Volume-10 , Issue-1 , Feb 2023, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  A Cascade System Reliability Model for Rama Distributed Random Variables

  Chumchum Doloi, Jonali Gogoi, Gitanjali Pradhani

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.1 , pp.1-9, Feb-2023

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  Abstract
  The reliability of a cascade system when the stress and strength are Rama-distributed random variables have been studied in this study. A standby redundancy system known as a "Cascade" replaces a failed component with a standby component that has independently dispersed strength and a lower stress value. A specific kind of stress-strength model is the cascade reliability model. The Cascade model`s system reliabilities for the parameters of this distribution about the cascade variables are calculated using the value of the marginal reliabilities for n=1,2 which is further used to find the system reliability R_2 2 of the Cascade model for the parameters of Rama distribution according to the cascade variables.

  Key-Words / Index Term
  cascade system, stress-strength, reliability, hazard rate function, mean residual life function, Rama distribution

  References
  [1]. C. Doloi, “Estimation of Cascade Reliability for two Stresses and Single Strength,” Advances and Applications in Statistics, Vol. 2, Issue 70, pp.129-136, 2021.
  [2]. D. Reddy, “Cascade and System Reliability for Exponential Distribution,” DJ Journal of Applied Mathematics, vol.2, issue 2, pp.1-5, 2016, doi: 10.18831/djmaths.org/2016021001.
  [3]. H. Dong, L. Cui, “System Reliability Under Cascading Failure Models,” IEEE Trans. Reliability, vol.65, issue 2, pp.929-940, 2016, doi:10.1109/TR.2015.2503751.
  [4]. K. C. Kapur, L. R. Lamberson, “Reliability in Engineering Design,” Wiley, 1991.
  [5]. M. Maryam, R. Kannan, Shabir A. Dar, “Improving the Reliability of System by Standby Redundancy Method,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue 1, pp.76-82, 2021.
  [6]. P. V. Pandit, K. N., “Estimation of Stress Strength Reliability for Transmuted Exponentiated Inverse Rayleigh Distribution,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.5, pp.57-62, 2019.
  [7]. R. E. Schafer, N. D. Singpurwalla, “Methods of Statistical Analysis of Reliability and Life Data,” Wiley-Blackwell, 1975.
  [8]. R. Shanker, “Rama Distribution and Its Application,” International Journal of Statistics and Applications, Vol.1, No.7, pp.26-35, 2017.
  [9]. S. N. N. Pandit, G. L. Sriwastav, “Studies in Cascade Reliability II,” IEEE Transactions on Reliability, Vol. 2, No. 27, pp.166-168, 1978.

  Citation
  Chumchum Doloi, Jonali Gogoi, Gitanjali Pradhani, "A Cascade System Reliability Model for Rama Distributed Random Variables," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.1, pp.1-9, 2023

• Open Access   Article

  Integral Solution of the Binary Quadratic Equation 3x2-y2=2 that Depicts Parabolas and Hyperbolas

  Janaki G., Gowri Shankari A.

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.1 , pp.10-13, Feb-2023

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  The distinct integral solution of the binary quadratic equation 3x2-y2=2 that depicts distinct parabolas and hyperbolas are examined. A number of non-zero integral solutions are discovered, and some intriguing recurring links between them are provided.

  Key-Words / Index Term
  Binary quadratic equation, Diophantine equation, Integral solutions, Hyperbola, Parabola & Pell’s equation.

  References
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  Citation
  Janaki G., Gowri Shankari A., "Integral Solution of the Binary Quadratic Equation 3x2-y2=2 that Depicts Parabolas and Hyperbolas," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.1, pp.10-13, 2023

• Open Access   Article

  Prediction of Heteroscedastic Data Using Linear Regression and Various Machine Learning Models

  Muhammad Danish Munir

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.1 , pp.14-19, Feb-2023

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  Abstract
  According to OLS assumption, “variance of error term should be constant”. Whenever this assumption is violated then heteroscedasticity problem arises. If we apply the OLS method to heteroscedastic data then predicted values are inaccurate and our inference may be wrong about data. In this research, an attempt has been made to implement various machine learning techniques to predict the values of heteroscedastic data. We take two different types of heteroscedastic datasets and split each dataset into two sections, training dataset and a testing dataset with 80% and 20% ratios. We apply different machine learning models including Decision Tree, Random Forest, Gradient Boosting, K Nearest Neighbor, and also apply Linear regression on training datasets and predict the values of testing datasets. All machine learning models provide minimum values of the sum of the square as compared to Linear regression. Some of machine learning models shows good results, its predicted values are nearest to observed values. As the results machine learning models provides high r-square and a low sum of the square. This research shows that we can deal heteroscedastic data with machine learning models.

