Distribution of residual system-life after partial failures

A general method is presented for determining the distribution of residual system life (RSL) of a coherent system after some partial failures. The RSL begins once all the system components of at least one member of the well-defined set of residual life sets have failed. The approach is based on the knowledge of a special distribution of component lives and system life. It is general with respect to statistical dependence of system component states, unless cold standby is included. It can be applied to any coherent system and can be useful for solving problems of safety forecasts for nuclear power plants, chemical systems, and other systems that could be dangerous environmentally. A computer program has been written that permits practical application of the method. The process of determining the distribution of the RSL is generally useful for theoreticians. Analytic and numerical examples of the method are included.