### Abstract

It is commonplace to replicate critical components in order to increase system lifetimes and reduce failure rates. The case of a general N-plexed system, whose failures are modeled as N identical, independent nonhomogeneous Poisson process (NHPP) flows, each with rocof (rate of occurrence of failure) equal to λ(t), is considered here. Such situations may arise if either there is a time-dependent factor accelerating failures or if minimal repair maintenance is appropriate. We further assume that system logic for the redundant block is 2-out-of-N:G. Reliability measures are obtained as functions of τ which represents a fixed time after which Maintenance Teams must have replaced any failed component. Such measures are determined for small λ(t)τ, which is the parameter range of most interest. The triplex version, which often occurs in practice, is treated in some detail where the system reliability is determined from the solution of a first order differential-delay equation (DDE). This is solved exactly in the case of constant λ(t), but must be solved numerically in general. A general means of numerical solution for the triplex system is given, and an example case is solved for a rocof resembling a bathtub curve.

Language | English |
---|---|

Article number | 1250003 |

Journal | International Journal of Reliability, Quality and Safety Engineering |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 2012 |

Externally published | Yes |

### Fingerprint

### Cite this

*International Journal of Reliability, Quality and Safety Engineering*,

*19*(1), [1250003]. https://doi.org/10.1142/S0218539312500039

}

*International Journal of Reliability, Quality and Safety Engineering*, vol. 19, no. 1, 1250003. https://doi.org/10.1142/S0218539312500039

**Reliability of 2-out-of-N:G systems with NHPP failure flows and fixed repair times.** / Dwyer, Vincent M.; Goodall, Roger M.; Dixon, Roger.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Reliability of 2-out-of-N:G systems with NHPP failure flows and fixed repair times

AU - Dwyer, Vincent M.

AU - Goodall, Roger M.

AU - Dixon, Roger

PY - 2012/2

Y1 - 2012/2

N2 - It is commonplace to replicate critical components in order to increase system lifetimes and reduce failure rates. The case of a general N-plexed system, whose failures are modeled as N identical, independent nonhomogeneous Poisson process (NHPP) flows, each with rocof (rate of occurrence of failure) equal to λ(t), is considered here. Such situations may arise if either there is a time-dependent factor accelerating failures or if minimal repair maintenance is appropriate. We further assume that system logic for the redundant block is 2-out-of-N:G. Reliability measures are obtained as functions of τ which represents a fixed time after which Maintenance Teams must have replaced any failed component. Such measures are determined for small λ(t)τ, which is the parameter range of most interest. The triplex version, which often occurs in practice, is treated in some detail where the system reliability is determined from the solution of a first order differential-delay equation (DDE). This is solved exactly in the case of constant λ(t), but must be solved numerically in general. A general means of numerical solution for the triplex system is given, and an example case is solved for a rocof resembling a bathtub curve.

AB - It is commonplace to replicate critical components in order to increase system lifetimes and reduce failure rates. The case of a general N-plexed system, whose failures are modeled as N identical, independent nonhomogeneous Poisson process (NHPP) flows, each with rocof (rate of occurrence of failure) equal to λ(t), is considered here. Such situations may arise if either there is a time-dependent factor accelerating failures or if minimal repair maintenance is appropriate. We further assume that system logic for the redundant block is 2-out-of-N:G. Reliability measures are obtained as functions of τ which represents a fixed time after which Maintenance Teams must have replaced any failed component. Such measures are determined for small λ(t)τ, which is the parameter range of most interest. The triplex version, which often occurs in practice, is treated in some detail where the system reliability is determined from the solution of a first order differential-delay equation (DDE). This is solved exactly in the case of constant λ(t), but must be solved numerically in general. A general means of numerical solution for the triplex system is given, and an example case is solved for a rocof resembling a bathtub curve.

KW - 2-out-of-N:G

KW - Minimal repair

KW - NHPP

KW - TMR

UR - http://www.scopus.com/inward/record.url?scp=84867000160&partnerID=8YFLogxK

U2 - 10.1142/S0218539312500039

DO - 10.1142/S0218539312500039

M3 - Article

VL - 19

JO - International Journal of Reliability, Quality and Safety Engineering

T2 - International Journal of Reliability, Quality and Safety Engineering

JF - International Journal of Reliability, Quality and Safety Engineering

SN - 0218-5393

IS - 1

M1 - 1250003

ER -