Extensions of system signatures to dependent lifetimes: Explicit expressions and interpretations

The concept of system signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. We consider its extension to the continuous dependent case and give an explicit expression for this extension as a difference of weighted means of the structure function values. We then derive a formula for the computation of the coefficients of these weighted means in the special case of independent continuous lifetimes. Finally, we interpret this extended concept of signature through a natural least squares approximation problem

On the Decreasing Failure Rate property for general counting process. Results based on conditional interarrival times

In the present paper we consider general counting processes stopped at a random time $T$, independent of the process. Provided that $T$ has the decreasing failure rate (DFR) property, we give sufficient conditions on the arrival times so that the number of events occurring before $T$ preserves the DFR property of $T$. These conditions involve the study of the conditional interarrival times. As a main application, we prove the DFR property in a context of maintenance models in reliability, by the consideration of Kijima type I virtual age models under quite general assumptions

Resume of James Daniel Esary, 1973

Naval Postgraduate School Faculty Resum

On the probability that integrated random walks stay positive

Let $S_n$ be a centered random walk with a finite variance, and define the new sequence $A_n:=\sum_{i=1}^n S_i$, which we call an integrated random walk. We are interested in the asymptotics of $$p_N:=P(\min_{1 \le k \le N} A_k \ge 0)$$ as $N \to \infty$. Sinai (1992) proved that $p_N \asymp N^{-1/4}$ if $S_n$ is a simple random walk. We show that $p_N \asymp N^{-1/4}$ for some other types of random walks that include double-sided exponential and double-sided geometric walks, both not necessarily symmetric. We also prove that $p_N \le c N^{-1/4}$ for lattice walks and for upper exponential walks, that are the walks such that $Law (S_1 | S_1>0)$ is an exponential distribution.Comment: Theorems 2 and 3 were restated and merged into one theorem; a new lemma (Lemma 1) added; Lemma 3 and Remark 1 were restated and merged into Proposition 1; the proof of Lemma 3 is reworked. The paper is accepted to SPA

Resume of James Daniel Esary, 1970

Naval Postgraduate School Faculty Resum

Review of interactions between the Naval Postgraduate School and the Naval Undersea Warfare Engineering Station, 1973-1986

http://archive.org/details/reviewofinteract00wilsDept. of Physics.N

Using reliability analysis to support decision making in phased mission systems

Due to the environments in which they will operate, future autonomous systems must be capable of reconfiguring quickly and safely following faults or environmental changes. Past research has shown how, by considering autonomous systems to perform phased missions, reliability analysis can support decision making by allowing comparison of the probability of success of different missions following reconfiguration. Binary Decision Diagrams (BDDs) offer fast, accurate reliability analysis that could contribute to real-time decision making. However, phased mission analysis using existing BDD models is too slow to contribute to the instant decisions needed in time-critical situations. This paper investigates two aspects of BDD models that affect analysis speed: variable ordering and quantification efficiency. Variable ordering affects BDD size, which directly affects analysis speed. Here, a new ordering scheme is proposed for use in the context of a decision making process. Variables are ordered before a mission and reordering is unnecessary no matter how the mission configuration changes. Three BDD models are proposed to address the efficiency and accuracy of existing models. The advantages of the developed ordering scheme and BDD models are demonstrated in the context of their application within a reliability analysis methodology used to support decision making in an Unmanned Aerial Vehicle

An efficient phased mission reliability analysis for autonomous vehicles

Autonomous systems are becoming more commonly used, especially in hazardous situations. Such systems are expected to make their own decisions about future actions when some capabilities degrade due to failures of their subsystems. Such decisions are made without human input, therefore they need to be well-informed in a short time when the situation is analysed and future consequences of the failure are estimated. The future planning of the mission should take account of the likelihood of mission failure. The reliability analysis for autonomous systems can be performed using the methodologies developed for phased mission analysis, where the causes of failure for each phase in the mission can be expressed by fault trees. Unmanned Autonomous Vehicles (UAVs) are of a particular interest in the aeronautical industry, where it is a long term ambition to operate them routinely in civil airspace. Safety is the main requirement for the UAV operation and the calculation of failure probability of each phase and the overall mission is the topic of this paper. When components or sub-systems fail or environmental conditions throughout the mission change, these changes can affect the future mission. The new proposed methodology takes into account the available diagnostics data and is used to predict future capabilities of the UAV in real-time. Since this methodology is based on the efficient BDD method, the quickly provided advice can be used in making decisions. When failures occur appropriate actions are required in order to preserve safety of the autonomous vehicle. The overall decision making strategy for autonomous vehicles is explained in this paper. Some limitations of the methodology are discussed and further improvements are presented based on experimental results

Normal approximation for strong demimartingales

We consider a sequence of strong demimartingales. For these random objects, a central limit theorem is obtained by utilizing Zolotarev’s ideal metric and the fact that a sequence of strong demimartingales is ordered via the convex order with the sequence of its independent duplicates. The CLT can also be applied to demimartingale sequences with constant mean. Newman (1984) conjectures a central limit theorem for demimartingales but this problem remains open. Although the result obtained in this paper does not provide a solution to Newman’s conjecture, it is the first CLT for demimartingales available in the literature

System design and maintenance modelling for safety in extended life operation

It is frequently the most cost effective option to operate systems and infrastructure over an extended life period rather than enter a new build programme. The condition and performance of existing systems operated beyond their originally intended design life are controlled through maintenance. For new systems there is the option to simultaneously develop the design and the maintenance processes for best effect when a longer life expectancy is planned. This paper reports a combined Petri net and Bayesian network approach to investigate the effects of design and maintenance features on the system performance. The method has a number of features which overcome limitations in traditionally used system performance modelling techniques, such as fault tree analysis, and also enhances the modelling capabilities. Significantly, for the assessment of aging systems, the new method avoids the need to assume a constant failure rate over the lifetime duration. In addition the assumption of independence between component failures events is no longer required. In comparison with the commonly applied system modelling techniques, this new methodology also has the capability to represent the maintenance process in far greater detail and as such options for: inspection and testing, servicing, reactive repair and component replacement based on condition, age or use can all be included. In considering system design options, levels of redundancy and diversity along with the component types selected can be investigated. All of the options for the design and maintenance can be incorporated into a single integrated Petri net and Bayesian network model and turned on and off as required to predict the effects of any combination of options selected. In addition this model has the ability to evaluate different system failure modes. The integrated Petri-net and Bayesian network approach is demonstrated through application to a remote un-manned wellhead platform from the oil and gas industry