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Multi-state supernetworks are capable of representing activity-travel patterns at a high level of detail and thus are a powerful tool for activity-travel scheduling (ATS) of multidimensional choice facets. To alleviate the limitations of the common deterministic network representation, travel time and activity duration uncertainty has been incorporated in multi-state supernetworks. However, the extension unrealistically assumed that all uncertain components are independent. This study suggests an approach of ATS considering spatially and temporally correlated travel times and activity durations in stochastic time-dependent (STD) multi-state supernetworks. Support points are used as a representation of the stochasticity of the STD multi-state supernetwork. ATS is formulated as a pathfinding problem subject to space–time constraints based on recursive formulations. A series of numerical experiments is implemented to demonstrate the applicability of the suggested approach.

The multi-state system (MSS) is a system that may exhibit multiple states or performance levels. Most existing studies assumed that the transition probabilities from states to states are known. However, in practical engineering, the complex stress conditions lead to great difficulty of collecting the statistical data of state transitions. In this paper, based on physics-of-failure theory, we consider different levels of damages caused by failure mechanisms (FMs) are the main reasons to components’ multiple states. Besides, the physical isolation (PI) effect on degradations of FMs is also studied, which is neglected in the existing studies about the MSS with functional dependence groups. Decision-diagram based methods are used for modeling the failure behavior of the MSS. An automatic collision avoidance system is analyzed for illustrating the proposed modeling and analyzing methods. The results show that comparing to the results without the consideration of PI effect, the probabilities of different states with PI effect of multi-state components and system may decrease or increase, which depends on the actual PI effects to the stress conditions.

In this paper, by considering two multi-state semi-coherent systems sharing some components, we define the multi-state joint signature. Then, some properties of this multi-state joint signature are discussed in detail, and some preservation results are established in terms of stochastic ordering. A south-east shift order for comparing the multi-state joint signature matrices is then discussed. Finally, some numerical examples are presented for illustrating all the theoretical results established here.

The joint signatures of binary-state and multi-state (semi-coherent or mixed) systems with i.i.d. (independent and identically distributed) binary-state components are considered in this work. For the comparison of pairs of binary-state systems of different sizes, transformation formulas of their joint signatures are derived by using the concept of equivalent systems and a generalized triangle rule for order statistics. Similarly, for facilitating the comparison of pairs of multi-state systems of different sizes, transformation formulas of their multi-state joint signatures are also derived. Some examples are finally presented to illustrate and to verify the theoretical results established here.

This study investigates the influence of different levels of urbanization, built environment, and socio-demographic features on the frequency of vehicle crashes associated with distracted driving (...

Although cancer diagnosis research has continuously made breakthroughs in a single indicator, it is a challenging task to improve its multiple joint indicators. This study proposes a multi-category multi-state information ensemble-based classification method. We fuse protein-coding and non-coding genes to construct co-expression profiles, which ensemble the field information of classical genetics and epigenetics. A hierarchical feature selection algorithm based on control groups is put forward to quickly remove irrelevant and redundant features without the bias caused by unbalanced dataset. Multiple heterogeneous diagnosis models, which ensemble multiple diagnosis model structures and model states, are constructed and a competition mechanism is then introduced to automatically select the best model from multiple heterogeneous models without deeply grasping the positive and negative fusion effects between different algorithms and features. We apply the proposed method to classify three high-incidence cancers, in which the classification accuracy and sensitivity are over 99.23% and the classification specificity is over 97.37%. This illustrates that the proposed method has upgraded the three joint indicators of cancer diagnosis at the same time. Compared with the state-of-the-art classification methods, the classification accuracy has been improved by 2.23–9.23%, the sensitivity by 6.25–37.40%, and the specificity by 0–12.02%. In addition, feature analysis reveals three biological findings.

The belief that additional time allows children to become more ready for school has affected public policy and individual practices. Prior studies estimated either associations between school entry...

