Reliability modeling of intelligent heat supply systems: A new class of cosine trigonometric based on non-homogeneous poisson process

Authors

  • Qusay Ahmed Taha Ministry of Education, The General Directorate of Education in Nineveh Governorate, Nineveh, Iraq
  • Mohammed Zaid Hussein Department of Mathematics, College of Basic Education, University of Telafer, Nineveh, Iraq
  • Adel S. Hussain IT Department, Amedi Technical Institutes, University of Duhok Polytechnic, Duhok, Iraq; Department of Administrative and Financial Affairs, Faculty Division, Al-Iraqi University, Baghdad, Iraq; Department of Computer Engineering, Al-Kitab University, Altun, Kupri, Kirkuk, Iraq
  • Mohammad A. Tashtoush Department of Basic Sciences, AL-Huson University College, AL-Balqa Applied University, Salt, Jordan; Faculty of Education and Arts, Sohar University, Sohar, Oman
  • Hasanain Jalil Alsaedi Business Information Technology Department, College of Business Information, University Information Technology and Communication, Baghdad, Iraq

Abstract

Heat supply system (HSS) is a very important and serious element of the urban infrastructure that has a direct impact on the comfort of the residence, energy consumption and the overall wellbeing of the people. The traditional reliability of HSS is mainly focused on hardware failure, whereas the reliability of software and intelligent control components are not fully studied and the reliability of the systems on an exact system level cannot be fully considered in the contemporary intelligent heat supply systems (IHSS). In order to surmount this constraint, this paper suggests a conditional, fused, and time-varying reliability model, which combines hardware, software, and consumer behavior. The IHSS is further broken down into hardware and software subsystems in which the hardware reliability is modeled by a cosine trigonometric Gompertz-based model, based on a recently introduced cosine pie-power odd-G family of distributions, whereas the software reliability is modeled by use of non-homogeneous Poisson process (NHPP). The proposed distribution has extremely flexible hazard rate forms, which is why it is convenient when it comes to modelling complex degradation processes in heat supply components. A consumer level topology of the reliability model with heating network topology and minimal path matrices are used to represent realistic operating conditions. Maximum likelihood estimation is used to estimate model parameters making them statistically efficient. Monte Carlo simulations confirm the performance of the suggested framework because they indicate that the bias and the mean square error decrease with the sample size. The analysis of two real-life data sets indicate that the proposed model is also always better than seven competing models in terms of various goodness-of-fit and model selection criteria. These findings affirm the strength and viable usefulness of the given method of IHSS reliability evaluation.

References

Li, Q. Y., & Pham, H. (2017). NHPP software reliability model considering the uncertainty of operating environments with imperfect debugging and testing coverage. Applied Mathematical Modelling, 51, 68–85. https://doi.org/10.1016/j.apm.2017.06.034

Nguyen, H. C., & Huynh, Q. T. (2022). New non-homogeneous Poisson process software reliability model based on a 3-parameter S-shaped function. IET Software, 16(2), 214–232. https://doi.org/10.1049/sfw2.12055

Liu, X. M., & Xie, N. M. (2022). Grey-based approach for estimating software reliability under nonhomogeneous Poisson process. Journal of Systems Engineering and Electronics, 33(2), 360–369. https://doi.org/10.23919/JSEE.2022.000038

Okamura, H., & Dohi, T. (2021). Application of EM algorithm to NHPP-based software reliability assessment with generalized failure count data. Mathematics, 9(9), 985. https://doi.org/10.3390/math9090985

Kim, Y. S., Song, K. Y., Pham, H., & Chang, I. H. (2025). Non-homogeneous Poisson process software reliability model and multi-criteria decision for operating environment uncertainty and dependent faults. Applied Sciences, 15(9), 5184. https://doi.org/10.3390/app15095184

Hou, Y. F., Huang, C. Y., & Fang, C. C. (2022). Using the methods of statistical data analysis to improve the trustworthiness of software reliability modeling. IEEE Access, 10, 25358–25375. https://doi.org/10.1109/ACCESS.2022.3154103

Dohi, T., Li, S. Q., & Okamura, H. (2024). Local polynomial software reliability models and their application. Information and Software Technology, 166, 107366. https://doi.org/10.1016/j.infsof.2023.107366

