System state monitoring and lifetime scales—II

The first part of this paper [Kordonsky, Kh. B. & Gertsbakh, I. B., System state monitoring and lifetime scales—I. Reliab. Engng & System Safety, 47 (1995) 1–14] was devoted to finding a time-scale for system state monitoring. The Best Monitoring Scale (BMS) was defined as a linear combination of several observable ‘principal’ time scales like the operational time, number of cycles, etc. These ‘principal’ time scales were chosen in such a way that they capture the significant dimensions of failure behaviour. In practice, the key issue is the estimation of the BMS. In the first part we suggested an estimation procedure when all observations (in two time-scales) are complete. This is rarely the case in real-life situations where most of observations are censored. The second part is devoted to finding the BMS on the basis of incomplete observations. We consider two types of data: observations up to a certain time or up to the first failure, and observations of a renewable system. We preserve the notation, abbreviations, and the terminology of part I of this paper.