This paper addresses two important useful extensions of binary reliability techniques to multi-state reliability techniques, namely: (a) the problem of complementation or inversion of the function of system success to that of system failure (or equivalently, of deriving the logical minimal cutsets in terms of the logical minimal paths), and (b) the associated problem of hand-checking of a symbolic reliability expression. The paper deals specifically with the reliability of a multi-state delivery network. It presents two complementation procedures, one via the application of multi-state De Morgan’s rules, and the other via the multi-state Boole-Shannon expansion. The paper also illustrates one case in which this complementation is needed, as it outlines a method for checking the reliability of the multi-state system in terms of its logical minimal paths and logical minimal cutsets.

Influence nets (INs) are proposed on the basis of causal logic for the purpose of depicting causal relationship strengths in complex systems. However, it is difficult to accurately determine the causal strength (CAST) parameters on the basis of expert knowledge only, particularly for practical problems with multiple attributes and multiple states. In this paper, the original IN with binary states is first extended into a multi-state IN, endowing the IN with the ability to model and infer under multiple states. Based on this method, an optimization framework is proposed to optimize the CAST parameters of multi-state INs. Finally, two practical cases are studied to verify the feasibility and efficiency of the proposed multi-state IN with an optimization framework in regression and classification.

CT screening has been commonly used to identify and diagnose lung cancer in its early stages. CT has been shown in clinical studies to reduce lung cancer mortality by 20% as compared to plain chest radiography; however, existing CT screening services face obstacles such as high over diagnosis rates, high costs, and elevated radiation exposure.The study develops computer and deep learning models for predictive lung cancer diagnosis and disease progression prediction in an effort to solve these difficulties. Using a symmetric chain code method and a machine learning system, a novel lung segmentation approach was first developed. The lung nodules connected to the lung wall are included in this process, which minimises over-segmentation error. Finally, to predict the inter disease progression of lung cancer, a Bayesian method was coupled with a prolonged Markov model.The resultant model calculates specific lung cancer state transition data, which can be used to make customised screening recommendations. Extensive trials and results have shown the efficacy of these approaches, paving the way for current CT screening systems to be optimised and improved.

Failures of safety-critical systems may result in irretrievable economic losses and significant safety hazards, thus enhancing the reliability of safety-critical system is crucial. As applied widely in engineering fields, protective devices are commonly equipped for the systems operating in shock environment to reduce external damage, which has not been taken into consideration in existing literatures. This paper investigates the reliability of multi-state systems with competing failure patterns supported by a protective device. According to the system failure modes, state-based and shock number-based triggering mechanism of the protective device are developed. That is, the protective device is triggered once the system state or cumulative number of shocks exceeds corresponding critical thresholds respectively. After being triggered, the protective device can reduce the probability of damaging shocks for the system. The protective device fails when the number of consecutive valid shocks reaches a threshold. Based on the constructed model, a finite Markov chain imbedding approach is employed to derive reliability indices including distribution functions of system lifetime and residual lifetime, together with expected operating time of the protective device. Moreover, two age-based replacement policies together with a condition-based replacement policy are developed to accommodate different maintenance scenarios and corresponding optimal solutions are acquired. Numerical illustrations based on the application of cooling systems in engines are presented to validate the results.

This paper deals with an emergent variant of the classical problem of computing the probability of the union of n events, or equivalently the expectation of the disjunction (ORing) of n indicator variables for these events, i.e., the probability of this disjunction being equal to one. The variant considered herein deals with multi-valued variables, in which the required probability stands for the reliability of a multi-state delivery network (MSDN), whose binary system success is a two-valued function expressed in terms of multi-valued component successes. The paper discusses a simple method for handling the afore-mentioned problem in terms of a standard example MSDN, whose success is known in minimal form as the disjunction of prime implicants or minimal paths of the pertinent network. This method utilizes the multi-state inclusion-exclusion (MS-IE) principle associated with a multi-state generalization of the idempotency property of the ANDing operation. The method discussed is illustrated with a detailed symbolic example of a real-case study, and it produces a more precise version of the same numerical value that was obtained earlier. The example demonstrates the notorious shortcomings and the extreme inefficiency that the MS-IE method suffers, but, on the positive side, it reveals the way to alternative methods, in which such a shortcoming is (partially) mitigated. A prominent and well known example of these methods is the construction of a multi-state probability-ready expression (MS-PRE). Another candidate method would be to apply the MS-IE principle to the union of fewer (factored or composite) paths that is converted (at minimal cost) to PRE form. A third candidate method, employed herein, is a novel method for combining the MS-PRE and MS-IE concepts together. It confines the use of MS-PRE to ‘shellable’ disjointing of ORed terms, and then applies MS-IE to the resulting partially orthogonalized disjunctive form. This new method makes the most of both MS-PRE and MS-IE, and bypasses the troubles caused by either of them. The method is illustrated successfully in terms of the same real-case problem used with the conventional MS-IE.

