Probability of Loss Assessment of Critical $k$-Out-of-$n$:G Systems Having a Mission Abort Policy

Abstract

The survival of an aircraft is dependent on continuous operation of its flight critical systems until it has safely landed. Such a system may utilize a mission abort policy, requiring termination of typical mission operations, and entering a recovery phase in the event of certain failures. If, subsequent to such a mission abort fault, the system is able to safely complete the recovery phase, it will have survived, but may have failed to complete its mission objectives. This type of system is of interest when 1) the system's survival is dependent on its unattended operational capability; 2) there exist circumstances under which system survival has a greater priority than completing a mission of defined length; or 3) a mission abort policy can be established which results in entering a recovery phase requiring less time than completing the mission. Computing the probability of mission survival for systems using a mission abort policy is not a classical reliability problem, generally defined as the probability of performing its intended mission for a specified period of time, because the assessment does not, in general, involve a mission of a specific period of time. The period of time of interest will be either the specified mission time, or the sum of the time prior to a mission abort plus the time required to complete a recovery phase. This paper addresses determining the probability of survival for redundant systems utilizing a mission abort policy. Systems having both perfect, and imperfect fault coverage are addressed; and numerical, and exact algebraic results are provided for i.i.d. <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -out-of- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> :G systems.