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All Journal Journal of Mathematics, Computation and Statistics (JMATHCOS)
Harianto
Universitas Muhammadiyah Bulukumba
Mathematics

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Autokorelasi Pada Pembentukan Grafik Kendali Komponen Utama Nur Ahniyanti Rasyid; Dhian Eka Wijaya; Dian Firmayasari; Harianto; Muhammad Isbar Pratama
Journal of Mathematics, Computations and Statistics Vol. 5 No. 2 (2022): Volume 05 Nomor 02 (Oktober 2022)
Publisher : Jurusan Matematika FMIPA UNM

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The formation of control chart for autocorrelated data can not be done. This research aims to analyse the effect of autocorrelated data on the formation of principal component control chart. A case study was performed on simulated data with two variables and they were applied on the data of climate elements in Makassar city including air temperature, solar radiation, air humadity,and wind speed. The analysis of the effect of the autocorrelated data was conducted inthree steps, namely: (1) the establishment of the structure of variance-covariance matrix of the autocorrelated data; (2) the establishment of principal component control chart based on the largest eigen valu; and (3) In forming of simulation with two variables. The result indicate that if the data are negatively autocorrelated with avalue of -0,9-(-0,5), the controllimits will be widened, and if the value is -0,5-(-0,1), the control limits will be narrowed.
Simulasi Numerik Model Matematika Arus Lalu Lintas Berbasis Fungsi Velositas Underwood Muh. Isbar Pratama; Dian Firmayasari; Nur Ahyaniyanti Rasyid; Harianto
Journal of Mathematics, Computations and Statistics Vol. 4 No. 1 (2021): Volume 04 Nomor 01 (April 2021)
Publisher : Jurusan Matematika FMIPA UNM

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Abstract. Mathematical traffic flow model was first developed by Lighthill, Whitham and Richards in 1956, known as (LWR) model. In LWR model, velocity function was most important. In this paper, Underwood velocity function was used. Implicit finite difference method used to found the numerical solution of LWR model with Underwood velocity model. Convergence the implicit finite difference method proved using the Lax equivalence theorem. The numerical simulation of 10 km highway of single lane was performed for 1 hours using the implicit finite difference method based on artificially generated initial and boundary data. Numerical simulation performed with two different parameters. An experimental result for the stability condition of the numerical scheme was also presented. Density, velocity, and fluks for 1 hours was experimental result of numerical simulation.
Co-Authors Dhian Eka Wijaya Dian Firmayasari Muhammad Isbar Pratama Nur Ahniyanti Rasyid Nur Ahyaniyanti Rasyid