On some properties of shock processes in a ‘natural’ scale

• Published in: Reliability engineering & system safety Vol. 145; pp. 104 - 110
• Main Authors: Cha, Ji Hwan, Finkelstein, Maxim
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2016
• Subjects: Delay; Discrete distribution; Mathematical analysis; Number theory; Poisson process; Reliability engineering; Renewal process; Scale (ratio); Shock process; Shot-noise process; Signature; Signatures; Survival; Time; Shot-noise process; Shock process; Poisson process; Discrete distribution; Renewal process; Signature
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2015.09.009

We consider shocks modeling in a ‘natural’ scale which is a discrete scale of natural numbers. A system is subject to the shock process and its survival probability and other relevant characteristics are studied in this scale. It turns out that all relations for the probabilities of interest become much easier in the new scale as compared with the conventional chronological time scale. Furthermore, it does not matter what type of the point process of shocks is considered. The shock processes with delays and the analog of a shot-noise process are discussed. Another example of the application of this concept is presented for systems with finite number of components described by signatures. •A novel approach to systems subject to shock processes is suggested.•Alternative to chronological time, the discrete time scale of natural numbers is considered.•Shock processes with delays and a shot-noise process are discussed in the new alternative scale.•As an application, n-component systems with structures described by signatures is suggested.