A simple model with applications in structural reliability, extinction of species, inventory depletion and urn sampling

This paper is devoted to a model which has applications in the study of reliability, extinction of species, inventory depletion, and urn sampling, among others. A series–parallel system consists of (k + 1) subsystems C0, C1, · · ·, Ck, also called cut sets. Cut set Ci contains ni components arranged in parallel, i = 0, 1, · · ·, k. No two cut sets have a component in common. It is assumed that after t components have failed, each of the remaining components is equally likely to fail, t = 0, 1, · · ·. It is also assumed that the components fail one at a time. In Part 1 of this paper we study the probability that the system fails because a specified cut set C0, say, fails first. We obtain several alternative expressions and recurrence relations for this probability. Some of these formulae are useful for computation, while others permit us to derive qualitative features such as monotonicity, Schur-concavity, asymptotic limits, etc. These results are extended to cover the case in which some cut set first drops to level a, where a is a specified positive integer. In Part 2, we compute the probability distribution, frequency function, and failure rate of the lifelengths of series–parallel systems. We also obtain corresponding recurrence relations and finite and asymptotic properties.

This paper is devoted to the study of che following tsodel:A series-parallel system consists of (k + 1) subsystem C0C1 ,…,Ck, , also called cut sets. Cut sec C1 has ni. com­ponents arranged in parallel, i = 0,1,…,k. Jo two cut sets have a component in comeon. This model was introduced and studied by El-Heweihi, Proschan, and Sethuraiaan (1978) under the assumption that component lifelengths are continuous, indepdent, and identically distributed random variables. They obtained several equivalent expressions for the probability that a specified cut set C0, say, fails first. These expressions aere then used to derive qualitative properties of this probability, such as monotonicity, Schur-concavity, etc. In this paper we obtain extensions of these results, tinder -he same assumptions ve study the probability that a. specified cut set C0say, fails in the rth place, r = l,2,…,k. This probability Is shown to retain most of the interesting qualitative features enjoyed in the special case r = 1. We then assure* that component lifelengths are identically distributed within a cut set, but allow then to vary a=ong cut sets. Under this more general assumption we derive expressions for and obtain properties of the probability that Co fails in the rth place This generalization of the model of El-Heveihi, Proschan, and Sethuranan (1978), also has applications in the study of reliabilityextinction of species, inventory depletion, urn sampling, among others.

A new sampling strategy is proposed to improve the robustness and efficiency of the Kriging-based response surface method. In the initial stage, the number-theoretic method is utilized to generate deterministic initial design samples, which are further optimized by an interpolation method. In the sequential iterative process, a new sampling criterion called reliability infill sampling criterion is proposed. Besides, a more reasonable two-process strategy is suggested where the iterative process is divided into two sub-processes using different sampling criteria. The proposed method ensures that the approximation can be accurately and efficiently fitted near the limit state. The numerical examples and the applications in structural reliability indicate the improved accuracy and efficiency of the proposed method.

Strategic defense and attack for reliability systems

An efficient numerical solution to the multinormal integral

A key challenge in cognitive radio networks is the unreliability of cognitive radio links due to the interruptions from primary users. To enable reliable data transmission over cognitive radio networks, the large available bandwidth obtained from cognitive radio can be used to improve the system redundancy in order to guarantee the system reliability. Using the terminology in the theory of optimal reliability design in industrial engineering, a single path data flow can be considered as a parallel-series system, in which each cut set represents a secondary user and contains several assigned channels. A heuristic algorithm is proposed to assign the channels in the licensed spectrum band to different cut sets in the parallel-series system to minimize the overall risk. By adopting the concept of cut set hazard, the algorithm is applied in both single path and multiple path situations. It is also extended to the decentralized scenario. Channel reuse, which incurs the correlation of failures in the system, is also considered for the channel assignment. Simulation shows that the proposed algorithms can significantly improve the reliability of cognitive radio networks.

