Multi-state homogeneous Markov models in reliability analysis

Examining annual transitions in healthcare spending among U.S. medicare beneficiaries using multistate Markov models: Analysis of medicare current beneficiary survey data, 2003–2019

The behavior of users concerning mobile Internet varies significantly throughout the day. Results from existing studies—which generally simply segment one day into morning, afternoon, and evening—often provide inaccurate predictions of the behavior of users. To improve prediction accuracy, we propose a segment-based multi-state Markov (SBMSM) model for the dynamic time interval segmentation of the sequential behavior of users. The specific procedure of this proposed model can be described as follows: first, we divide each user’s behaviors into minimum unit according to time dimension; then, we merge adjacent time intervals or ensure they are constant according to the similarities in behavior; and finally, a multi-state Markov (MSM) model is trained using the newly constructed data individually. The experimental results illustrate that for 95.78% of users, an SBMSM model performs much better than a naive MSM model and hidden Markov model.

ORDMKV: a computer program fitting proportional odds model for multi-state Markov process

An accurate method for the analysis of remaining life for pressure vessels already in service would certainly help operation managers facing the question of when to replace mayor pieces of processing equipment. Operating companies would also realize the consequent savings derived from knowing in advance the probability of failure, or from safely extend the operating life of facilities. In this paper the first steps are undertaken towards a probabilistic analysis model for predicting the reliability of cracked pressure vessels as a function of applied operating loads using fracture mechanics. The analysis takes into account the variability in material properties, uncertainty in operating loads, continuing degradation of structural residual strength due to crack initiation and propagation and the combined effect of existing crack and newly initiating crack. The information gathered from inspections and non-destructive tests can be incorporated, together with the stresses caused by the operating loads, into the calculations. A numerical example is provided to demonstrate the methodology. Introduction The development of cracks due to fatigue is one of the main causes of interruption of service for pressure vessels. Cracked pressure vessels would generally be out of service and receive appropriate repair. However, sometimes the vessels need to continue to service until the maintenance or repair condition becomes available. In addition, leaving the cracked pressure vessel in service, provided that it maintains acceptable reliability and safety level, has great economical benefit. Because of these reasons, analysis and assessment of the reliability and safety of cracked pressure vessels becomes an increasingly interesting topic for the petroleum and gas industries. Traditional analysis for the reliability of cracked pressure vessels are based on classical fracture mechanics methods, such as the application of Paris-Erdogan formulation[1,2], and focus generally on single crack initiation and propagation using deterministic analysis. This deterministic technique does not take into consideration the variability and uncertainty of material properties and working loads that, as measurements show, demonstrate significant variation. In this paper a new reliability analysis model is proposed for cracked pressure vessels based on probabilistic fracture mechanics technique. This new model takes into account an extended set of variables such as:variability in material properties;uncertainty in working loads;continuing degradation of structural residual strength due to crack initiation and propagation andthe combined effect of existing and newly initiating cracks. Compared to traditional analysis models based on deterministic analysis techniques, the probabilistic model it is expected to provide a more accurate prediction for the reliability and the safety of cracked pressure vessels. This increased accuracy will improve the decision making process and should translate into significant savings in inspection, repair and replacement expenses for cracked pressure vessels. Reliability Analysis Model The basic procedure for calculation of reliability of cracked pressure vessels in the proposed analysis model is as follows: 1) identify the probability of fracture failure at loading cycle N due to the crack initiating at loading cycle Nd (Nd < N);

Modular multi‐level converter (MMC) with press‐packing IGBT devices is the popular and key equipment of VSC‐HVDC system, its reliability is directly related to the equipment safe operation. However, it is difficult to analyse the reliability using the failure statistical approach due to less fault data. In order to improve the reliability analyses accuracy, it is necessary to use the physical failure method by considering the main components fatigue failure mode. The reliability analysis models are presented for the MMC sub‐module with the press‐packing IGBT device and metallised film capacitors. First, based on the MMC‐HVDC simulation model, the losses and the junction temperatures of the IGBT devices were derived by the temperature field model, which the failure rates can be calculated. Furthermore, based the corrosion failure mode, the failure rate calculation of the metallised film capacitor was investigated using the voltage stress and thermal stress, the reliability calculation of the MMC sub‐module was presented by combining the main components failure rates. Finally, the reliability of the VSC‐HVDC based MMC was also presented with the different operation mode. The achievement is helpful to assess and improve the reliability of the VSC‐HVDC.

Fault trees are a key model in reliability analysis. Classical static fault trees (SFT) can best be analysed using binary decision diagrams (BDD). State-based techniques are favorable for the more expressive dynamic fault trees (DFT). This paper combines the best of both worlds by following Dugan’s approach: dynamic sub-trees are analysed via model checking Markov models and replaced by basic events capturing the obtained failure probabilities. The resulting SFT is then analysed via BDDs. We implemented this approach in the Storm model checker. Extensive experiments (a) compare our pure BDD-based analysis of SFTs to various existing SFT analysis tools, (b) indicate the benefits of our efficient calculations for multiple time points and the assessment of the mean-time-to-failure, and (c) show that our implementation of Dugan’s approach significantly outperforms pure Markovian analysis of DFTs. Our implementation Storm-dft is currently the only tool supporting efficient analysis for both SFTs and DFTs.

