Estimation of $rm P[Y≪X]$ for Weibull Distributions

Debasis Kundu; R. D. Gupta

doi:10.1109/tr.2006.874918

June 1, 2006IEEE Transactions on Reliability

Estimation of $rm P[Y≪X]$ for Weibull Distributions

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Key Points

To develop and evaluate statistical estimators for the stress-strength reliability parameter R = P[Y < X] when stress and strength follow Weibull distributions.
Formulated mathematical frameworks for calculating the probability that component strength (X) exceeds applied stress (Y) under independent Weibull distribution models.
Derived point estimation procedures, such as maximum likelihood and Bayesian estimators, to evaluate the reliability parameter across varying sample sizes and shape parameters.
Established analytical formulations for the stress-strength parameter R under shared and differing Weibull shape parameters.
Demonstrated consistent estimator behavior across varying stress-strength scenarios, enabling quantification of failure probabilities under mechanical loads.

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Implication

Statistical modeling analysis develops estimation methods for stress-strength probability in Weibull-distributed components, indicating improved reliability assessments for engineering systems.

Abstract

This paper deals with the estimation of R=P[Y

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Kundu et al. (2006) studied this question.

synapsesocial.com/papers/6a88fb1b523ac130647b3adb https://doi.org/10.1109/tr.2006.874918

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Estimation of $rm P[Y≪X]$ for Weibull Distributions

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Estimation of $rm P[Y≪X]$ for Weibull Distributions

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