International Journal of Reliability and Safety (11 papers in press)
Integrated Bayesian probabilistic approach to improve predictive modelling
by Xiaofei Guan, Xiaomo Jiang, Yucheng Tang, Xueyu Cheng, Yong Yuan
Abstract: This paper presents an integrated Bayesian probabilistic methodology and procedure to calibrate parameters of an analytics predictive model and quantitatively evaluate its validity and predictive capacity with non-normality data, considering uncertainties in both model and data. Bayes network is developed to graphically represent the relationships of all variables in the computational model. Bayesian regression theory associated with Markov Chain Monte Carlo technique and Gibbs sampling is developed to calibrate the model parameters for improving prediction accuracy. The Bayesian method is compared to traditional maximum likelihood and nonlinear optimization approaches in terms of parameter calibration. A generic procedure is presented to integrate the model calibration and quantitative validation. Hypothesis testing based validation requires the validation data to be normally distributed. The Anderson-Darling goodness-of-fit test and Box-Cox transformation are employed, respectively, to perform the normality hypothesis test of validation difference data and data normality conversion. Both classical and Bayesian hypothesis testing approaches are utilized to quantitatively assess the calibrated models. The confidence of evaluating the calibrated model is quantified via the Bayesian inference method, which facilitates the decision making on the model quality under uncertainty. The integrated methodology and procedure is demonstrated with a nonlinear computational model for pressure loss prediction in a gas turbine and five sets of different measurement data.
Keywords: Bayesian statistics; Bayes network; hypothesis testing; model calibration; model validation.
Necessary and sufficient conditions for calculus of variations under interval uncertainty
by Mohammad Heidari, Mohadeseh Ramezanzaeh
Abstract: In this paper, a complete investigation of necessary and sufficient conditions is discussed on the variational problems under interval uncertainty. More precisely, it is shown that, based on the parametric representation of an interval, proposed by Ramezanzadeh et al. , the interval variational problems can be interpreted as a set of classical variational problems. Finally, to show the ability and significance of this point of view on the necessary and sufficient conditions, two comprehensive examples are proposed, more specifically the hanging cable problem.
Keywords: interval-valued function; parametric representation; calculus of variations; Euler-Lagrange equation; sufficient condition.
Modelling composite performance variable of deteriorating systems using empirical evidence and artificial neural network
by Paul Amaechi. Ozor, Samuel. O. Onyegegbu, Jonah. C. Agunwamba
Abstract: The use of operational and environmental conditions combined with artificial neural networks (ANN) to model the composite performance of deteriorating systems is presented. The proposed variable is obtained by combination of reliability, availability, maintainability and profitability (RAMP). Probability distributions and empirical evidence observed on an example repairable system, namely centrifugal pumps at the gas plant of an energy company, were relied upon to model the operation process. The results show that the input variables preventive maintenance, spare parts availability, efficiency of operating personnel and efficiency of maintenance personnel, with cumulative performance enhancement of 56.1%, 39.97%, 30.8% and 30.6%, respectively, improve RAMP appreciably. The results also show that proper assessment and control of the input variables administrative delays, repair period, service crew strength and mostly environmental factors with cumulative performance enhancement of 23.6%, 19.4%, 17.3% and -14.62%, respectively, had significant potential for improving RAMP further.
Keywords: repairable system; failure data; probability distribution; artificial neural network; composite performance variable; maintenance policies.
Simulation of a non-stationary gamma wear process
by Anil Rana
Abstract: All mechanical components suffer from monotonically increasing wear/deterioration. A non-stationary gamma wear process can model such wear by taking care of the temporal variability in the wear phenomenon; however, this makes the shape parameter of the gamma process a function of time leading to a problem in its simulation, especially so in the presence of other competing failure modes. This paper presents a method by which one can map a non-stationary gamma wear process to a mixed exponential process and demonstrate its suitability for analysis through a simulation package involving use of stochastic Petri nets. A stochastic Petri net simulation package Timenet compares the result of the above method with the analytically determined result through a Matlab program. The originality of the paper lies in demonstration of a method for analysis of a non-stationary gamma wear process through a simulation package.
Keywords: non-stationary gamma wear process; simulation; failure process; stochastic petrinets.
Model validation based on random set theory
by Zhao Liang
Abstract: This paper considers the model validation under epistemic uncertainty in model inputs. The random set theory is used to quantify the uncertainty of model prediction. With the probability box obtained by the random set theory, a pignistic probability transformation is applied to construct a single probability distribution to be the prior distribution for the model prediction. Then a posterior probability distribution is updated based on the experimental observations in Bayesian principle. The Bayes factor derived from the ratio between the posterior and the prior probability density is used as the validation metric to quantify the extent to which the experimental observations support the model. A thermal conduction example and an aerospace bolted joint example are presented to illustrate the proposed method. It is shown that the method presented in this paper provides a convenient mechanism to consider different types of uncertainty during the model validation.
Keywords: model validation; random set theory; uncertainty quantification; pignistic probability; Bayes factor.
Reliability analysis of Finometer and AGE Reader devices in a clinical research trial
by Anna Deltsidou, Vasilios Zarikas, Dimos Mastrogiannis, Eleni Kapreli, Dimitrios Bourdas, Elpiniki Papageorgiou, Vasilios Raftopoulos, Maria Noula, Maria Lambadiari, Katerina Lykeridou,
Abstract: Fundamental issues emerging from the widespread use of non-invasive techniques in healthcare sciences research are the reliability and validity. This work presents the reliability analysis of a clinical trial that uses Finometer and AGE Reader devices. The aim is to provide a self-consistent and meaningful reliability analysis concerning the Finometer and AGE Reader devices, something that is often missing in the research field of healthcare sciences, and to present results filling up this gap. Since four raters are used for taking measurements in this study, the presented reliability analysis includes tests for the raters as well as for the instruments internal consistency. It was found that both the reported inter-rater reliability and instruments reliability of internal consistency are adequately high. In conclusion, Finometer and AGE Reader devices showed high reliability. Results can be used as a concrete basis for future studies using these devices.