Structural system inspection practices for floating offshore facilities, such as FPSO's and FSO's, have for the most part followed the practice employed and developed via trading ships/maritime practice. Often, the influence of a particular repeated service/cargo loading regime, cargo corrosivity, or site environmental influence can play a major role for a particular asset. More specifically, there has been only cursory attempts made to first understand and then, where possible, take advantage of site-specific conditions and loading in the development of in-service inspection plans. In recent years there has been significant interest by the marine and offshore industry to apply structural reliability techniques to risk based inspection planning for marine vessels and floating production installations. In this regard, structural reliability based methods can assist in providing a framework for quantifying site-specific loading and degradation mechanisms (such as fatigue and corrosion), through a systematic consideration of the probabilistic uncertainty in each degradation mechanism. By applying structural reliability analysis and risk assessment techniques to inspection planning, the operator is given a tool by which he can justify the allocation of resources to those structural components with a higher risk profile, and at the same time potentially relax inspection activities for low risk components to optimize and target inspection efforts. In a companion paper [1], available structural reliability methods developed to date were summarized, and then applied to determine the inspection intervals based on site specific loading as applied to strength considerations of the hull girder as well as to stiffened and un-stiffened plate panels. By tracing the time-varying reliability index for these structural components, the risk-based inspection intervals can be determined. This methodology has recently been implemented to provide the foundation in a risk-based inspection (RBI) plan for a floating production unit offshore West Africa. The current paper will further consider the sensitivities resulting from the following two conditions for the strength reliability:environmental load for different regions of the world, andcorrosion rate corresponds to offshore environment as well as storage conditions. Another two conditions are considered for fatigue reliability:assumed initial crack size for a connection, andcrack growth parameter for either the air environment or marine environment that a connection may be subjected to. The sensitivity studies presented in this paper provide a quick reference to understand the RBI plans benefits via work scope optimization and cost reductions for floating production units operating in various regions of the world. Introduction Figure 1 - A risk-based inspection planning reliability analysis flow chart [1] (Available in full paper) Details of a structural reliability methodology applicable to risk based inspections on a ship-shaped floating production vessel have been published in a companion paper [1]. From that paper, a flow chart of this methodology is shown in Figure 1. This methodology starts with information gathering, such as obtaining the vessel gauging data, vessel past history, current service condition, etc.

This paper outlines the essential steps taken in performing structural reliability calculations during the process of laying out a risk-based inspection program. The structural reliability analysis described in this paper essentially takes the deterministic finite element method (FEM) stress/fatigue analysis results, coupled with uncertain degradation mechanisms (e.g. corrosion rate, crack propagating parameters, etc.), and tracks the time-varying structural reliability index of the structural components under consideration. This can then be used to determine the timing for inspection of structural components. For the assessment of structural strength, an efficient and straightforward method is proposed to calculate the time-variant reliability index. This method is verified by an example problem and compared to the random process first-passage reliability solutions. Load combination issue is briefly discussed, in which an approach stems from the ABS Dynamic Loading Approach (DLA) coupled with concepts from Turkstra’s rule. This proposed simplistic load combination approach is verified through an example problem in which the result is compared to the solution calculated from a more sophisticated approach. Establishment of target reliability levels is also briefly discussed. For the assessment of fatigue behavior for welded connections, both S-N curve based and fracture mechanics based reliability methods are discussed. Their usefulness will be discussed in terms of both inspection interval as well as selecting the proper sampling percentage of connections to inspect. Statistical correlation among a group of similar connections is discussed to assist the selection of appropriate locations in the population of the aforementioned sampling. The usefulness of fatigue reliability analysis is also demonstrated by an example problem.

