### Abstract

A new three-parameter probability distribution called the omega probability distribution is introduced, and its connection with the Weibull distribution is discussed. We show that the asymptotic omega distribution is just the Weibull distribution and point out that the mathematical properties of the novel distribution allow us to model bathtub-shaped hazard functions in two ways. On the one hand, we demonstrate that the curve of the omega hazard function with special parameter settings is bathtub shaped and so it can be utilized to describe a complete bathtub-shaped hazard curve. On the other hand, the omega probability distribution can be applied in the same way as the Weibull probability distribution to model each phase of a bathtub-shaped hazard function. Here, we also propose two approaches for practical statistical estimation of distribution parameters. From a practical perspective, there are two notable properties of the novel distribution, namely, its simplicity and flexibility. Also, both the cumulative distribution function and the hazard function are composed of power functions, which on the basis of the results from analyses of real failure data, can be applied quite effectively in modeling bathtub-shaped hazard curves.

Original language | English |
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Journal | Quality and Reliability Engineering International |

DOIs | |

Publication status | Accepted/In press - Jan 1 2018 |

### Fingerprint

### Keywords

- hazard function modeling
- omega distribution
- reliability analysis
- Weibull distribution

### ASJC Scopus subject areas

- Safety, Risk, Reliability and Quality
- Management Science and Operations Research

### Cite this

*Quality and Reliability Engineering International*. https://doi.org/10.1002/qre.2425

**The omega probability distribution and its applications in reliability theory.** / Dombi, József; Jónás, Tamás; Tóth, Z.; Árva, Gábor.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The omega probability distribution and its applications in reliability theory

AU - Dombi, József

AU - Jónás, Tamás

AU - Tóth, Z.

AU - Árva, Gábor

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A new three-parameter probability distribution called the omega probability distribution is introduced, and its connection with the Weibull distribution is discussed. We show that the asymptotic omega distribution is just the Weibull distribution and point out that the mathematical properties of the novel distribution allow us to model bathtub-shaped hazard functions in two ways. On the one hand, we demonstrate that the curve of the omega hazard function with special parameter settings is bathtub shaped and so it can be utilized to describe a complete bathtub-shaped hazard curve. On the other hand, the omega probability distribution can be applied in the same way as the Weibull probability distribution to model each phase of a bathtub-shaped hazard function. Here, we also propose two approaches for practical statistical estimation of distribution parameters. From a practical perspective, there are two notable properties of the novel distribution, namely, its simplicity and flexibility. Also, both the cumulative distribution function and the hazard function are composed of power functions, which on the basis of the results from analyses of real failure data, can be applied quite effectively in modeling bathtub-shaped hazard curves.

AB - A new three-parameter probability distribution called the omega probability distribution is introduced, and its connection with the Weibull distribution is discussed. We show that the asymptotic omega distribution is just the Weibull distribution and point out that the mathematical properties of the novel distribution allow us to model bathtub-shaped hazard functions in two ways. On the one hand, we demonstrate that the curve of the omega hazard function with special parameter settings is bathtub shaped and so it can be utilized to describe a complete bathtub-shaped hazard curve. On the other hand, the omega probability distribution can be applied in the same way as the Weibull probability distribution to model each phase of a bathtub-shaped hazard function. Here, we also propose two approaches for practical statistical estimation of distribution parameters. From a practical perspective, there are two notable properties of the novel distribution, namely, its simplicity and flexibility. Also, both the cumulative distribution function and the hazard function are composed of power functions, which on the basis of the results from analyses of real failure data, can be applied quite effectively in modeling bathtub-shaped hazard curves.

KW - hazard function modeling

KW - omega distribution

KW - reliability analysis

KW - Weibull distribution

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U2 - 10.1002/qre.2425

DO - 10.1002/qre.2425

M3 - Article

JO - Quality and Reliability Engineering International

JF - Quality and Reliability Engineering International

SN - 0748-8017

ER -