A new broadcast stochastic recruitment approach to the control of shape memory alloy (SMA) cellular actuators is proposed. The control design is based on a Markov chain model of multi-state cells, which is able to better characterize the inherent hysteresis of SMA in phase transition. The closed-loop and open-loop control laws are derived from random Lyapunov stability analysis and the stability conditions are analyzed. Simulation experiments demonstrate the effectiveness of the proposed method.

Dynamic reliability measures are important characteristics for understanding the lifetime behaviour of multi-state systems. This study aims to analyze the mean residual lifetime (MRL) function for a one-unit three-state system.The system considered has just three states such as “0, 1, 2”. State “2” and “1” signify the perfect functioning and partially working states, respectively while state “0” is the failure state. We let [Formula: see text] and [Formula: see text] be the lifetimes of the system spent at state “1” and “2,” respectively. We assess a particular performance characteristic, MRL, of this three-state system via conditional survival functions, when [Formula: see text] and [Formula: see text] are both independent and dependent. In case of independency, MRL functions are obtained and the results are discussed with reference to a case study. The effect of different distributions on the MRLs are also investigated in this case study. In case of dependency, on the other hand, the effect of dependency on MRL functions is especially underlined given that the system is at state “ j” ([Formula: see text]) for [Formula: see text]. To understand the time dependent behaviour of the related MRL functions, certain graphical illustrations are also presented.

This paper deals with the reliability of a multi-state delivery network (MSDN) with multiple suppliers, transfer stations and markets (depicted as vertices), connected by branches of multi-state capacities, delivering a certain commodity or service between their end vertices. We utilize a symbolic logic expression of the network success to satisfy the market demand within budget and production capacity limitations even when subject to deterioration. This system success is a two-valued function expressed in terms of multi-valued component successes, and it has been obtained in the literature in minimal form as the disjunction of prime implicants or minimal paths of the pertinent network. The main contribution of this paper is to provide a systematic procedure for converting this minimal expression into a probability-ready expression (PRE). We successfully extrapolate the PRE concept from the two-valued logical domain to the multi-valued logical domain. This concept is of paramount importance since it allows a direct transformation of a random logical expression, on a one-to-one one, to its statistical expectation form, simply by replacing all logic variables by their statistical expectations, and also substituting arithmetic multiplication and addition for their logical counterparts (ANDing and ORing). The statistical expectation of the expression is its probability of being equal to 1, and is simply called network reliability. The proposed method is illustrated with a detailed symbolic example of a real-case study, and it produces a more precise version of the same numerical value that was obtained earlier by an alternative means. This paper is a part of an ongoing activity to develop pedagogical material for various candidate techniques for assessing multi-state reliability.

PurposeThis paper presents the performance analysis of the automatic ticket vending machine (ATVM) through the functioning of its different hardware and software failures.Design/methodology/approachFrequent failures in the working of ATVM have been observed; therefore, the authors of the paper intend to analyze the performance measures of the same. Authors have developed a mathematical model based on different hardware and software failures/repairs, which may occur during the operation, with the help of the Markov process. The developed model has been solved for two kinds of failure/repair rates namely variable failures (very much similar to real-time failure) and constant failures. Lagrange's method and Laplace transformation are used for the solution of the developed model.FindingsReliability and mean time to failure of the ATVM are determined. Sensitivity analysis for ATVM is also carried out in the paper. Critical components of the ATVM, which affect the performance of the same, in terms of reliability and MTTF are also identified.Originality/valueA mathematical model based on different hardware and software failures/repairs of ATVM has been developed to analyze its performance, which has not been done in the past.

