### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 325-345 |

Number of pages | 21 |

Journal | Mathematical Methods of Operations Research |

Volume | 45 |

Issue number | 3 |

State | Published - 1997 |

### Fingerprint

### Keywords

- Amplitude Process
- Reliability
- Stochastic Processes

### ASJC Scopus subject areas

- Management Science and Operations Research
- Applied Mathematics

### Cite this

*Mathematical Methods of Operations Research*,

*45*(3), 325-345.

**Range reliability in random walks.** / Vallois, Pierre; Tapiero, Charles.

Research output: Contribution to journal › Article

*Mathematical Methods of Operations Research*, vol. 45, no. 3, pp. 325-345.

}

TY - JOUR

T1 - Range reliability in random walks

AU - Vallois, Pierre

AU - Tapiero, Charles

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

KW - Amplitude Process

KW - Reliability

KW - Stochastic Processes

UR - http://www.scopus.com/inward/record.url?scp=0030713248&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030713248&partnerID=8YFLogxK

M3 - Article

VL - 45

SP - 325

EP - 345

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

SN - 1432-2994

IS - 3

ER -