  Key-Words / Index Term
  Machine Learning Prediction, Prediction of Heteroscedastic Data, Heteroscedasticity, Heteroscedastic Data

  References
  [1] O. L. O. Astivia and B. D. Zumbo, “Heteroskedasticity in Multiple Regression Analysis?: What it is , How to Detect it and How to Solve it with Applications in R and Heteroskedasticity in Multiple Regression Analysis?: What it is , How to Detect it and How to Solve it with Applications in R,” Pract. Assessment, Res. Eval. Vol., vol. 24, 2019.
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  [6] Rahul, A. Gupta, A. Bansal, and K. Roy, “Solar energy prediction using decision tree regressor,” Proc. - 5th Int. Conf. Intell. Comput. Control Syst. ICICCS 2021, no. Iciccs, pp. 489–495, 2021, doi: 10.1109/ICICCS51141.2021.9432322.
  [7] D. Karir, A. Ray, A. Kumar Bharati, U. Chaturvedi, R. Rai, and M. Khandelwal, “Stability prediction of a natural and man-made slope using various machine learning algorithms,” Transp. Geotech., vol. 34, no. September 2021, 2022, doi: 10.1016/j.trgeo.2022.100745.
  [8] C. Bienefeld, E. Kirchner, A. Vogt, and M. Kacmar, “On the Importance of Temporal Information for Remaining Useful Life Prediction of Rolling Bearings Using a Random Forest Regressor,” Lubricants, vol. 10, no. 3, p. 48, 2022, doi: 10.3390/lubricants10030048.
  [9] W. Cai, R. Wei, L. Xu, and X. Ding, “A method for modelling greenhouse temperature using gradient boost decision tree,” Inf. Process. Agric., vol. 9, no. 3, pp. 343–354, 2021, doi: 10.1016/j.inpa.2021.08.004.
  [10] A. G. Klein, C. Gerhard, R. D. Büchner, S. Diestel, and K. Schermelleh-Engel, “The detection of heteroscedasticity in regression models for psychological data model fit of nonlinear structural equation models view project,” Psychol. Test Assess. Model., vol. 58, no. 4, pp. 542–568, 2016, [Online]. Available: https://www.researchgate.net/publication/311518028

  Citation
  Muhammad Danish Munir, "Prediction of Heteroscedastic Data Using Linear Regression and Various Machine Learning Models," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.1, pp.14-19, 2023

• Open Access   Article

  Determination of Priority Structure through Fuzzy AHP-TOPSIS Approach in Agricultural Sector: A Comparative Study

  Apurwa Bharti, Babita Mishra

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.10 , Issue.1 , pp.20-26, Feb-2023

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  Abstract
  The real life situation of finding an optimal crop production under conflicting criteria is uncertain, imprecise, and vague which makes it necessary to introduce fuzziness. TOPSIS is a well-known technique that has enhanced the accuracy for prioritizing the alternatives. Here the author uses the multi-criteria decision-making (MCDM) technique that includes the fuzzy TOPSIS technique and analytic hierarchy process employing triangular fuzzy numbers. This paper demonstrates the application of fuzzy AHP-TOPSIS for finding the priority of crops and obtaining the weight of the different criteria in linguistic terms which in turn proves to be very easy and involves minimal calculation. At present, there are many methods to find the priorities but one major drawback of these methods were that the methods are tedious to do. This paper proposes to saturate the mathematical calculation as much as possible and at the same time achieve the desired priority for the optimal solution. The author used a technique that combines the fuzzy analytic hierarchy process with the fuzzy TOPSIS. The result of this study could also serve as a guide for decision-makers in the agricultural sector. Later we consider the work done by Pal and Biswas, Mishra, and Singh to verify and compare the ranking and claim that the ranking of crops is almost the same thereby same profit, but the calculation done was easy to understand and less time taking.

  Key-Words / Index Term
  MCDM, AHP-TOPSIS, Linguistic Variable, Weighted priority, Fuzzy goal programming

  References
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  Citation
  Apurwa Bharti, Babita Mishra, "Determination of Priority Structure through Fuzzy AHP-TOPSIS Approach in Agricultural Sector: A Comparative Study," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.1, pp.20-26, 2023