Human Activity Recognition (HAR) is one of the main research fields in pattern recognition. In recent years, machine learning and deep learning have played important roles in Artificial Intelligence (AI) fields, and are proven to be very successful in classification tasks of HAR. However, there are two drawbacks of the mainstream frameworks: 1) all inputs are processed with the same parameters, which would cause the framework to incorrectly assign an unrealistic label to the object; 2) these frameworks lack generality in different application scenarios. In this paper, an adaptive multi-state pipe framework based on Set Pair Analysis (SPA) is presented, where pipes are mainly divided into three kinds of types: main pipe, sub-pipe and fusion pipe. In the main pipe, the input of classification tasks is preprocessed by SPA to obtain the Membership Belief Matrix (MBM). The sub-pipe shunt processing is performed according to the membership belief. The results are merged through the fusion pipe in the end. To test the performance of the proposed framework, we attempt to find the best configuration set that yields the optimal performance and evaluate the effectiveness of the new approach on the popular benchmark dataset WISDM. Experimental results demonstrate that the proposed framework can get the good performance by achieving a result of 1.4% test error.

In order to improve the lifetime and reliability of equipment operation stage, it is necessary to carry out maintenance for components. The typical selective maintenance model does not consider the maintenance quality uncertainty and the failure effects, which may make the decision-maker overestimates the reliability of completing the next task after system maintenance, resulting in incorrect maintenance decision and prone to serious consequences of failure. In this paper, the potential discrepancy between the target maintenance quality and the actual maintenance quality of the decision maker is considered. At the same time, a multi-state FMECA is proposed to measure the failure effects under different states. Finally, the selective maintenance model of the multi-state series systems is established and solved by the genetic algorithm. The results show that considering the effect of component failure and the uncertainty of maintenance quality has an influence on maintenance decision. The maintenance decision made in this way is more consistent with the engineering practice.

Background: In a multi-state system, either the entire system or its components will have more than two states. Different kind of multi-state systems have been investigated, such as multistate series-parallel systems, multi-state k-out-of-n systems and multi-state linear consecutive-k-outof- n systems. Methods: Performability analysis is concerned with the calculation of probability distribution of different system performance levels. In this paper, Multi-valued Decision Diagram (MDD) based approaches are discussed to conduct the performability analysis of multi-state systems. Results: Examples are provided to illustrate the use of MDD approaches for three types of multistate systems, e.g. multi-state series-parallel systems, multi-state k-out-of-n systems and multi-state linear consecutive-k-out-of-n systems. Conclusion: The empirical results show that the MDD approaches have lower computational complexity than the traditional methods in model generation and evaluation.

This article considers an one-unit multi-state system with a general α-series process and an order-replacement policy. It is supposed that the working times of the system after repair become shorte...

The mission for a type of transportation system is to complete a certain transportation volume within a predetermined period, during which maintenance is also performed. In such a system, any unit selected to be maintained is often connected to the system to participate in the system operation immediately after its maintenance, and its participation in the system operation at different moments has different effects. Based on this consideration, this paper proposes a new selective maintenance model for a multi-state system wherein the maintenance sequence arrangement is considered. In this selective maintenance problem, to maximise the system reliability, a sub-set of all desired maintenance activities is selected, and the sequence of the selected maintenance activities to be performed is arranged, with the transportation volume requirement and the limited budget considered. An ant colony optimisation algorithm is tailored for the resulting optimisation problem. Two example analyses are presented to illustrate the effectiveness of the tailored ant colony optimisation algorithm and the effect of the proposed selective maintenance. The results show that the tailored ant colony optimisation algorithm is effective for the proposed selective maintenance model. This selective maintenance can significantly improve the system reliability when the predetermined period is relatively short, and this maintenance effect of improving the system reliability gradually weakens as the predetermined period becomes longer. Increasing the budget and decreasing the transportation volume requirement can slow this weakening of the maintenance effect.

