapiro-Wilk normality test indicated that the data was not normally distributed (p < 0.05), therefore correlation analysis was performed using the non parametric Spearman’s Rank test. The results show that the relationship between material thickness and completion time is very weak and not significant (r = 0.126 and p = 0.507). Similarly, the relationship between welding length and completion time is weak and not significant (r = 0.301 and p = 0.106). In conclusion, material thickness and welding length are not proven to have a statistically significant relationship with the completion duration of static mixer products. This finding implies that project time estimation requires consideration of factors other that these technical parameters.
Forecasting the Consumption of Welding Consumables Using Markov Chain Models for Inventory Optimization at PT Buana Cipta Mandala Palevi, Muhammad Reza Rafella; Hayati, Nahrul
JURNAL SINTAK Vol. 4 No. 2 (2026): MARET 2026
Publisher : LPPM-ITEBA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62375/jsintak.v4i2.822

Abstract

This study aims to analyze the monthly withdrawal patterns of welding consumables (welding cup, black lens, clear lens) and develop a forecasting model to support inventory policy optimization at PT Buana Cipta Mandala, Batam. Employing a quantitative case study approach with time series data from Januari to August 2025. Withdawal volume data was categorized into three states (low, medium, high). The Markov chain model was constructed by calculating transition frequency matrices, transition probability matrices, and steady-state probabilities for each item. Preliminary descriptive statistical analysis was conducted to understand data characteristics. The findings reveal distinct transition patterns. The welding cup exhibits a rapid cycle dynamic with a steady-state probability 0.286 for low, 0.286 for medium, and 0.428 for high state, indicating a long term dominance of the high state. Conversely, the welding lenses have a transition matrix where the low state acts as an absorbing state, with a steady-state probability 1 for low, and 0 for medium and high state, predicting a convergence of demand to a low level. The resulting model recommends differentiated inventory strategies. A moderate to high stock policy with sufficient safety stock for welding cups, and a lean inventory policy based on base demand for welding lenses. The application of this Markov chain model provides a quantitative foundation for more precise procurement decision making, reducing the risks of stockout and overstocking, thereby supporting supply chain efficiency and shipyard operations.
APPLICATION OF DISCRETE HIDDEN MARKOV MODELS IN ANALYZING BLOOD TYPE INHERITANCE PATTERNS Nahrul Hayati; Eko Sulistyono; Andini Setyo Anggraeni
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/barekengvol20iss2pp1501-1512

Abstract

This research investigates the application of a Discrete Hidden Markov Model (DHMM) to analyze inheritance patterns of ABO blood types. Leveraging the DHMM’s ability to model systems with hidden states, the study aims to improve the understanding of blood type inheritance dynamics in populations. The model employs six hidden states representing ABO genotypes (IAIA, IAi, IBIB, IBi, IAIB, and ii) and four observable states corresponding to blood type phenotypes (A, B, AB, and O). The transition and emission matrices followed Mendelian inheritance principles using population allele frequencies, whereas the initial probabilities were computed under Hardy-Weinberg Equilibrium (HWE) assumptions, with parameters calibrated to Indonesian blood type distributions. As a case study, we calculated the likelihood of observing phenotype A across five consecutive generations. Using the forward-backward algorithm, the probability of this sequence was calculated as 19%. The Viterbi algorithm further identified the most probable sequence of hidden genotypes, revealing a transition from the heterozygous IAi to the homozygous IAIA genotype over the five generations. One iteration of the Baum-Welch algorithm improved model accuracy, increasing log-likelihood from -1.661 to 0. Our results demonstrate the DHMM’s efficacy in decoding complex inheritance dynamics and provide a foundation for future population genetics research.
Identifying Leading Hazards in Riau Islands: A Monthly Markov Chain Analysis of Disaster Dominance Patterns Nahrul Hayati; Eko Sulistyono; Andini Setyo Anggraeni; Vitri Aprilla Handayani; Sabarinsyah; Laras Devikaduri
Jurnal Matematika UNAND Vol. 15 No. 3 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.3.436-448.2026

