SIMULATION OF RELIABILITY, RELIABILITY INDEX,  PROBABILITY DENSITY FUNCTION AND FAILURE FUNCTIONS FROM WEIBULL DISTRIBUTION FOR ENGINEERING APPLICATIONS:

Isaiah A. Oke; Ufuoma. P.  Williams Bello; Opeyemi K. Olayanju; Oyeyemi Temitayo   Oyewole; Oluwaseun K. Akinmusere; Akintunde O. Fasuba; Ebenezer O. Fakorede; Ayotunde Oluyemisi  Akanni

doi:10.33003/fjs-2024-0803-2234

Isaiah A. Oke Obafemi Awolowo University, Ile-Ife
Ufuoma. P. Williams Bello Federal Ministry of Works and Housing Highway Construction & Rehabilitation Department
Opeyemi K. Olayanju Department of Civil Engineering, Redeemer’s University, Ede
Oyeyemi Temitayo Oyewole Department of Computer Engineering Elizade University, Ilara- Mokin,
Oluwaseun K. Akinmusere Department of Civil and Environmental Engineering, Elizade University, Ilara – Mokin,
Akintunde O. Fasuba Department of Civil and Environmental Engineering, Elizade University, Ilara – Mokin,
Ebenezer O. Fakorede Department of Civil and Environmental Engineering, Elizade University, Ilara – Mokin,
Ayotunde Oluyemisi Akanni Department Civil Engineering : Federal Polytechnical, Ile- Oluji

DOI: https://doi.org/10.33003/fjs-2024-0803-2234

Keywords: Probability distribution, Probability density function, Reliability, Reliability index, Failures, Weibull distribution

Abstract

In modelling and simulating future rainfall for a selected location, the probability distributions have been established to be an effective tool. In this study, the different methods utilised in the estimation of the probability distributions’ parameters were evaluated and presented using Weibull's two parameters. Different estimator methods (mean rank, median rank, symmetric, graphical, least square, empirical, maximum likelihood, general probability, modified maximum likelihood, Mabchour, alternative maximum likelihood, equivalent energy, moment expression, Lysen and Moment methods) were used to determine probability density function, reliability, reliability index and failure functions of rainfall data from Maiduguri. The performances of these different methods were compared probability density function, reliability, reliability index and failure functions of Weibull two parameters. The study revealed that the values of probability distribution dimensionless shape variables were between 1.0193 and 4.205, and probability distribution scale factor constants were between 0.302 and 7.254. These values are all positive (non-negative values or less than zero) values. It was established that there were significant differences (F_{108, 1728}was 162.1976 and the probability (p) was zero) between the individual reliabilities and Weibull estimators (F_{15, 1620}was 14928.98 and probability was zero) at a 95 % confidence level (p less than 0.05). It was concluded that caution must be taken in the utilization of general probability, equivalent energy, Alternative Maximum Likelihood Method and moment expression methods in any engineering applications to prevent failure of devices or infrastructure.

References

Abaza, M. A., El-Maghlany, W. M., Hassab, M., and Abulfotuh, F. (2020). 10 MW Concentrated Solar Power (CSP) plant operated by 100% solar energy: Sizing and techno-economic optimization. Alexandria Engineering Journal, 59(1), 39–47. https://doi.org/10.1016/j.aej.2019.12.005 DOI: https://doi.org/10.1016/j.aej.2019.12.005

Akintola, J.O (1986).: Rainfall Distribution in Nigeria 1892–1983, 1st edn. Impact Publishers Nigeria Ltd, Ibadan.

Alizadeh N., H., and Jarrahiferiz, J. (2018). Moments of nonparametric probability density functions of entropy estimators applied to testing the inverse Gaussian distribution. Journal of Statistical Computation and Simulation, 88(16), 3217–3229. DOI: https://doi.org/10.1080/00949655.2018.1508464

Almazah , M.A and Ismail, M. (2021). Selection of Efficient Parameter Estimation Method forTwo-Parameter Weibull Distribution. Mathematical Problems in Engineering. 2021, Article ID 5806068, 8 pages. https://doi.org/10.1155/2021/5806068 DOI: https://doi.org/10.1155/2021/5806068

Baseer, M.A., Meyer, J.P., Rehman, S. and Alam, M.M. (2017), “Wind power characteristics of seven data collection sites in Jubail, Saudi Arabia using Weibull parameters”, Renewable Energy, 102, 35-49. DOI: https://doi.org/10.1016/j.renene.2016.10.040

Casas M.C, Rodr´iguez R, and Reda˜no A. (2010a). Analysis of extreme rainfall in Barcelona using a microscale rain gauge network. Meteorological Applications 17(1): 117–123. DOI: https://doi.org/10.1002/met.166

Casas, M.C, Rodr´iguez, R., Prohom, M, Gazquez, G and Redano, A. (2010b). Estimation of the probable maximum precipitation in Barcelona (Spain). International Journal Of Climatology 17(1): 117–123

Chaurasiya PK, Ahmed S and Warudkar V (2018) Study of different parameters estimation methods of Weibull distribution to determine wind power density using ground based Doppler SODAR instrument. Alexandria Engineering Journal 57(4): 2299–2311.

