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3 Journal of Polish Safety and Reliability Association

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Lifetime distributions with wave-like bathtub hazard

Guo R., Thiart C., Cui Y., Guo D.

Journal of Polish Safety and Reliability Association

2011

Vol. 2, No. 1

115--122

In this paper, we argue the necessity of dealing with lifetime distributions with wave-like bathtub hazard function. Four classes of wave-like bathtub hazards are investigated. For preparing maximum likelihood estimation of the hazard parameters, the first-order and second-order partial derivatives are derived.

Reliability concept under general uncertainty

Guo R., Cui Y., Thiart C., Guo D.

Journal of Polish Safety and Reliability Association

2010

Vol. 1, No. 1

105--114

The Toyota crisis is tearing off the brand image of quality and reliability and therefore it is logical to question whether the dominating position of probability theory, on which Japanese quality and reliability engineering practices are established, should be examined. In general, reliability analysis is an exercise under uncertain environment. Foundationally speaking, uncertain modeling is a matter of choosing what kind of uncertain measure as its standing point. In this paper, we introduce the uncertainty reliability concept on the platform of the axiomatic uncertain measure theory and compare it to probabilistic reliability concept based on Kolmogorov’s probability measure theory, on which the traditional quality and reliability engineering is established. It is expecting that a foundational work can be established for a more rigorous reliability engineering and risk analysis under general uncertainty environments.

Hybrid reliability modelling under general uncertainty

Guo R., Cui Y., Thiart C., Guo D.

Journal of Polish Safety and Reliability Association

2010

Vol. 1, No. 1

115--122

The real world phenomena are often facing the co-existence reality of different formality of uncertainty and thus the probabilistic reliability modeling practices are very doubtful. Under complicated uncertainty environments, hybrid variable modeling is important in reliability and risk analysis, which includes Bayesian distributional theory, random fuzzy distributional theory, as well as fuzzy random distributional theory as special distribution families. In this paper, we define a new hybrid lifetime which is specified by a random lifetime distribution with an uncertain distributed parameter, which is called as random uncertain hybrid lifetime. We furthermore define the average chance distribution as a quality index for quantifying the hybrid lifetime and accordingly the average chance reliability is derived.