The investigation of risk factors associated with hypertension patients has been extensively studied in the past decades. However, the pattern of natural progressive trajectories to hypertension from nonhypertensive states was rarely explored. In this study, we are interested in discovering the underlying transition patterns between different blood pressure states, namely normal state, elevated state, and hypertensive state among the working population in the United States. A multi-state Markov model was built based on 88,966 clinical records from 34,719 participants we collected during the worksite preventive screening from 2012 to 2018. We first investigated the various risk factors, and we found that body mass index (BMI) is the most critical factor for developing new-onset hypertension. The transition probabilities, survival probabilities, and sojourn time of each state were derived given different levels of BMI, age groups, and gender categories. We found the underweight participants are more likely to remain in the current nonhypertensive states within 3 years, while extremely obese participants have a higher probability of developing hypertension. We discovered the distinct transition patterns among male and female participants. On average, the sojourn time in the normal state for normal-weight participants is 4.33 years for females and 2.18 years for their male counterparts. For the extremely obese participants, the average sojourn time in the normal state is 1.38 years for females and 0.71 years for males. In the end, a web-based graphical user interface (GUI) application was developed for clinicians to visualize the impact of behavioral interventions on delaying the progression of hypertension. Our analysis can provide a unique insight into hypertension research and proactive interventions.

Uni-directional multi-state fluorochromic scaffolds are valuable photofunctional molecules and yet scarce. We report a general approach for their design, i.e., mechanodonor-acceptor coupling (MDAC). A photochromic molecule is a mechanodonor, due to its capability to convert photonic energy into mechanical force. Upon proper coupling, it can be used to drive a mechanochromic molecule for uni-directional multi-state fluorochromism. The embodiment of this approach is a rhodamine-dithienylethylene hydride (RDH), which has been successfully employed in super-resolution localization microscopy

Seventeen Sustainable Development Goals (SGDs) were adopted by the World Health Organization (WHO) in 2015 for the 2030 Agenda for Sustainable Development. Sustainable Development Goal 3 (SDG3) is ‘Better health and well-being by 2030’. According to WHO, good health in the context of SDG3 is assessed with respect to the level and distribution of individuals’ and communities’ healthy life, conditions that affect health and well-being and risk factors whose presence would affect health and well-being. The overall aim is that each SDG target is achieved by 2030. In 2018 the WHO used statistical methods to assess the state of health in Africa in the context of SDG3. Their analysis revealed successes and shortfalls towards attaining SDG3. Backed by public health and other activities, statistics play an important role in improving the health and well-being of Africa. This paper explains how statistics can be used to help African countries to attain SDG3, in its role in modeling event histories, diagnosis, evidence-based medicine, determination of risk factors of exposures of morbidity and mortality, determination of risk factors of morbidity and mortality, the computation of the level and distribution of vital events, measuring disease frequency and progress, quantification of life expectancy and monitoring and evaluation.

Multi-state series-parallel systems are widely-used for representing engineering systems. In real-life cases, engineers need to select an optimal system structure among many different multi-state s...

Survival signature technology has recently attracted increasing attention for its merits on quantifying reliability of systems with multiple types of components. In order to implement reliability evaluation of multi-state system (MSS), computing methods of survival signature are studied for reliability analysis of several different systems in this paper. For an MSS consisting of multi-state components, its survival signature can be developed based on the different state definition of system. For the binary-state system with multi-state components, its survival signature is based on the generalization of survival signature for multi-state components. For a real life engineering MSS consisting of subsystems, the computing method of survival signature of system has also been derived based on the survival signature of subsystems and mapping of subsystems’ states to system's states. This enables consecutive application of the new method to substantial realistic MSS, with no theoretical limit on the size of the systems. Examples illustrate the applicability of the analysis approach for systems reliability.