Chaurasiya, P. K., Ahmed, S., and Warudkar, V. (2017). Study of different parameters estimation methods of Weibull distribution to determine wind power density using ground based Doppler SODAR instrument. Alexandria Engineering Journal. https://doi.org/10.1016/j.aej.2017.08.008 DOI: https://doi.org/10.1016/j.aej.2017.08.008

Gokarna R. A., and Chris P. T. (2011) Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distribution European Journal of Pure And Applied Mathematics. 4(2), 89-102

Gupta, S.; Kanwar, S. and Sharma, N. (2023) Materials Today: Proceedings reliability. 3rd Biennial International Conference on Future Learning Aspects of Mechanical Engineering (FLAME 2022) https://www.sciencedirect.com/science/article/pii/S2214785323005199

Idi, M. D. Aladesanmi, T. A. Lukman, S. Asani, M. A, Usman, Y. M and Oke, I.A. (2020). A Numerical Formula And Cost Benefit Of Groundwater Recharge In Maiduguri, Nigeria . (FUTA Journal of Technology, Akure). FUTAJEET, 14(2), 126 -138 https://futajeet.com/index.php/jeet/article/view/158

Jamali, H., Ebrahimi, A., Ardestani, E. G., and Pordel, F. (2020). Evaluation of plotless density estimators in different plant density intensities and distribution patterns. Global Ecology and Conservation, e01114. https://doi.org/10.1016/j.gecco.2020.e01114 DOI: https://doi.org/10.1016/j.gecco.2020.e01114

Jean-François, A. and Ben, S. (2013) The Poisson quasi-maximum likelihood estimator: a solution to the ‘adding up’ problem in gravity models, Applied Economics Letters, 20:6, 515-519, DOI: https://doi.org/10.1080/13504851.2012.718052

Jones, L.D.; Vandeperrea, L.J. Haynes, , T.A. and Wenman, M.R.(2020). Theory and application of Weibull distributions to 1D peridynamics for brittle solids. Comput. Methods Appl. Mech. Engrg. 363, 112903 DOI: https://doi.org/10.1016/j.cma.2020.112903

Kang, D, Kyungnam, K and Jongchul H.(2018). Comparative Study of Different Methods for Estimating Weibull Parameters: A Case Study on Jeju Island, South Korea. Energies, 11, 356; https://doi.org/10.3390/en11020356 www.mdpi.com/journal/energies DOI: https://doi.org/10.3390/en11020356

Kasara M., Omid, A., Ali, M.; Navid, G. and Mahdi, J. (2016). Assessing different parameters estimation methods of Weibull distribution to compute wind power density. Energy Conversion and Management 108, 322–335 DOI: https://doi.org/10.1016/j.enconman.2015.11.015

Kayid, M.; and Alshehri, M.A. (2023). Modified Maximum Likelihood Estimation of the Inverse Weibull Model. Axioms 2023, 12, 961. https://doi.org/10.3390/axioms12100961 DOI: https://doi.org/10.3390/axioms12100961

Khahro, S.F., Tabbassum, K., Soomro, A.M., Dong, L. and Liao, X. (2014), “Evaluation of wind power production prospective and Weibull parameter estimation methods for Babaurband, Sindh Pakistan”, Energy Conversion and Management, 78, 956-967 DOI: https://doi.org/10.1016/j.enconman.2013.06.062

Kidmo, D.K., Danwe, R., Doka, S.Y. and Djongyang, N. (2015), “Statistical analysis of wind speed distribution based on six Weibull methods for wind power evaluation in Garoua, Cameroon”, Revue des Energies Renouvelables, . 18 (1), 105-125.