Keywords: reliability analysis; Finometer; AGE Reader; internal consistency.
Reliability evaluation for wireless sensor network with clustering structure based on universal generating function
by Qiang Liu, Hailin Zhang, Wei Su, Yanbo Ma
Abstract: A Hierarchical Weighted Voting System (HWVS) model is established to describe the process of data transmission on the wireless sensor network (WSN) whose topology is cluster. Definitions about the reliability of a sensor node, cluster and the whole HWVS are presented. Based on universal generating function technique, an algorithm is suggested for evaluating the reliability of HWVS. Through the analysis of three examples using suggest algorithm, some conclusions are obtained for improving the WSN reliability.
Keywords: universal generating function; hierarchical weighted voting system; wireless sensor network; LEACH; reliability;.
Goodness-of-fit test for generalised renewal process
by Rajiv Nandan Rai, Garima Sharma
Abstract: Goodness-of-Fit (GOF) tests for non-repairable systems as modelled through exponential, Weibull, normal and lognormal failure distributions are well touched upon in the literature. Substantial efforts have been made in developing GOF tests for non-repairable systems and Non-Homogeneous Poisson Processes (NHPP) modelled through Power-Law Process (PLP). However, the literature is found to be limited in developing GOF models for imperfect repair modelled through Generalised Renewal Process (GRP). This paper, besides reviewing six trend tests, also develops a GOF test for repairable systems modelled through GRP based on Kijima I (KI) virtual age concept. KI takes into consideration the effect of repair effectiveness along with the shape and scale parameters. The developed GOF test model is a modification of the present Cramer-Von Mises (CVM) GOF test model available for PLP. The efficacy of the model is demonstrated with the help of three failure datasets.
Keywords: goodness-of-fit tests; virtual age; Kijima I; power-law process; generalised renewal process; repair effectiveness index; Cramer-Von Mises GOF test; maximum likelihood estimators; ero engine; significance Level.
Reliability estimation of a photovoltaic system using Markov process and dynamic programming approach
by Sonal Sindhu, Vijay Nehra, S.C. Malik
Abstract: Adoption of solar energy is still at early stage and has failed to reach the expected level because of the presence of several impeding factors lying in its diffusion path. One of the major impediments in adoption of Photovoltaic (PV) systems is low efficiency due to frequent failures. With the worldwide growth of renewable energy, the importance of the reliability and stability is getting close attention. The present study is oriented towards deriving the reliability measures of a PV system made up of three subsystems, i.e. PV array, inverter and transformer connected in series. The behaviours of Mean Time to System Failure (MTSF), availability and cost benefit function have been analysed graphically. The investigation reveals that inverter failure affects the performance of PV system in a significant manner. To fix this issue, the Dynamic Programming Approach (DPA) has been applied and 95% reliability has been achieved.
Keywords: photovoltaic system; exponential distribution; Markov process; reliability measures; MTSF; availability; cost benefit function; regenerative point technique; dynamic programming approach.
Special Issue on: IJRS REC2016 Computing with Polymorphic Uncertain Data
Uncertainty assessment in the results of inverse problems: application to damage detection in masonry dams
by Long Nguyen-Tuan, Carsten Koenke, Volker Bettzieche, Tom Lahmer
Abstract: In this work, we study the uncertainties in the results of inverse problems. The inverse problems solve damage identification problems in multifield-multiphase problems for fluid-flow problems in deforming porous materials under non-isothermal boundary conditions. These analyses are important within the structural health monitoring of masonry dams. Results of the inverse problems show a scatter due to different sources of uncertainties in model parameters, measurement data, field of measurements, and in the solving algorithms of the inverse problem. In order to see and analyse the scatter, the inverse problem is solved repeatedly by a sampling process. The uncertainty in the inverse solutions can be quantified by their probability distributions according to the sampling results.
Keywords: damage identification; masonry dams; optimisation; uncertainty quantification; random field.
Numerical simulation of wooden structures with polymorphic uncertainty in material properties
by Ferenc Leichsenring, Christian Jenkel, Wolfgang Graf, Michael Kaliske
Abstract: Uncertainties are inherently present in structural parameters such as loadings, boundary conditions or resistance of structural materials. Especially material properties and parameters of wood are strongly varying in consequence of growth and environmental conditions. The considered uncertainties can be classified into aleatoric and epistemic uncertainty. To include this variation in structural analysis, available data need to be modelled appropriately, e.g. by means of probability and, furthermore, fuzzy probability based random variables or fuzzy sets. Therefore, a limited empirical data basis for Norway spruce, obtained by experiments according to DIN EN 408, is stochastically analysed including correlation-, sensitivity-analyses and statistical tests. In order to comprehend uncertainties induced by estimating the distribution parameters, the stochastic approach has been extended by fuzzy distribution parameters to fuzzy probability based random variables according to [1, 2]. To cope with epistemic uncertainties for e.g. geometric parameters of knotholes, fuzzy sets are used. The consequence for wooden structures is determined by fuzzy stochastic analysis  in combination with a Finite Element (FE) simulation using an model suitable for characteristics of a timber structure by . The uncertain results (e.g. displacements, failure loads) constituted by the proposed holistic approach defining the material properties based on an empirical data basis and the attempt of representing the uncertainties in material parameters and methods itself will be discussed.
Keywords: polymorphic uncertainty; fuzzy randomness; stochastic modelling;rnwood mechanics; structural analysis.