A notable reliability model is the binary threshold system (also called the weighted-k-out-of-n system), which is a dichotomous system that is successful if and only if the weighted sum of its component successes exceeds or equals a particular threshold. The aim of this paper is to extend the utility of this model to the reliability analysis of a homogeneous binary-imaged multi-state coherent threshold system of (m+1) states, which is a non-repairable system with independent non-identical components. The paper characterizes such a system via switching-algebraic expressions of either system success or system failure at each non-zero level. These expressions are given either (a) as minimal sum-of-products formulas, or (b) as probability–ready expressions, which can be immediately converted, on a one-to-one basis, into probabilities or expected values. The various algebraic characterizations can be supplemented by a multitude of map representations, including a single multi-value Karnaugh map (MVKM) (giving a superfluous representation of the system structure function S), (m+1) maps of binary entries and multi-valued inputs representing the binary instances of S, or m maps, again of binary entries and multi-valued inputs, but now representing the success/failure at every non-zero level of the system. We demonstrate how to reduce these latter maps to conventional Karnaugh maps (CKMs) of much smaller sizes. Various characterizations are inter-related, and also related to pertinent concepts such as shellability of threshold systems, and also to characterizations via minimal upper vectors or via maximal lower vectors.

To improve system performance, redundancy is widely used in different kinds of industrial applications such as power systems, aerospace, electronic, telecommunications and manufacturing systems. Designing high performant systems which meet customer requirements with a minimum cost is a challenging task in these industries. This paper develops an efficient approach for the redundancy optimization problem of series-parallel structures modeled as multi-state systems. To reach the target system availability, redundancies are used for components among a list of products available in the market. Each component is characterized by its own availability, cost and performance. The goal is to minimize the total cost under a system availability constraint. Discrete levels of performance are considered for the system and its components. The extreme values of such performance levels correspond to perfect functioning and complete failure. A piecewise cumulative load curve represents consumer demand. System availability corresponds to the aptitude to fulfill this demand. The multi-state system availability evaluation uses the universal moment generating function technique. The proposed optimization algorithm is based on the non-linear threshold accepting metaheuristic, while using a self-adjusting penalty guided strategy. The obtained results demonstrate the approach efficiency for solving the redundancy optimization problem of multi-state systems. Its effectiveness is also tested using the classical redundancy optimization problem of binary-state systems. The algorithm is evaluated by comparison to the best known methods. For multi-state systems, it is compared to genetic algorithm and tabu search. For binary-state systems, it is compared to genetic algorithm, tabu search, ant colony optimization and harmony search. The obtained results demonstrate that the proposed approach outperforms these state-of-the-art benchmark methods in finding, for all considered instances, a high-quality solution in a minimum computational time.

A GNSS/INS integrated navigation system has been intensively developed and widely applied in multiple areas. It can provide high accuracy position, velocity and attitude for vehicle with appropriat...

In the reliability literature, several results have been presented to compare binary (two states) systems. Often, such results are obtained from copula-based extensions of fuzzy measures, where a fuzzy measure describes the structure of a system and a copula describes the stochastic dependence among the lifetimes of its components. Other similar results have been obtained in terms of the concept of signature. Here, we extend all those results to multi-state systems made up from binary components by suitably constructing corresponding mixed binary systems. For such a construction, we show how any fuzzy measure can be decomposed as a convex combination of { 0 , 1 } -valued fuzzy measures and how such a decomposition extends to the corresponding aggregation function. For a mixed system we can furthermore consider its signature and so we can also define a signature for the multi-state system. For mixed systems associated to different multi-state systems, we can thus obtain different comparison results, which can be translated into the corresponding comparisons for the parent multi-state systems. Stochastic comparisons are obtained for the discrete random variables which represent the states of two systems at time t, as well. The arguments in the paper will be illustrated by means of examples and related remarks.

