TY - JOUR

T1 - Kernel-based estimation of P(X < Y) when X and Y are dependent random variables based on progressive type II censoring

AU - Musleh, Rola

AU - Helu, Amal

AU - Samawi, Hani

N1 - Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.

PY - 2020/6/12

Y1 - 2020/6/12

N2 - The most widely used approach for reliability estimation is the well-known stress-strength model, θ = P(X < Y), where X and Y are random variables. In this model, the reliability, θ, of the system is the probability that the system is strong enough to overcome the stress imposed on it. In most cases, X and Y are assumed to be independent. Nevertheless, in reality, the strength variable Y could be highly dependent on the stress variable X. In this paper, we discuss the kernel-based estimation of θ when X and Y are dependent random variables under progressive type II censored sample. The asymptotic properties of the kernel-based estimators of θ based on progressive type II censoring are proposed. An extensive computer simulation is conducted to gain insight into the performance of the proposed estimators. A real data example is provided to illustrate the process.

AB - The most widely used approach for reliability estimation is the well-known stress-strength model, θ = P(X < Y), where X and Y are random variables. In this model, the reliability, θ, of the system is the probability that the system is strong enough to overcome the stress imposed on it. In most cases, X and Y are assumed to be independent. Nevertheless, in reality, the strength variable Y could be highly dependent on the stress variable X. In this paper, we discuss the kernel-based estimation of θ when X and Y are dependent random variables under progressive type II censored sample. The asymptotic properties of the kernel-based estimators of θ based on progressive type II censoring are proposed. An extensive computer simulation is conducted to gain insight into the performance of the proposed estimators. A real data example is provided to illustrate the process.

KW - Dependence

KW - estimation

KW - kernel

KW - progressive type II censoring

KW - stress-strength model

UR - https://digitalcommons.georgiasouthern.edu/bee-facpubs/299

UR - https://doi.org/10.1080/03610926.2020.1774058

U2 - 10.1080/03610926.2020.1774058

DO - 10.1080/03610926.2020.1774058

M3 - Article

JO - Communication in Statistics: Theory and Methods

JF - Communication in Statistics: Theory and Methods

ER -