Das, S., Kundu, D., & Dewanji, A. (2022). Software reliability modeling based on NHPP for error occurrence in each fault with periodic debugging schedule. Communications in Statistics–Theory and Methods, 51(14), 4890–4902. https://doi.org/10.1080/03610926.2020.1828462

Song, K. Y., Chang, I. H., & Pham, H. (2019). NHPP software reliability model with inflection factor of the fault detection rate considering the uncertainty of software operating environments and predictive analysis. Symmetry, 11(4), 521. https://doi.org/10.3390/sym11040521

Luo, H., Xu, L. J., He, L., Jiang, L. D., & Long, T. (2023). A novel software reliability growth model based on generalized imperfect debugging NHPP framework. IEEE Access, 11, 71573–71593. https://doi.org/10.1109/ACCESS.2023.3292301

Al-Mutairi, N. N., Al-Turk, L., & Al-Rajhi, S. A. (2020). A new reliability model based on Lindley distribution with application to failure data. Mathematical Problems in Engineering, 2020, 4915812. https://doi.org/10.1155/2020/4915812

Hussain, A., Oraibi, Y., Mashikhin, Z., Jameel, A., Tashtoush, M., & Az-Zo’bi, E. (2025). New software reliability growth model: Piratical swarm optimization-base parameter estimation in environments with uncertainty and dependent failures. Statistics, Optimization & Information Computing, 13(1), 209–221. https://doi.org/10.19139/soic-2310-5070-2109

Yang Ziganshin, S. G., Vankov, Y. V., & Gorbunova, T. G. (2016). Reliability of thermal networks for city development. Procedia Engineering, 150, 2327–2333. https://doi.org/10.1016/j.proeng.2016.07.315

Svintsov, A. P., Shchesnyak, E. L., Galishnikova, V. V., & Fediuk, R. S. (2020). Monitoring of heating systems as a factor of energy safety of buildings. Journal of Building Engineering, 31, 101384. https://doi.org/10.1016/j.jobe.2020.101384

Postnikov, I. (2023). Methods for the reliability optimization of district-distributed heating systems with prosumers. Energy Reports, 9, 584–593. https://doi.org/10.1016/j.egyr.2022.11.085

Postnikov, I., & Mednikova, E. (2022). A reliability analysis of fuel supply for district heating systems based on statistical test method. Energy Reports, 8, 304–311. https://doi.org/10.1016/j.egyr.2022.08.020

Postnikov, I., & Penkovskii, A. (2022). Comprehensive price-reliability analysis for district heating systems. Energy Reports, 8, 129–136. https://doi.org/10.1016/j.egyr.2022.08.050

Rocco S., C. M. (2003). A rule induction approach to improve Monte Carlo system reliability assessment. Reliability Engineering & System Safety, 82(1), 85–92. https://doi.org/10.1016/S0951-8320(03)00137-6

Shu, L., Chen, L., Jin, J., Yu, J., Sun, F., & Wu, C. (2005). Functional reliability simulation for a power-station’s steamturbine. Applied Energy, 80(1), 61–66. https://doi.org/10.1016/j.apenergy.2004.02.004

Hussain, A., Pati, K., Atiyah, A., & Tashtoush, M. (2025). Rate of occurrence estimation in geometric processes with Maxwell distribution: A comparative study between artificial intelligence and classical methods. International Journal of Advances in Soft Computing and Its Applications, 17(1), 1–15. https://doi.org/10.15849/IJASCA.250330.01

Aslett, L. J. M., Nagapetyan, T., & Vollmer, S. J. (2017). Multilevel Monte Carlo for reliability theory. Reliability Engineering & System Safety, 165, 188–196. https://doi.org/10.1016/j.ress.2017.03.003

Cheng, Q., Wang, S., & Yan, C. (2017). Sequential Monte Carlo simulation for robust optimal design of cooling water system with quantified uncertainty and reliability. Energy, 118, 489–501. https://doi.org/10.1016/j.energy.2016.10.051

Benchiha, S., Sapkota, L. P., Al Mutairi, A., Kumar, V., Khashab, R. H., Gemeay, A. M., Nassr, S. G., & Elgarhy, M. (2023). A new Sine family of generalized distributions: Statistical inference with applications. Mathematical and Computational Applications, 28(4), 83. https://doi.org/10.3390/mca28040083