This paper treats with the reliability assessment of a Repairable Multi-State System (RMSS) by means of a Nonhomogeneous Continuous-Time Markov Chain (NH-CTMC). A RMSS run on different operating conditions that may be considered acceptable or unacceptable according to a defined demand level. In these cases, the commonly used technique is Homogeneous Continuous-Time Markov Chain (H-CTMC), since its solution is mathematically tractable. However, the H-CMTC involve that the time between state transitions is exponentially distributed, and the failure and repair rates are constants. It's certainly not true if the system components age with the operation or if the repair activities depend on the instant of time when the failure occurred. In these cases, the failure and repair rates are time-varying and the NH-CTMC is needed to be considered. Nevertheless, for these models the analytical solution may not exist and the use of others techniques is required. This paper proposes the use of an Equivalent Systems Dynamics Model (ESDM) to model a NH-CTMC. A ESDM represent the Markov Model (MM) by means of the language and the tools of the Systems Dynamics (SD), and the results are obtained by simulation. As an example, an RMSS with three components, failure rates associated with the Weibull distribution and repair rates associated with the Log-logistic distribution is developed. This example serves to identify the advantages and disadvantages of a ESDM to make model a RMSS and evaluate some reliability measures.

This work addresses an optimal bilinear control design representing the corrective maintenance for a reparable multi-state system. The primary interest is to optimise the availability of the system...

Nanobubble is a rising research field, which attracts more and more attentions due to its potential applications in medical science, catalysis, electrochemistry and etc. To better implement these applications, it is urgent to understand one of the most important mechanisms of nanobubbles, the evolution. However, few attentions have been paid in this aspect because of the methodology difficulties. Here we successfully used dark-field microscopy to study the evolution process of single nanobubbles generated from formic acid dehydrogenation on single Pd-Ag nanoplates. We found some of the nanobubbles in this system can exhibit three distinct states representing different sizes, which can transform among each other. These transitions are not direct but through some intermediate states. Further kinetic analysis reveals complicated mechanisms behind the evolution of single nanobubbles. The results acquired from this study can be applicable to nanobubble systems in general and provide insights into the understanding of mechanisms affecting the stability of nanobubbles and their applications.

The system signatures of multi-state coherent or mixed systems with i.i.d. (independent and identically distributed) binary-state components are considered in this paper. For any multi-state coherent or mixed system with m i.i.d. components, the signature of its equivalent system of size m + l can be written as a mixture of signatures of several multi-state vector k -out-of- m + l: F systems. This facilitates the comparison of two multi-state systems of different sizes upon transforming the signature of the system of smaller size to the signature of its equivalent system of larger size along the lines of Navarro et al. (2008) for the usual Samaniego signature. Some numerical examples are finally presented to illustrate all the results established here.

Motivated by real-world complex engineering systems, this research proposes a multi-state system with two levels of performance sharing. In this system, there exists a unique performance transmitter between any two adjacent subsystems and any two adjacent elements within each subsystem. Surplus performance of a subsystem or an element can only be transmitted to its adjacent subsystems or elements. We build the reliability model of the proposed system and suggest a corresponding reliability evaluation algorithm by extending the existing universal generating function technique. Since the performance sharing is only allowed between adjacent subsystems and elements, the element allocation and sequencing will affect the system reliability. Due to the complexity of the combinatorial optimization problem, we use the genetic algorithm to find the optimal allocation and sequencing of the elements. An analytical example is provided to illustrate the reliability evaluation algorithm. Numerical experiments are carried out to demonstrate how the optimal allocation and sequencing as well as the capacities of the performance transmitters affect the system reliability.

Many real-world engineering systems such as aerospace systems, intelligent transportation systems and high-performance computing systems are designed to complete missions in multiple phases. These types of systems are known as phased-mission systems. Inspired by an industrial heating system, this research proposes a generalized linear sliding window system with phased missions. The proposed system consists of N nodes with M multi-state elements that are subject to degradation. The linear sliding window system fails if the cumulative performance of any r consecutive nodes is less than the pre-determined demand in any phase. The degradation process of each element is modeled by a continuous-time Markov chain. A novel reliability evaluation algorithm is proposed for the linear sliding window system with phased missions by extending the universal generating function technique. Furthermore, the optimal element allocation strategy is determined using the particle swarm optimization. The effectiveness of the proposed algorithm is confirmed by a set of numerical experiments.