In engineering problems, many random variables have correlation, and the correlation of input random variables has a great influence on reliability analysis results of the mechanical systems. However, correlated variables are often treated as independent variables or modeled by specific parametric joint distributions due to difficulty in modeling joint distributions. Especially, when there are insufficient correlated data, it becomes more difficult to correctly model the joint distribution. In this study, multivariate kernel density estimation with bounded data is proposed to estimate various types of joint distributions with highly nonlinearity. Since it combines given data with bounded data, which are generated from confidence intervals of uniform distribution parameters for given data, it is less sensitive to data quality and number of data. Thus, it yields conservative statistical modeling and reliability analysis results, and its performance is verified through statistical simulation and engineering examples.

Abstract
 1. 서 론
 2. 결합확률분포함수의 추정 방법
  2.1 다변량 커널 밀도 추정(MKDE)
  2.2 경계데이터를 이용한 다변량 커널 밀도 추정(MKDE-ebd)
 3. 통계적 시뮬레이션
 4. 신뢰성 해석 예제
 5. 결 론
 References
 요 지

• 강영진(부산대학교 기계기술연구원) | Young-Jin Kang (Research Institute of Mechanical Technology, Pusan Nat’l Univ.)
• 노유정(부산대학교 기계공학부) | Yoojeong Noh (Research Institute of Mechanical Technology, Pusan Nat’l Univ.) Corresponding author
• 임오강(부산대학교 기계공학부) | O-Kaung Lim (School of Mechanical Engineering, Pusan Nat’l Univ)