To effectively perform the reliability analysis of the flap deflection angle, the reliability analysis framework is developed by introducing fault logic and a data-driven model. Herein, the fault logic analysis is used to study the fault mechanism and filter out the characteristic fault parameters that can be used to collect input data for data-driven modelling; the data-driven modelling is employed to establish a reliability analysis model with a small amount of input data. Under this proposed framework, the improved dung beetle optimization algorithm for back propagation (IDBO-BP) method is developed to perform the reliability modelling of the flap deflection angle. To validate the effectiveness of the proposed framework, we study the fault logic of flap symmetry and establish a surrogate model of flap deflection based on the fault parameters and the IDBO-BP algorithm. According to the predicted results of the flap deflection angle, the reliability model based on the fault mechanism can reflect the actual flap motion. At the same time, the proposed IDBO-BP algorithm has excellent modelling and simulation property by comparing with other optimization algorithms. Thus, the efforts of this study provide a new solution to the problem of reliable analysis with uncertain fault parameters. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Traditional reliability analysis generally uses probability approach to quantify the uncertainty, while it needs a great amount of information to construct precise distributions of the uncertain parameters. In this paper, a new reliability analysis technique is developed based on a hybrid uncertain model, which can deal with problems with limited information. All uncertain parameters are treated as random variables, while some of their distribution parameters are not given precise values but variation intervals. Due to the existence of the interval parameters, a limit-state strip enclosed by two bounding hyper-surfaces will be resulted in the transformed normal space, instead of a single hyper-surface as we usually obtain in conventional reliability analysis. All the limit-state strips are then summarized into two different classes and corresponding reliability analysis models are proposed for them. A monotonicity analysis is carried out for probability transformations of the random variables, through which effects of the interval distribution parameters on the limit state can be well revealed. Based on the monotonicity analysis, two algorithms are then formulated to solve the proposed hybrid reliability models. Three numerical examples are investigated to demonstrate the effectiveness of the present method.

Preface. On the Entropies and Mutual Information of Some Bivariate Continuous Distributions Used in Reliability M. Ahsanullah, M. Habibullah. Initial Conditions Problem in Event History Analysis: An Indirect Inference Procedure M.Y. An. Analysis of Survival Data Under Competing Risks with Missing Cause of Death Information: Application and Implications for Study Design J.W. Andersen, et al. Conditional Proportional Hazards Models B.C. Arnold, Y.H. Kim. A Comparison of Conditional and Unconditional Inference Relating to Log-Gamma Distribution N. Balakrishnan, P.S. Chan. Universal Formulas for Treatment Effects from Noncompliance Data A.A. Balke, J. Pearl. Fundational Issues Concerning the Analysis of Censored Data R.E. Barlow, P. Tsai. Burn-in at the Component and System Level H.W. Block, et al. Identificationof Dependent Competing Risks Models K. Carling, T. Jacobson. Reliability Modelling for Optical Amplified Communication Systems M. Chown, G.A. Whitmore. A Parametric Approach to Measurement Errors in Receiver Operating Characteristic Studies M. Coffin, S. Sukhatme. Models for Degradation Processes and Event Times Based on Gaussian Processes K. Doksum, S.-L. Normand. A Non-Parametric Two-Sample Survival Test Based on a Single Occupancy Fermi-Dirac Model for the Discrete Range Distribution J.T. Efird, F. Pardo. Probability Approximations and Inequalities for Sequential Tests J. Glaz, J.R. Kenyon. Cure Mixture Models in Breast Cancer Survival Studies N.H. Gordon. A General Approach to Derive Chi-Square Type of Goodness-of-Fit Tests for Lifetime Data S. Hawala, J.-L. Wang. Prediction in Survival Analysis: Model or Medic? R. Henderson, M. Jones. Dynamic Reliability Models M. Hollander, E.A. Pena. Generalizations of Current Status Data with Applications N.P. Jewell, M. van der Laan. Trend Analysis of Multiple Counting Processes T. Kamakura. Historical Controls and Model Survival Analysis N. Keiding. A Random Effects Model for Multivariate Life Data A.C. Kimber. Statistical Challenges in Comparing Chemotherapy and Bone Marrow Transplantation as a Treatment for Leukemia J.P. Klein, M.-J. Zhang. Maximum Likelihood Estimation and the Multivariate Bernoulli Distribution: An Application to Reliability P.H. Kvam. Intermediate Clinical Events, Surrogate Markers and Survival M. Lefkopoulou, M. Zelen. A Semiparametric Bootstrap for Proportional Hazards Models T.M. Loughin, K.J. Koehler. Application of Cox Regression with a Change Point in Clinical Studies X. Luo, et al. Burn-in with Age Replacement A.W. Marshall. Fitting Cox's Proportional Hazards Model Using Grouped Survival Data I.W. McKeague, M.-J. Zhang. Statistical Methods for Dependent Competing Risks M.L. Moeschberger, J.P. Klein. Orthogonal Functions of Inverse Gaussian Disbrituions R. Nishii. Statistical Models for Quality of Life Measures Y. Palesch, A.J. Groos. Nonparametric Estimation of Regression Parameters from Censored Data with Two Discrete Covariates M.H. Rahbar. Locally Efficient Median Regressionwith Random Censoring and Surrogate Markers J.M. Robins. Survival Models for Heterogeneity Using the Non-Central Chi-Squared Distribution with Zero Degrees of Freedom C.S. Rocha. Efficiently Weighted Estimating Equations with Application to Proportional Excess Hazards P. Sasieni. Sequential Multi-Hypothesis Testing in Software Reliability J.S. Shieh, Y.L. Tong. Assessing Gamma Frailty Models for Clustered Failure Time Data J.H. Shih,

