On the joint distribution of component failures for monotone load-sharing systems

In load-sharing systems, dependencies between components are introduced through load-sharing considerations. Components either fail as the system undergoes increasing load (a phase I type of failure) or instantaneously due to load transfer from components that have just failed (a phase II type of failure). The essence of the main result is that, given the breaking pattern, the joint distribution of the breaking strengths of the phase I type of failures under monotone load-sharing is the same as a conditional distribution of ordered independent gamma-type scale mixed random variables when the component strengths are independent with a Weibull distribution. The shape parameter in the gamma is the number of phase II failures caused by the phase I failure due to load transfer. (C) 1999 Elsevier Science B.V. All rights reserved.