Jaya algorithm in estimation of P[X &gt; Y] for two parameter Weibull distribution

Saurabh L. Raikar; Dr. Rajesh S. Prabhu Gaonkar; Saurabh L. Raikar; Dr. Rajesh S. Prabhu Gaonkar

doi:10.3934/math.2022156

AIMS Mathematics

2022, Volume 7, Issue 2: 2820-2839. doi: 10.3934/math.2022156

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Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution

Saurabh L. Raikar ^{1
,
,},
Dr. Rajesh S. Prabhu Gaonkar ²

1.
Mechanical Engineering Department, Goa College of Engineering (affiliated to Goa University), Farmagudi, Ponda, Goa 403401, India
2.
Indian Institute of Technology Goa (IIT Goa), Farmagudi, Ponda, Goa 403401, India

Received: 15 September 2021 Accepted: 04 November 2021 Published: 19 November 2021
MSC : 62F10, 37N40

Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.
- reliability,
- Weibull distribution,
- parameter estimation,
- optimization,
- Jaya algorithm
Citation: Saurabh L. Raikar, Dr. Rajesh S. Prabhu Gaonkar. Jaya algorithm in estimation of P[X > Y] for two parameter Weibull distribution[J]. AIMS Mathematics, 2022, 7(2): 2820-2839. doi: 10.3934/math.2022156

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Abstract

Jaya algorithm is a highly effective recent metaheuristic technique. This article presents a simple, precise, and faster method to estimate stress strength reliability for a two-parameter, Weibull distribution with common scale parameters but different shape parameters. The three most widely used estimation methods, namely the maximum likelihood estimation, least squares, and weighted least squares have been used, and their comparative analysis in estimating reliability has been presented. The simulation studies are carried out with different parameters and sample sizes to validate the proposed methodology. The technique is also applied to real-life data to demonstrate its implementation. The results show that the proposed methodology's reliability estimates are close to the actual values and proceeds closer as the sample size increases for all estimation methods. Jaya algorithm with maximum likelihood estimation outperforms the other methods regarding the bias and mean squared error.

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