Klimenko D. Y. (2020). Estimating the Probable Maximum Precipitation by Physical Methods Using Satellite and Radiolocation Observation Data: Case Study of the Middle Urals Water Resources, 47(4), 641–650. DOI: https://doi.org/10.1134/S0097807820040065

Kopala, I , Dana, B., Pavel, K. , Zora, J., Jan, V. , and Marta, H. (2016). Weibull distribution application on temperature dependence of polyurethane storage modulus. Int. J. Mater. Res. (formerly Z. Metallkd.) 107 (2016) 5, 472-476 DOI: https://doi.org/10.3139/146.111359

Laurence, T. A. and Chromy, B. A. Efficient Maximum Likelihood Estimator Fitting of Histograms. Nat. Methods 2010, 7 (5), 338-339. DOI: https://doi.org/10.1038/nmeth0510-338

Lukman S., Sani S.B., Asani A.M., Ojo S.O. and Oke A.I. (2023). Performance Evaluation of Nine Methods for Estimation of Weibull Distribution Parameters, FUOYE Journal of Engineering and Technology (FUOYEJET), 8(1), 100-108. http://doi.org/10.46792/fuoyejet.v8i1.947 DOI: https://doi.org/10.46792/fuoyejet.v8i1.947

Martel, J.L; Brissette, F. P.; Lucas-Picher, P.; Troin, M.; and Arsenault, R. (2021). Climate Change and Rainfall Intensity–Duration–Frequency Curves: Overview of Science and Guidelines for Adaptation. ASCE J. Hydrol. Eng.,26(10): 03121001 DOI: https://doi.org/10.1061/(ASCE)HE.1943-5584.0002122

Mohammed, M. and Ahmed A. (2019). Efficiency of the Reliability Function and Scheduling Method in Determining the Optimal Preventive Maintenance Time for Digital X-Ray Devices. International Journal of Statistics and Applications 2019, 9(2): 53-58 https://doi.org/10.5923/j.statistics.20190902.02

Nathan, R., Jordan, P., Scorah, M., Lang, S., Kuczera, G., Schaefer, M., and Weinmann, E. (2016). Estimating the exceedance probability of extreme rainfalls up to the probable maximum precipitation. Journal of Hydrology, 543, 706–720. DOI: https://doi.org/10.1016/j.jhydrol.2016.10.044

Nawafleh, N. A., Mack, F., Evans, J., Mackay, J., and Hatamleh, M. M. (2013). Accuracy and Reliability of Methods to Measure Marginal Adaptation of Crowns and FDPs: A Literature Review. Journal of Prosthodontics, 22(5), 419–428. DOI: https://doi.org/10.1111/jopr.12006

Noughabi, H. A., and Jarrahiferiz, J. (2020). Nonparametric probability density functions of entropy estimators applied to testing the Rayleigh distribution. Journal of Statistical Computation and Simulation, 1–15. DOI: https://doi.org/10.1080/00949655.2020.1781123

Nwobi, F. N and Ugomma, C.A (2014). A Comparison of Methods for the Estimation of Weibull Distribution Parameters. Metodološki zvezki, 11(1), 65-78. DOI: https://doi.org/10.51936/bddv8875

Oke, I. A (2008) Utilization of Weibull Techniques For Short-Term Data In Environmental Engineering. Environmental Engineering and Sciences. 25 (7),1099- 1107. DOI: https://doi.org/10.1089/ees.2007.0306

Parajuli, A. (2016), “A statistical analysis of wind speed and power density based on Weibull and Rayleigh models of Jumla, Nepal”, Energy and Power Engineering, 8(7), 271-282. DOI: https://doi.org/10.4236/epe.2016.87026

Pichugina, S. V. (2008). Application of the Theory of Truncated Probability Distributions to Studying Minimal River Runoff: Normal and Gamma Distributions. Water Resources, 35(1), 23–29. DOI: https://doi.org/10.1134/S009780780801003X

Pisarenko, V. F. Bolgov, M. V. Osipova, N. V. and Rukavishnikova, T. A. (2002). Application of the Theory of Extreme Events to Problems of Approximating Probability Distributions of Water Flow Peaks. Water Resources, 29(6), 593–604. DOI: https://doi.org/10.1023/A:1021124426653

Pobocikova I, and Sedliackova Z (2014) Comparison of four methods for estimating the Weibull distribution parameters. Appl Math Sci 8(83):4137–4149 DOI: https://doi.org/10.12988/ams.2014.45389

SIMULATION OF RELIABILITY, RELIABILITY INDEX, PROBABILITY DENSITY FUNCTION AND FAILURE FUNCTIONS FROM WEIBULL DISTRIBUTION FOR ENGINEERING APPLICATIONS

WEIBULL DISTRIBUTION and ENGINEERING APPLICATIONS

Abstract

References

Most read articles by the same author(s)

Announcements

FUDMA Journal of Sciences - Vol. 8_2024 Call for Manuscript Submission