Reliability Of Repairable Systems Research Articles

On Reliability of Repairable Hot Double Redundant System with Arbitrarily Distributed Life- and Repair Times of Its Elements

The article introduces the concept of Marked Markov processes, which are used to study a repairable hot double redundant system with a single repair facility. It is assumed that components’ life- and repair times follow arbitrary distributions. The proposed approach allows for calculating the system’s reliability function, and its mean lifetime, as well as conducting the sensitivity analysis to the shape of input distributions. The new method was validated with numerical examples by comparing it with previously obtained analytical results and showed high accuracy.

Reliability and availability analysis of high-altitude platform stations through semi-Markov modeling

In the development and deployment of both tethered and autonomous High Altitude Platform Station (HAPS), flight modules such as hexacopter and octocopter with 6 or 8 rotors are most often used. The primary focus of this article is to compute the reliability of tethered HAPS by analyzing the effectiveness of their redundant rotor systems. To measure the performance of such systems, it is convenient to consider mathematical models as k-out-of-n models. Although Markov models have extensively been reported to analyze the reliability of repairable k-out-of-n models, this work introduces an alternative and more thorough methodology. In this work, a semi-Markov model (SMM) is proposed to calculate the probability of rotors being operational after the failure of some rotors in order to analyze system reliability. We emphasize that an SMM model is more appropriate as it provides a more accurate assessment of the probability of system failure over time through non-exponential sojourn time. Further, the efficacy of the proposed SMM is studied through the evaluation of steady-state availability, mean time to failure and reliability. Overall, the findings of this study enhance our comprehension of the reliability of repairable systems and extend the existing knowledge base of HAPS reliability analysis.

Bayesian estimation of the mean time between failures of subsystems with different causes using interval‐censored system maintenance data

AbstractEnsuring an acceptable level of reliability stands as a primary imperative for any mission‐focused operation since it serves as a critical determinant of success. Inadequate reliability can lead to severe repercussions, including substantial expenses for repairs and replacements, missed opportunities, service disruptions, and in the worst cases, safety violations and human casualties. Within national defense organizations such as the USAF, the precise assessment and maintenance of system reliability play a pivotal role in ensuring the success of mission‐critical operations. In this research, our primary objective is to model the reliability of repairable subsystems within the framework of competing and complementary risks. Subsequently, we construct the overall reliability of the entire repairable system, utilizing day‐to‐day group‐censored maintenance data from two identical aircraft systems. Assuming that the lifetimes of subsystems follow non‐identical exponential distributions, it is theoretically justified that the system reliability can be modeled by homogeneous Poisson processes even though the number of subsystems of any particular type is unknown and the temporal order of multiple subsystem failures within a given time interval is uncertain due to interval censoring. Using the proposed model, we formulate the likelihood function for the mean time between failures of subsystems with different causes, and subsequently establish an inferential procedure for the model parameters. Given a considerable number of parameters to estimate, we explore the efficacy of a Bayesian approach, treating the contractor‐supplied estimates as the hyperparameters of prior distributions. This approach mitigates potential model uncertainty as well as the practical limitation of a frequentist‐based approach. It also facilitates continuous updates of the estimates as new maintenance data become available. Finally, the entire inferential procedures were implemented in Microsoft Excel so that it is easy for any reliability practitioner to use without the need to learn sophisticated programming languages. Thus, this research supports an ongoing, real‐time assessment of the overall mission reliability and helps early detection of any subsystem whose reliability is below the threshold level.

Assessment of Reliability of Power Systems Under Adverse Weather Condition Using Markov System Dynamic Method

Abstract We aim to extend the Markov System Dynamic method (MSD) to evaluate the reliability of repairable systems in two-state weather (2SW) models. Increasing the number of components in real practices has limited the use of the Markov method, because of increasing the number of equations and the complexity of the problem. There is no such restriction in the MSD method. Thus, it can be applied to complex systems. Theoretically, we indicate that the 2SW model is a type of linear dynamical system. Therefore, we can use MSD to solve it. Through an example, the validity of the proposed method is confirmed in comparison to the Markov method for the 2SW model. Since the MSD method does not use equations, it can be a preferred alternative for calculating the reliability of 2SW models. Accordingly, we apply the MSD method for assessing the reliability of a four-component system.

