STATISTICAL AND INFORMATION-BASED (PHYSICAL) MINIMAL REPAIR FOR K OUTOF N SYSTEMS

The 'minimal' repair of a system can take several forms. Statistical o r black box minimal repair at failure time t is equivalent to replacin g the system with another functioning one of the same age, but without knowledge of precisely what went wrong with the system. Its major att ribute is its mathematical tractability. In physical minimal repair at system failure time t, we minimally repair the 'component' which brou ght the system down at time t. The work of Arjas and Nones, Finkelstei n, and Natvig is reviewed. The concept of a rate function for minimal repairs of the statistical and physical types are discussed and develo ped. It is shown that the number of physical minimal repairs is stocha stically larger than the number of statistical minimal repairs for k o ut of n systems with similar components. Some majorization results are given for physical minimal repair for two component parallel systems with exponential components.