Abstract

This study analyzes disaster dominance patterns in the Riau Islands using a monthly Markov chain model with five states: non hazard (S0), hydrological (S1,flood), geomorphological (S2,landslide), meteorological (S3,extreme weather), and ecological (S4,wildfire) hazard. Based on 2019-2024 data from Indonesia’s National Disaster Management Agency (BNPB), the research quantifies transition probabilities between hazard states and computes steady-state distributions to identify long-term risks. Key findings reveal wildfires dominate the system with 40.6% steady-state probability and high persistence (63% monthly recurrence), reflecting the region’s dry-seasonal vulnerability. Extreme weather and floods show significant but secondary prevalence (24.1% and 12.5%, respectively). Landslides are rare (2.5%) but often escalate to wildfires. The transition matrix highlights wildfire transitions following floods (44.5% probability), suggesting delayed risk cascades. Methodologically, this study advances archipelagic hazard modeling by integrating monthly timesteps and hazard taxonomy, offering granular insights for policymakers. Practical implications include prioritizing peatland restoration, flood-resistant infrastructure, and ASEAN-wide early warning systems to address transboundary haze.
Optimizing Classroom Allocation using Markov Chain Model for Shifted Lecture Schedules Nahrul Hayati; Eko Sulistyono; Bulan Purnama Utami
Jurnal Matematika UNAND Vol. 15 No. 1 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.1.17-29.2026

Abstract

This study aims to optimize classroom allocation for shift lecture schedules at the Batam Institut of Technology (ITEBA) using a Markov chain model. Classroom utilization data from the Odd and EVen Semesters of the 2024/2025 Academic Year were analyzed by defining four classroom usage states: occupied in the morning shift and vacant in the evening shift (OV), vacant in the morning shift and occupied in the evening shift (VO), occupied in both morning and evening shifts (OO), and vacant in both morning and evening shifts (VV). State transition analysis revealed patterns in classroom allocation dynamics between semesters, while steady-state analysis projected long term utilization. The results show a steady-state probability of 74.04% for the OO state (optimal utilization), but 15.48% of classrooms remain in the VV state (chronic underutilization). Based on these findings, the study recommends a classroom consolidation strategy based on complementary patterns, implementation of a digital reservation system, and optimization of single shift usage. This study concludes that the Markov chain model provides a scientific basis for strategic decision making in educational facility management.
Pemodelan dan Pembentukan Tabel Morbiditas-Mortalitas Stroke dan Penyakit Serebrovaskular dengan Model Multi Status Rantai Markov Waktu Kontinu Andini Setyo Anggraeni; Nahrul Hayati
Limits: Journal of Mathematics and Its Applications Vol. 23 No. 2 (2026): Limits: Journal of Mathematics and Its Applications Volume 23 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v23i2.8716

Abstract

Stroke and cerebrovascular disease are major health challenges in Indonesia, with morbidity and mortality rates influenced by age and gender. This study aims to model the and to construct a morbidity-mortality table based on age and gender. The method used is Continuous Time Multistate Markov Chain modeling, combined with flow equations, orientation equations, and integration equations to form a decrement table. Transition probabilities  are calculated using Kolmogorov's forward differential equation. The results show that transition probability tables for men and women aged 20–90 years (t=1) are successfully formed and can be detailed down to a monthly or daily scale. Non-hemorrhagic stroke is the most common type of stroke, especially in healthy individuals aged over 40 years. Young hemorrhagic stroke patients are at high risk of recurrence, while men over 45 years are more susceptible to sequelae such as aphasia and hemiparasis, while women are at higher risk of non-hemorrhagic stroke. In patients with SNH, both men and women showed a sharp decline in the probability of recurrence after age 25, but the risk remained higher than for other types of stroke or sequelae. Stroke sequelae tended to persist in men until age 51 and in women until age 56, before declining. The risk of death within one year increased significantly with advancing age, with a dominant pattern of death from non-hemorrhagic stroke in men and hemorrhagic stroke in women. These findings provide important contributions to the health and actuarial world in planning interventions and managing stroke risk.
Co-Authors Ahmad Andrevi Alrasyidin Ananda, Serly Tri Andini Setyo Anggraeni Andini Setyo Anggraeni Andini Setyo Anggraeni Anggraeni, Andini Setyo Arrafi, Adamsyam Auwalia, Farda Bahri, Salsabila Berlian Setiawaty Bulan Purnama Utami Devikaduri, Laras Dia Cahya Wati Eko Sulistyono Eko Sulistyono Eko Sulistyono Eko Sulistyono Sulistyono Gusrita, Rani Handayani, Vitri Aprilla I Gusti Putu Purnaba Laras Devikaduri Lilies Handayani Lunardi, Louis Nur Asikin Oktavia, Rantini Dwi Palevi, Muhammad Reza Rafella Putri, Tia Aura Rani Gusrita Sabarinsyah Sabarinsyah, Sabarinsyah Sadiq Ardo Wibowo, Sadiq Ardo Sembiring, Rinawati Taufiq Rahman Utami, Arli Magfirah Vitri Aprilla Handayani