Engineering fuzzy heat conduction problem with subjective uncertainties in input parameters constitutes a significant challenge. Based on fuzzy and interval theory, this paper presents novel numerical methods to efficiently identify the effect of fuzzy uncertainty on the system reliability analysis and optimization design. Firstly using the interval ranking strategy, the interval safety possibility in the transition state can be precisely quantified, and the eventual fuzzy safety possibility is calculated by integral operation. Then a fuzzy reliability-based optimization model is established with considerable computational cost caused by the two-layer nested loop. In order to improve the computational efficiency, a subinterval perturbation method based on the first-order Taylor series is presented to replace the inner loop. Comparing numerical results with traditional reliability model, two numerical examples are provided to evidence the superiority of proposed model and method for fuzzy reliability analysis and optimization in practical engineering.

Quantifying coal rib stability and support requirements using bonded block modeling and reliability analysis based on the random set theory

This paper examines multi-platform phased missions, which involves a number of platforms working together to achieve a common objective. A simulation model for multi-platform phased mission system reliability analysis is proposed. The model simulates the fault processes of various platforms within mission life by using a modularized multi-platform phased mission system model. With the Monte Carlo method together, the reliability of entire mission and mission phases can be analyzed. A hypothetical example system is used to show the application of this simulation model and the result exhibits that the reliability conditions of system within the mission and each mission phase can be evaluated and controlled effectively.

The capabilities of smart meters and the potential vulnerabilities they introduce make the Advanced Metering Infrastructure (AMI) a critical components of the Smart Grid. A virus propagating among meters and massively issuing remote disconnect commands could have catastrophic consequences. To understand and assess the risk posed by a given set of meter devices getting compromised, we introduce a novel modeling approach based on fuzzy Markov chain. Markov modeling is one of the main approaches used to analyze the reliability of critical systems. Markov models are usually analyzed using mathematical approaches or Monte-Carlo Simulation. For large and complex systems, traditional Markov models suffer from the state explosion problem and quickly become intractable. The key idea of our approach to solve this issue in the context of the smart grid is to leverage the hierarchical topology of AMI to build a high-level model where components represent Neighborhood Area Networks (NAN) instead of individual meters. The fuzzy Markov formalism enables our solution to take into account gradual component degradation. We propose a Fuzzy Markov Model (FMM) for reliability analysis of a Smart Grid. The reliability of each NAN is represented by a number in [0, 1] which denotes the state of that component in the FMM.We define the transition probabilities between states of the fuzzy Markov model based on the fuzzy time-to-failure value for each NAN. We utilize the Fuzzy Monte Carlo Simulation (FMCS) approach to calculate the fuzzy time-to-failure value of each NAN. Our proposed method enables us to assess the reliability of the entire AMI at the meter level while keeping the model manageable.

Due to multiple implicit limit state functions needed to be surrogated, adaptive Kriging model for system reliability analysis with multiple failure modes meets a big challenge in accuracy and efficiency. In order to improve the accuracy of adaptive Kriging meta-model in system reliability analysis, this paper mainly proposes an improved AK-SYS by using a refined U learning function. The improved AK-SYS updates the Kriging meta-model from the most easily identifiable failure mode among the multiple failure modes, and this strategy can avoid identifying the minimum mode or the maximum mode by the initial and the in-process Kriging meta-models and eliminate the corresponding inaccuracy propagating to the final result. By analyzing three case studies, the effectiveness and the accuracy of the proposed refined U learning function are verified.

This paper is devoted to the use of a proportional hazards model (PHM) for reliability analysis of solder joints through two case studies: a drop-impact test and a vibration test. The lifetime data collected under various load conditions can be integrated in establishing a PHM for reliability analysis of solder joints. PHM has the capability of evaluating the influence of load conditions (e.g. drop height, power spectrum density in random vibration) on the life span of solder joints. Using this capability, this paper focuses on the implementation of PHM for estimating the reliability characteristics (MTTF and probability density function (p.d.f.) of failure) of solder joints whose load conditions are not contained in the training dataset of the PHM. In comparison with the naive use of lifetime data by simply ignoring the effect of load conditions, the two case studies verify the effectiveness of PHM in providing consistent reasonable estimation of the reliability characteristics of solder joints. The perspectives and the procedures of the use of PHM in this paper are generic and can be directly adopted for other systems/products.