A study on a stochastic process with state classifications based on sojourn times. Issue 2 (3rd April 2017)

• Record Type: Journal Article
• Authors: Zhang, Quan; Cui, Lirong; Kong, Dejing
• Is Part Of: Quality technology & quantitative management. Volume 14:Issue 2(2017)
• Page Start: 214
• Page End: 236
• Publication Date: 2017-04-03
• Subjects: Sojourn time -- alternative renewal process -- point state probability -- interval state probability -- renewal equation -- convolution; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2016.1208493
• Languages: English
• ISSNs: 1684-3703

Abstract

Abstract: The indexes for measuring the performances of systems, availability, reliability and others are important issues in the system design and analysis. Although there are many indices being used, they still cannot meet the various requirements in both theory and practice, so the study on these indices is a significant task. In this paper, we develop some new useful indexes classified into two categories, by introducing a stochastic process in terms of two threshold values on sojourn time. The two-category indices are named as point state and interval state probability measures, respectively. The corresponding computation formulae including some special cases are presented. These introduced indices can be used to describe the degrees of stable, semi-stable and unstable for the operation system. We also believe that the indices can be used in reliability engineering, survival analysis, actuarial study, financial analysis, economy and others, and this work definitely enriches the contents of theory of stochastic processes.