It is shown in the article, that the tasks of estimation to reliability of infocommunication network (ICN) acquire all greater actuality both in the sphere of planning and during exploitation ICN. Reliability remains one of requirements to ICN, presented in recommendations of the ITU. ICN behave to the structural systems, that is why the special value for ICN acquire the question of estimation of structural reliability. It is marked, that at the calculation of structural reliability ICN most applied is a method that is based on taking into account of totality of ways and cuts, here a structural reliability of network index probability of faultless work of directions of connection, that is used for an information transfer in ICN, is considered. Insufficient scientific of question of determination of lower bound of structural reliability is shown ICN, that determines the assured level of structural reliability of both separate connections and network on the whole. The method for determining the lower bound of the structural reliability of ICN based on the formation of a set of sections is proposed. The idea of the method is based on binary coding of cuts, which leads to a clear formalization of the procedure for constructing a set of cuts in disjunctive normal form and, as a result, to the practical possibility of using the proposed method to determine the lower bound of structural reliability in modern ICN. An example of application of the proposed method is given, which showed the efficiency of the method in comparison with the known method based on the formation of a dual logical function of a set of paths, and then its transformation into a disjunctive normal form to obtain a set of cuts. Further development of this area of work can be: • search for a set of cuts to assess the lower bound of the structural reliability of individual links and the network as a whole for networks with an uncertain topology; • development of approaches to obtaining weighting factors that determine the importance of the lower and upper boundaries of structural reliability, as well as the importance of individual areas of communication.

References

In order to find a way to study the structure reliability further, the basic system of structural and the methods of analyzing were introduced. For the series system and parallel system, the calculation can be categorized into Point estimated method and interval estimated method. The point estimated method includes Stevenson-Moses method, Probability Network Evaluation Technique, Conditional Probability Method and Integrated Correlation Coefficient Method. The interval estimated method includes General boundaries of range and the narrow boundaries of range. The principle of method and the calculation steps methods were depicted in detail. This study has significance in theory and practice for the study of structural reliability.

A relationship between rth partial derivatives of the reliability function h(p) of a coherent system and its minimal cut (path) sets is studied (r ≥ 2). It is shown that (−1)r(∂rh(p)/∂pi1, …, ∂pir)((−1)(∂rh (p)/∂pi1, …, ∂pir)) is nonnegative for all i1, …, ir and all p implies that all minimal cut (path) sets have cardinality r − 1 or less, r = 2, …, n. When r = 2, a simple characterization is obtained for series (parallel) system. Interpretations of such characterization in terms of reliability importance of components are given and a simple proof of a known characterization of series system is obtained.

: Our research efforts have been concentrated on two main areas: Design of experiments and Reliability. In the area of design of experiments we have studied problems of data collection relevant to virtually all Air Force technical areas. There is a strong need in the Air Force to reduce costs and save time in the collection of large amounts of data. The reduction in costs and time should be done clearly without any damage to the statistical quality of the data being collected. Our research problems not only add to our store of knowledge about multifacet of data collection and data analysis in general, but they have immediate applications to many important problems which the United States Air Force is faced with. In the area of reliability our efforts have been mainly directed towards developing comprehensive treatments of various reliability models which have useful applications in determining and improving levels of performance and reliabilities of complex systems and their components. These models include: 1) A simple model in structural reliability which has applications in various areas such as inventory depletion, urn models, etc.; 2) Multivariate life distributions useful in modeling system with dependent components; and 3) Multistate (Degradable) Coherent Systems.

The actual structural systems have many failure modes. Due to the same random sources owned by the performance functions of these failure modes, there usually exist some nonlinear correlations between the various failure modes. How to handle the nonlinear correlations is one of the main scientific problems in the field of structural system reliability. In this paper, for the two-component systems and multiple-component systems with multiple failure modes, the mixed copula models for time-independent reliability analysis of series systems, parallel systems, series-parallel systems, and parallel-series systems are presented. These obtained mixed copula models, considering the nonlinear correlation between failure modes, are obtained with the chosen optimal copula functions with the Bayesian selection criteria and Monte Carlo Sampling (MCS) method. And a numerical example is provided to illustrate the feasibility and application of the built mixed models for structural system reliability.

This paper proposes a new method for analyzing the fuzzy system reliability of a parallel-series and series-parallel systems using fuzzy confidence interval, where the reliability of each component of each system is unknown. To compute system reliability, we are estimated reliability of each component of the systems using fuzzy statistical data with both tools appropriate for modeling fuzzy data and suitable statistical methodology to handle these data. Numerical examples are given to compute fuzzy reliability and its cut set and the calculating was performed by using programming in software R.