Estimation of the reliability system in model of stress- strength according to distribution of inverse Rayleigh

Kalaf, Bayda Atiya; Raheem, Sairan Hamza; Salman, Abbas Najim

doi:10.21533/pen.v9i2.1811

Cited by 4 publications

(4 citation statements)

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“…We assume a system having 𝐾 𝑡ℎ components with strengths 𝑋 1 , 𝑋 2 , … , 𝑋 𝑘 independently distributed Inverse Kumaraswamy random variables with unknown shape parameter 𝛽 𝑖 , 𝑖= 1,2, … , 𝑘 and known other shape parameter 𝛼 subjected to stress random variable 𝑌 such that 𝑌~𝐼𝐾𝑢𝑚𝐷(𝛼, 𝛽 𝑘+1 ) with unknown shape parameter 𝛽 𝑘+1 and known 𝛼. The formula of Parallel S-S model can be derived as fellows [14][15][16]:…”

Section: Reliability System Of Parallel S-s Modelmentioning

confidence: 99%

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Estimation of a Parallel Stress-strength Model Based on the Inverse Kumaraswamy Distribution

Kalaf

Hameed²,

Salman

et al. 2023

IHJPAS

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The reliability of the stress-strength model attracted many statisticians for several years owing to its applicability in different and diverse parts such as engineering, quality control, and economics. In this paper, the system reliability estimation in the stress-strength model containing Kth parallel components will be offered by four types of shrinkage methods: constant Shrinkage Estimation Method, Shrinkage Function Estimator, Modified Thompson Type Shrinkage Estimator, Squared Shrinkage Estimator. The Monte Carlo simulation study is compared among proposed estimators using the mean squared error. The result analyses of the shrinkage estimation methods showed that the shrinkage functions estimator was the best since it has a minor mean squared error than the other methods followed by the additional shrinkage estimator. The stress and strength belong to the In verse Kumaraswamy distribution

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Section: Reliability System Of Parallel S-s Modelmentioning

confidence: 99%

“…When substituting the equation (15) in equation ( 5), the reliability system for estimating of R using the modified Thompson type shrinkage estimator become:…”

Section: Modified Thompson Type Shrinkage Estimator (Th)mentioning

confidence: 99%

Estimation of a Parallel Stress-strength Model Based on the Inverse Kumaraswamy Distribution

Kalaf

Hameed²,

Salman

et al. 2023

IHJPAS

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“…In this context, the statistical implications were calculated to compare the performance of the offered estimators. Following is how a Monte Carlo simulation was employed in this situation; [6,16,17].…”

Section: Monte Carlo Simulation Techniquementioning

confidence: 99%

Comparison Various Estimation Methods for R = P (Y1 < X < Y2) Utilizing Restricted Generalized Weibull Distribution

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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The stress-strength S-S method employs a variety of estimation techniques, including maximum likelihood, shrinkage and least square, to determine and estimate the reliability of a particular system R = P (Y 1 < X < Y 2 ) while the system contains a single component with strength X subject to two stresses, Y 1 and Y 2 . With the consumption of Monte Carlo simulation and the statistical measurement Mean Squared Error (MSE), the various estimation methods have been evaluated according to the Restricted Generalized Weibull Distribution (RGWD), the stresses Y 1 and Y 2 and the strength X constitute independent, non-identical random variables in our S-S model.

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“…In addition, it happens when we are unable to detect or record events that take place inside or outside of a predetermined range or below or above a given threshold. The truncation can be from the left side, the right side, or both sides [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Truncated Inverse Generalized Rayleigh Distribution and Some Properties

Kalaf,

Abdul Ameer Jabar,

Madaki

2023

IHJPAS

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Truncated distributions arise naturally in many practical situations. It’s a conditional distribution that develops when the parent distribution's domain is constrained to a smaller area. The distribution of a right truncated is one of the types of a single truncated that is restricted within a specific field and usually occurs when the specified period for the study is complete. Hence, this paper introduces Right Truncated Inverse Generalized Rayleigh Distribution (RTIGRD) with two parameters is introduced. Then, provided some properties such as; (probability density function, cumulative distribution function (CDF), survival function, hazard function, ‎rth moment, mean, variance, Moment Generating Function, Skewness, kurtosis, Median, and Mode for Right Truncated Inverse Generalized Rayleigh Distribution on [0,1].

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Estimation of the reliability system in model of stress- strength according to distribution of inverse Rayleigh

Cited by 4 publications

References 0 publications

Estimation of a Parallel Stress-strength Model Based on the Inverse Kumaraswamy Distribution

Estimation of a Parallel Stress-strength Model Based on the Inverse Kumaraswamy Distribution

Comparison Various Estimation Methods for R = P (Y1 < X < Y2) Utilizing Restricted Generalized Weibull Distribution

Truncated Inverse Generalized Rayleigh Distribution and Some Properties

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