Reliability of repairable systems with Non-Central Gamma frailty

Maintenance actions on industrial equipment are essential to reduce expenses associated with equipment failures. Based on a well-fitted model, it is possible, through the estimated parameters, to predict several functions of interest, such as the cumulative average and reliability functions. In this paper, a new frailty model is proposed to analyze failure times of repairable systems subject to unobserved heterogeneity actions. The Non-Central Gamma distribution is assumed to the frailty random variable effect. The class of minimal repair models for repairable systems is explored considering an approach that includes the frailty term to estimate the unobserved heterogeneity over the systems’ failure process. Classical inferential methods were used to parameter estimation and define the reliability prediction functions. A simulation study was conducted to confirm the properties expected in the estimators. Two real-world data known in literature were used to illustrate the estimation procedures and validate the proposed model as a viable alternative to those already established in the literature. The results obtained highlight the potential of our proposed approach, particularly for industries dealing with such systems, where unquantifiable factors may impact equipment failure times.

A Cocktail of Bidirectional Tests for Power Symmetry and Repairable System Reliability

To a practitioner who chooses to test the robustness while keeping track of all the perspectives, angles, and elements of a study's conclusions in the data analysis, we offer an option between a cocktail of tests (a quintet) and a solo one-size-fits-all test as a needed antidote to power asymmetries evidenced by real data and simulations characterized by a variety of alternative distributions and two sampling schemes. The strategy is to be considered in equipment performance assessments of repairable systems and, by implication, other applications. Two bidirectional tests are first established to empower a basic pair of tests, documented in the literature as tests with asymmetrical performances. Unsurprisingly, we have seen either bidirectional device championing in one alternative setting but also being turned against the very setting altered with just one of the composed elements. Progressing by filtering out the bad and enhancing the good, we assemble a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> -value-induced dual bidirectional hybrid from the empowered pair to streamline the statistical data robustness analysis and restore power symmetries. Data elaborated by the maximum power deficits, made for facilitating the power comparisons and acknowledging the asymmetries, certify that the hybrid is robust with essential quality assurance in addition to a user-friendly version for the practitioners conducting the work.

GENERAL PRINCIPLES OF FORECASTING THE RELIABILITY OF COMPLEX TECHNICAL SYSTEMS IN THE OIL AND GAS INDUSTRY

In the oil and gas industry, various high-risk facilities operate, among which pipeline systems occupy a leading position due to their specific characteristics (structural, technological, operational conditions, etc.).&#x0D; Pipeline systems, distributed over a large area, are characterized by a high level of risk of emergencies. Therefore, the risk analysis of accidents and failures, the main essence of which is to identify hazards and assess the possibility of their occurrence, is a crucial part of the industrial safety management system of technical systems (TS) [1]. One of the main tasks of this system is to prevent the possibility of accidents and failures, i.e., to ensure reliability. The authors emphasize the importance of assessing the reliability of high-risk objects, both when put into operation and during their operation. It is noted that reliability management during the operation stage can be carried out by determining the optimal allowable deviations of structural parameters of the technical condition and other measures. The paper provides an overview of key quantitative reliability indicators, such as the reliability function and the "unreliability function," and discusses their significance in determining failure probabilities and life-to-failure. Changes in failure intensity according to the Weibull distribution and the exponential distribution law are examined in detail. Reliability indicators for non-repairable systems include the probability of non-failure operation, failure intensity, and mean time to failure, while maintainability indicators for repairable systems are the probability of recovery and mean recovery time. The comprehensive indicator of the reliability of repairable systems is determined through the coefficient of operational readiness. The conclusions of the paper highlight the importance of using statistical data and reliability indicators to assess systems and components, in particular the oil and gas pipeline systems in Europe, which have significant importance for industrial safety and the reliability of technical facilities.

Reliability analysis of a two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system

Most of the existing studies on the two-dimensional consecutive system have focused on the non-repairable case. Nevertheless, considering the repairable case of components in engineering, it is necessary to study the reliability of the two-dimensional consecutive repairable system. Owing to the more complex spatial structure of the two-dimensional consecutive system, the analysis methods of the one-dimensional consecutive repairable system are not applicable to the two-dimensional case. In this work, we give a general method to analyze the reliability of a two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system. Firstly, to calculate the number of different cases of the system in a certain state, a key issue in the analysis of the consecutive repairable system, we propose the sliding window search method and inverse search method, whose computational complexities are compared and correctness is verified. Next, under the assumption that the repair time follows a general distribution, we analyze the reliability of the two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system using the supplementary variable method. Finally, we use an example of a wireless sensor network to analyze the effects of system parameters on system reliability indices, such as steady-state availability, steady-state failure frequency, and MTTFF.

