Range reliability in random walks

Pierre Vallois, Charles S. Tapiero

Research output: Contribution to journalArticlepeer-review


This paper introduces a definition of reliability based on a process range. Thus, process failure is defined when the range of a process first reaches a given and unacceptable level. The Mean Time To Failure (MTTF) which is defined as the mean of the first time for a range to attain a given amplitude is then calculated for an asymmetric random walk process. The probability distribution of the range is then given and the process reliability over long periods of system operations are then calculated. Applications such as the control of wings movements, stock price and exchange rates volatility (defined in terms of reliability) are also used to motivate the usefulness of range processes in reliability studies. Finally, we point out that there is necessarily a relationship between the range reliability and the propensity of a series to become chaotic.

Original languageEnglish (US)
Pages (from-to)325-345
Number of pages21
JournalMathematical Methods of Operations Research
Issue number3
StatePublished - 1997


  • Amplitude Process
  • Reliability
  • Stochastic Processes

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Management Science and Operations Research


Dive into the research topics of 'Range reliability in random walks'. Together they form a unique fingerprint.

Cite this