Trivariant Lagrange Factor Polynomial for Discrete Rayleigh Distributed Reliability Analysis of Aeroengine Combustion Chamber Cylinder

In most of the existing stress-strength interference (SSI) models, stress and strength are assumed to be independent structural variants. However, under severe thermal conditions, such as in aeroengine combustion chamber, this assumption may not hold. One structural variant, such as strength, may become unilateral dependent on another variant, such as stress or temperature. In addition, to evaluate the discrete reliability of structures using unilateral dependent structural variants, discrete SSI models were developed using not just linear polynomial or line segments, but higher order polynomials. These models are based on the trivariant Lagrange factor polynomial approach. Normal distributed temperature dependent stress and Rayleigh distributed thermal stress dependent strength are represented by discrete structural variants that possess unilateral dependent probability mean functions. Based on their dependence formulations, the trivariant Lagrange factor polynomial of the discrete SSI model was generated. Applicability of this method was validated by a specific aeroengine combustion chamber cylinder using different molding alloys. Meanwhile the application range of some existing SSI models is extended for interval shifted data. Comparing machinability, reliability, and economic factors, 1Cr11MoV was the most suitable alloy in the design.