The ENBIS‐21 quality and reliability engineering international special issue

The ENBIS-21 Quality and Reliability Engineering International Special Issue is related to the contributions to the 21st Annual Conference of the European Network for Business and Industrial Statistics (ENBIS) held online from 13 to 15 September, 2021. The topics covered by the 12 papers included in this special issue fall within the scope of ENBIS, whose ultimate goal is to bridge the gap between methodology and application in the field of business and industrial statistics and foster networking between statisticians in academic and commercial settings. It becomes evident from the papers on this issue that classical methods of industrial statistics are still having a wide range of applications and expansions towards complex and big data structures as well as they are increasingly cross-fertilized by artificial intelligence and machine learning perspectives and approaches. The issue is opened by the contribution of Yang et al.1 in the Statistical Process Monitoring (SPM) of data in the form of tensors. The authors develop a hierarchical in-situ process monitoring approach for anomaly detection, which is applied to thermal video streams acquired during a metal additive manufacturing process for highly complex parts. A more traditional SPM approach based on generalized likelihood ratio (GLR) control charts is elaborated by Rizzo and Di Bucchianico2 to set up tailor-made monitoring for high-purity (high-quality) processes and deals with issues arising in GLR control charts for discrete processes. Along the line of developing statistical methods for complex data structures, Gril et al.3 set up a tensor-on-tensor regression model able to dynamically predict repetitive human motions helpful in avoiding unwanted collisions at the interface with robots in industrial assembly tasks. Chuquin et al.4 present a straightforward extension of the K-means clustering to spatially correlated functional data, with an application in the analysis of the normalized difference vegetation index in a large region of Ecuador. From a more general perspective, Vanacore et al.5 address the problem of assessing prediction performance in the multi-class classification of imbalanced data sets. In the optimal Design of Experiments (DoE) Pesce et al.6 offer new results that are oriented to bias reduction in large datasets and protection against confounders. Whereas, Kirchhoff et al.7 use DoE as the initial solution for the optimization of shift planning in high-bay warehouse operations based on Gaussian process models with low-rank correlation kernels. Risk assessment and management is the topic of the following three papers. Testik and Unlu8 compare traditional and fuzzy failure modes and effect analysis to rank risks in different areas of testing and calibration laboratories. Meynaoui et al.9 deal with an accidental scenario in a sodium-cooled fast nuclear reactor by means of a global sensitivity analysis of the input parameter distribution used in numerical simulator outputs to model physical phenomena. Lai and Zwetsloot10 offer a data-driven ensemble ranking system of product quality, which is validated in the identification of high-risk manufacturers in a solar industry case study. The final two papers are devoted to the Reliability and Maintenance of repairable systems. El-Aroui and Gaudoin11 propose a general goodness-of-fit test for imperfect repair models that has the favorable property of being asymptotically distribution-free for renewal and power law processes. Fouladirad et al.12 develop a new bounded transformed gamma process model to describe and predict degradation phenomena by relaxing the typical assumption that the degradation level can grow indefinitely, which is often unrealistic for technological units. The proposed model is also applied to a set of wear measures of cylinder liners that equip a diesel engine for marine propulsion. We are deeply grateful to the journal staff for their professional assistance in the editorial process, as well as to the anonymous referees for the time and effort spent to provide careful and constructive comments, and to all the authors, who made revisions on a very tight timescale.

Novel approach to analyse vague reliability of repairable industrial systems

The purpose of the study is to develop some novel approaches to evaluate the vague reliability of repairable industrial systems by considering uncertainty and hesitation factors in data assessment. The paper introduces two novel vague reliability assessment techniques, named as generalized vague lambda-tau methodology (GVLTM), and generalized Tω (weakest t-norm) based vague lambda-tau methodology (GTBVLTM). These two techniques commonly apply fault-tree analysis, the lambda-tau method, and vague sets with different shapes for different components of a system. To compute system vague reliability, the GVLTM applies α-cut and interval arithmetic operations, whereas GTBVLTM employs α-cut and Tω coupled arithmetic operations defined on vague sets. To demonstrate the effectiveness of the developed approach, both proposed techniques and five other existing techniques are applied to analyse the vague reliability of a washing system in a paper plant. Long run reliability assessment, sensitivity analysis, and ranking of the system’s critical components have also been conducted to improve its performance. Results concluded that the proposed techniques are simple, easy to apply, and provide optimized vague reliability indices, when different vague sets for different components are applied to handle uncertainty and hesitation factors in data. Results can be used to design suitable action plans to enhance system performance.