Nassar, M., Alzaatreh, A., Abo-Kasem, O., Mead, M., & Mansoor, M. (2018). A new family of generalized distributions based on alpha power transformation with application to cancer data. Annals of Data Science, 5, 421–436. https://doi.org/10.1007/s40745-018-0144-5

Souza, L., Junior, W., De Brito, C., Chesneau, C., Ferreira, T., & Soares, L. (2019). On the sin-G class of distributions: Theory, Model and Application. Journal of Mathematical Modeling, 7(3), 357–379. https://doi.org/10.22124/jmm.2019.13502.1278

Souza, L., Júnior, W. R. O., Brito, C., Chesneau, C., Fernandes, R. L., & Ferreira, T. A. E. (2021). Tan-G class of trigonometric distributions and its applications. Cubo (Temuco), 23 (1), 1–20. https://doi.org/10.4067/S0719-06462021000100001

Mahmood, Z., Chesneau, C., & Tahir, M. H. (2019). A new sine-G family of distributions: Properties and applications. Bulletin of Computational and Applied Mathematics, 7(1), 53–81. https://hal.science/hal-03580871v1

Jamal, F., & Chesneau, C. (2021). The sine Kumaraswamy-G family of distributions. Journal of Mathematics Extension, 15(2), 1–33. https://doi.org/10.30495/JME.2021.1332

Muhammad, M., Alshanbari, H. M., Alanzi, A. R. A., Liu, L., Sami, W., Chesneau, C., & Jamal, F. (2021). A new generator of probability models: The exponentiated sine-G family for lifetime studies. Entropy, 23(11), 1394. https://doi.org/10.3390/e23111394

Chaudhary, A. K., & Kumar, V. (2021). The ArcTan Lomax distribution with properties and applications. International Journal of Scientific Research in Science, Engineering and Technology, 4099, 117–125. https://doi.org/10.32628/IJSRSET218117

Isa, A. M., Ali, B. A., & Zannah, U. (2022). Sine Burr XII distribution: Properties and application to real data sets. Arid Zone Journal of Basic and Applied Research, 1, 48–58. https://doi.org/10.55639/607lkji

Alghamdi, A. S., & Abd El-Raouf, M. M. (2023). A new alpha power Cosine-Weibull model with applications to hydrological and engineering data. Mathematics, 11(3), 673. https://doi.org/10.3390/math11030673

Ahmad, A., Jallal, M., & Mubarak, S. A. M. (2023). New Cosine-generator with an example of Weibull distribution: Simulation and application related to banking sector. Reliability: Theory & Applications, 18(1), 133–145. https://gnedenko.net/Journal/2023/012023/RTA_1_2023-11.pdf

Wu, X., Ahmad, Z., Hussam, E., Alhelali, M. H., Aldallal, R., Almuqrin, M. A., & Riad, F. H. (2023). A new Cosine-Weibull model: Distributional properties with applications to basketball and medical sectors. Alexandria Engineering Journal, 66, 751–767. https://doi.org/10.1016/j.aej.2022.10.068

Jia, J., Yan, Z., Peng, X., & An, X. (2020). A new distribution for modeling the wind speed data in Inner Mongolia of China. Renewable Energy, 162, 1979–1991. https://doi.org/10.1016/j.renene.2020.10.019

Breneman, J. E., Sahay, C., & Lewis, E. E. (2022). Introduction to reliability engineering. John Wiley & Sons. https://www.wiley.com/en-us/Introduction+to+Reliability+Engineering%2C+3rd+Edition-p-9781119640653

Rahman, M. M. (2021). Arcsine-G family of distributions. Journal of Statistical Applications and Probability Letters, 8(3), 169–179. https://doi.org/doi:10.18576/jsapl/080303

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Published

2026-05-30

How to Cite

Qusay Ahmed Taha, Mohammed Zaid Hussein, Adel S. Hussain, Mohammad A. Tashtoush, & Hasanain Jalil Alsaedi. (2026). Reliability modeling of intelligent heat supply systems: A new class of cosine trigonometric based on non-homogeneous poisson process. Results in Nonlinear Analysis, 9(1), 117–148. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/812

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Vol. 9 No. 1 (2026): Volume 9 issue 1 - Current Issue

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