Estimating the Long-Term Reliability of Steel and Cast Iron Pipelines Subject to Pitting Corrosion

Water-injection, oil production and water-supply pipelines are prone to pitting corrosion that may have a serious effect on their longer-term serviceability and sustainability. Typically, observed pit-depth data are handled for a reliability analysis using an extreme value distribution such as Gumbel. Available data do not always fit such monomodal probability distributions well, particularly in the most extreme pit-depth region, irrespective of the type of pipeline. Examples of this are presented, the reasons for this phenomenon are discussed and a rationale is presented for the otherwise entirely empirical use of the ‘domain of attraction’ in extreme value applications. This permits a more rational estimation of the probability of pipe-wall perforation, which is necessary for asset management and for system-sustainability decisions.

The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory

The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide class of distributions. This approach allows us to take into account important information about modeling the failure-free operation of equipment that has worked reliably for a long time. An analysis of the domain of attraction for popular distributions with “heavy tails” is given.

Change of the Most Probable Escape Path in a Fast-Slow Insect Outbreak System Under Different Noise Amplitude Ratios

In the present paper, noise-induced escape from the domain of attraction of a stable fixed point of a fast-slow insect outbreak system is investigated. According to Dannenberg's theory(Dannenberg PH, Neu JC, 2014)[1], different noise amplitude ratios μ lead to the change of the Most Probable Escape Path(MPEP). Therefore, the research emphasis of this paper is to extend their study and discuss the changes of the MPEPs in more detail. Firstly, the case for μ=1, wherein the MPEP almost traces out the critical manifold, is considered. Via projecting the full system onto the critical manifold, a reduced system is obtained and the quasi-potential of the full system can be partly evaluated by that of this reduced system. In order to test the accuracy of the computed MPEP, a new relaxation method is then presented. Then, as μ converges to zero, an improved analytical method is given, through which a better approximation for the MPEP at the turning point is obtained. And then, in the case that the value of μ is moderate, wherein the MPEP will peel off the critical manifold, to determine the changing point of the MPEP on the critical manifold, an effective numerical algorithm is given. In brief, in this paper, a complete investigation on the structural changes of the MPEPs of a fast-slow insect outbreak system under different values of μ is given, and the results of the numerical simulations match well with the analytical ones.

Nonparametric extrapolation of extreme quantiles: a comparison study

The extrapolation of quantiles beyond or below the largest or smallest observation plays an important role in hydrological practice, design of hydraulic structures, water resources management, or risk assessment. Traditionally, extreme quantiles are obtained using parametric methods that require to make an a priori assumption about the distribution that generated the data. This approach has several limitations mainly when applied to the tails of the distribution. Semiparametric or nonparametric methods, on the other hand, allow more flexibility and they may overcome the problems of the parametric approach. Therefore, we present here a comparison between three selected semi/nonparametric methods, namely the methods of Hutson (Stat and Comput, 12(4):331–338, 2002) and Scholz (Nonparametric tail extrapolation. Tech. Rep. ISSTECH-95-014, Boeing Information and Support Services, Seattle, WA, United States of America, 1995) and kernel density estimation. While the first and third methods have already applications in hydrology, Scholz (Nonparametric tail extrapolation. Tech. Rep. ISSTECH-95-014, Boeing Information and Support Services, Seattle, WA, United States of America, 1995) is proposed in this context for the first time. After describing the methods and their applications in hydrology, we compare their performance for different sample lengths and return periods. We use synthetic samples extracted from four distributions whose maxima belong to the Gumbel, Weibull, and Fréchet domain of attraction. Then, the same methods are applied to a real precipitation dataset and compared with a parametric approach. Eventually, a detailed discussion of the results is presented to guide researchers in the choice of the most suitable method. None of the three methods, in fact, outperforms the others; performances, instead, vary greatly with distribution type, return period, and sample size.