Towards the Formal Reliability Analysis of Oil and Gas Pipelines

It is customary to assess the reliability of underground oil and gas pipelines in the presence of excessive loading and corrosion effects to ensure a leak-free transport of hazardous materials. The main idea behind this reliability analysis is to model the given pipeline system as a Reliability Block Diagram (RBD) of segments such that the reliability of an individual pipeline segment can be represented by a random variable. Traditionally, computer simulation is used to perform this reliability analysis but it provides approximate results and requires an enormous amount of CPU time for attaining reasonable estimates. Due to its approximate nature, simulation is not very suitable for analyzing safety-critical systems like oil and gas pipelines, where even minor analysis flaws may result in catastrophic consequences. As an accurate alternative, we propose to use a higher-order-logic theorem prover (HOL) for the reliability analysis of pipelines. As a first step towards this idea, this paper provides a higher-order-logic formalization of reliability and the series RBD using the HOL theorem prover. For illustration, we present the formal analysis of a simple pipeline that can be modeled as a series RBD of segments with exponentially distributed failure times.Comment: 15 page

Asymptotic behavior of mixture failure rates

Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually this property is observed asymptotically as time tends to infinity , which is due to the fact that a mixture failure rate is ‘bent down’, as the weakest populations are dying out first. We consider a survival model, generalizing a very well known in reliability and survival analysis additive hazards, proportional hazards and accelerated life models. We obtain new explicit asymptotic relations for a general setting and study specific cases. Under reasonable assumptions we prove that asymptotic behavior of the mixture failure rate depends only on the behavior of the mixing distri-bution in the neighborhood of the left end point of its support and not on the whole mixing distribution.

Software timing analysis for complex hardware with survivability and risk analysis

The increasing automation of safety-critical real-time systems, such as those in cars and planes, leads, to more complex and performance-demanding on-board software and the subsequent adoption of multicores and accelerators. This causes software's execution time dispersion to increase due to variable-latency resources such as caches, NoCs, advanced memory controllers and the like. Statistical analysis has been proposed to model the Worst-Case Execution Time (WCET) of software running such complex systems by providing reliable probabilistic WCET (pWCET) estimates. However, statistical models used so far, which are based on risk analysis, are overly pessimistic by construction. In this paper we prove that statistical survivability and risk analyses are equivalent in terms of tail analysis and, building upon survivability analysis theory, we show that Weibull tail models can be used to estimate pWCET distributions reliably and tightly. In particular, our methodology proves the correctness-by-construction of the approach, and our evaluation provides evidence about the tightness of the pWCET estimates obtained, which allow decreasing them reliably by 40% for a railway case study w.r.t. state-of-the-art exponential tails.This work is a collaboration between Argonne National Laboratory and the Barcelona Supercomputing Center within the Joint Laboratory for Extreme-Scale Computing. This research is supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under contract number DE-AC02- 06CH11357, program manager Laura Biven, and by the Spanish Government (SEV2015-0493), by the Spanish Ministry of Science and Innovation (contract TIN2015-65316-P), by Generalitat de Catalunya (contract 2014-SGR-1051).Peer ReviewedPostprint (author's final draft

Redundancy and Aging of Efficient Multidimensional MDS-Parity Protected Distributed Storage Systems

The effect of redundancy on the aging of an efficient Maximum Distance Separable (MDS) parity--protected distributed storage system that consists of multidimensional arrays of storage units is explored. In light of the experimental evidences and survey data, this paper develops generalized expressions for the reliability of array storage systems based on more realistic time to failure distributions such as Weibull. For instance, a distributed disk array system is considered in which the array components are disseminated across the network and are subject to independent failure rates. Based on such, generalized closed form hazard rate expressions are derived. These expressions are extended to estimate the asymptotical reliability behavior of large scale storage networks equipped with MDS parity-based protection. Unlike previous studies, a generic hazard rate function is assumed, a generic MDS code for parity generation is used, and an evaluation of the implications of adjustable redundancy level for an efficient distributed storage system is presented. Results of this study are applicable to any erasure correction code as long as it is accompanied with a suitable structure and an appropriate encoding/decoding algorithm such that the MDS property is maintained.Comment: 11 pages, 6 figures, Accepted for publication in IEEE Transactions on Device and Materials Reliability (TDMR), Nov. 201