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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi JTAM (Jurnal Teori dan Aplikasi Matematika)
Kalista, Yovita Karin
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Mathematics

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Analysis of Unmet Need for Health Services Based on the Percentage of Public Health Complaints with a Kernel Estimator Approach Rifada, Marisa; Amelia, Dita; Setyaningrum, Jeny Praesti; Septiandini, Niswah; Kalista, Yovita Karin; Dwitya, Shabrina Nareswari
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.v9i4.32555

Abstract

Healthcare services are a fundamental need that governments must guarantee to ensure optimal health outcomes for all citizens. However, many individuals still face significant barriers in accessing necessary healthcare services. This quantitative research employs a spatial analysis to examine the unmet need for health services based on public health complaints, utilizing a nonparametric regression approach with Kernel estimator. The Kernel estimator method was chosen for its flexibility in capturing unstructured data patterns, allowing the analysis to better reflect real-world conditions. The study uses health complaint data from the Central Bureau of Statistics, covering 38 provinces in Indonesia in 2024. However, data from 4 provinces were incomplete, so only 34 provinces were included in the analysis. The independent variable is the percentage of public health complaints, while the dependent variable is the percentage of unmet healthcare needs. A Gaussian kernel function was applied for nonparametric regression, identified as the optimal method based on the lowest Generalized Cross Validation (GCV) value of 1.052939 at a bandwidth of 0.33. The model demonstrates high predictive accuracy, with an R² of 82.44% and a Mean Squared Error (MSE) of 30.7%. These findings provide actionable insights for targeting healthcare disparities and improving service accessibility.
Step-Stress Accelerated Life Testing with Type II Censoring and Exponential Distribution for Solar-Powered Lighting Systems Kurniawan, Ardi; Ananda, Vanisia Suci; Kalista, Yovita Karin
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41076

Abstract

This study addresses the reliability assessment of solar-powered lighting systems using a partial step-stress accelerated life testing (ALT) model with Type-II censoring. The research aims to estimate the mean failure time and quantify the acceleration effect due to elevated stress. Secondary data from an experiment involving 31 lighting devices were analyzed. Initially, devices were tested at a normal temperature (293 K) until 16 failures occurred. Subsequently, the stress was increased to 353 K, and testing continued until all units failed or were censored. Under the assumption of an exponential lifetime distribution and a linear accelerated failure-time model, the maximum likelihood estimation (MLE) method was applied for parameter inference. The results show that the estimated mean failure time under normal conditions is approximately 711.6 hours, which reduces to about 38.7 hours under accelerated stress, yielding an acceleration factor of 18.354. Furthermore, a 95% confidence interval for the mean failure time under normal conditions is between 460.2 and 1245 hours. The reliability and percentile life at various stress levels were also derived. This research provides a practical statistical framework for evaluating the reliability of solar-powered lighting devices, offering a more efficient alternative to conventional life testing methods.
Co-Authors Ananda, Vanisia Suci Ardi Kurniawan Dita Amelia, Dita Dwitya, Shabrina Nareswari Marisa Rifada Septiandini, Niswah Setyaningrum, Jeny Praesti