Reliability Analysis for Multi-Component Systems Subject to Multiple Dependent Competing Failure Processes

Abstract

For complex multi-component systems with each component experiencing multiple failure processes due to simultaneous exposure to degradation and shock loads, we developed a new multi-component system reliability model, and applied two different preventive maintenance policies. This new model extends previous research, and is different from related previous research by considering an assembled system of degrading components with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$s$</tex></formula> -dependent failure times resulting from shared shock exposure. Previous research primarily pertained to a single component or simple system, or systems with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$s$</tex></formula> -independent failure processes and failure times. In our new system model, the individual failure processes for each component and the component failure processes are all <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$s$</tex></formula> -dependent. These models can be applied directly, or customized for many complex systems with multiple components that experience <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$s$</tex> </formula> -dependent competing failure processes. In this model, each component can fail due to a soft failure process, or a hard failure process. These two component failure processes are mutually competing and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$s$</tex></formula> -dependent. If one component fails relatively frequently, it is likely that the number of shocks is relatively large, and these shocks impact all components potentially causing them to fail more often as well. Therefore, failure processes of all components are also <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$s$</tex></formula> -dependent. An age replacement policy and an inspection-based maintenance policy are applied for a system with multiple components. The optimal replacement interval or inspection times are determined by minimizing a cost rate function. The model is demonstrated on several examples.