A Log-weighted Power Function Distribution and Its Statistical Properties

The Power function distribution is a flexible life time distribution that has applications in finance and economics. It is, also, used to model reliability growth of complex systems or the reliability of repairable systems. A new weighted Power function distribution is proposed using a logarithmic weight function. Statistical properties of the weighted power function distribution are obtained and studied. Location measures such as mode, median and mean, reliability measures such as reliability function, hazard and reversed hazard functions and the mean residual life are derived. Shape indices such as skewness and kurtosis coefficients and order statistics are obtained. Parametric estimation is performed to obtain estimators for the parameters of the distribution using three different estimation methods; namely: the maximum likelihood method, the L-moments method and the method of moments. Numerical simulation is carried out to validate the robustness of the proposed distribution.

Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns

This study involves the evaluation of the availability and reliability of a repairable system containing warm standby components and undergoing switching failure under a Markovian environment. A single repairperson is responsible for repairing failed components. As soon as the system is free of failed components, the repairperson takes multiple vacations. The repairperson is also subject to breakdown while repairing failed components. When the repairperson experiences a breakdown, there is a probability of 1−δ that he/she is sent for recovery, or a probability of δ that he/she continues to work at a lower rate. For the Markov model, we establish a finite set of differential equations governing the repairable system. A numerical approach based on the Runge–Kutta method is employed to solve the differential equations. Numerical solutions for the time-dependent availability can then be obtained. For the reliability model, we use the Laplace transform method to find the explicit form of the reliability function and the mean time to failure (MTTF) of the system. Finally, we conduct a numerical sensitivity analysis of the time-dependent availability, system reliability and MTTF with respect to various system parameters.

Reliability Assessment of Repairable Systems Using Simple Regression Models

The statistical nature of failures in repairable systems does not have a behaviour similar to non-repairable systems. The statistical models developed for the study of the reliability of repairable systems mostly based on the application of stochastic processes. However, there is a group of prediction models for reliability based on time series analysis. Below are the results and conclusions of the application of simple regression models in the escalators Avante model (TNE), in order to assess their potential use by maintenance organizations.

Reliability assessment of repairable closed-loop process systems under uncertainties

System reliability assessment plays a crucial role in making maintenance decisions and reducing hazard frequencies. Although many engineering methods can effectively evaluate the process reliability, most of them are often unreasonable for closed-loop systems because of the combination of closed-loop structures, maintenance characteristics, and dynamic failure mechanisms. Also, uncertainties generally exist in the reliability assessment due to the insufficient reliability data and expert knowledge. Therefore, an integrated approach is proposed in present works to assess the dynamic reliability of repairable closed-loop systems with the consideration of uncertainties. Firstly, Bayesian inference and fuzzy theorem are developed to characterize system uncertainties and estimate lifetime parameters of components. After that, a closed-loop probabilistic reliability assessment (CPRA) method is proposed for the dynamic reliability assessment of closed-loop systems by integrating cyclic Bayesian network modeling and dynamic Bayesian network solving. Besides, a novel non-probabilistic reliability assessment (NPRA) approach based on the probabilistic method and Monte Carlo simulation is presented to make maintenance decisions for repairable systems. Finally, an application of reliability assessment for the offshore crude oil separation system is introduced to verify the proposed methods.

Nonzero repair times dependent on the failure hazard

AbstractIt is common in the literature on the reliability and maintenance of repairable systems to model the repair times as instantaneous. However, this is an unreasonable assumption for some complex systems, especially those requiring a high level of reliability, and such systems may spend a significant proportion of their lifetimes under maintenance and repair. We model the ageing of such a system with alternating stochastic processes. Operational times are generated at random and may have an increasing failure rate. Repair times are generated from a random process where the repair time is related to the hazard rate at failure. This yields lengthened repair times at late stages in a system subject to an increasing failure hazard rate but also accommodates long repair times at young ages in systems with a bathtub‐shaped hazard rate function. We derive analytic results for a set of special cases of the model, show how simulation and inference can be carried out, and apply our method to real data from a large car manufacturer.

Reliability of repairable multi-state two-phase mission systems with finite number of phase switches

In this article, a repairable multi-state two-phase mission system with finite number of phase switches is considered. System states can be divided into a subset of working states and a subset of failed states, and the system can be repaired from the failed subset to the working subset. However, when the number of switches between two phases exceeds a specified integer, the system will be permanently damaged and cannot be repaired any more. The closed-form formulas of the probability density function of the time to first failure of the system, the point-wise availability, the interval availability and other reliability indexes are obtained by using the theory of aggregated stochastic processes. Finally, a detailed example of lithium-ion batteries is given to illustrate the proposed model and obtained results.

Analysis of Large Heterogeneous Repairable System Reliability Data With Static System Attributes and Dynamic Sensor Measurement in Big Data Environment

ABSTRACTIn the age of Big Data, one pressing challenge facing engineers is to perform reliability analysis for a large fleet of heterogeneous repairable systems with covariates. In addition to static covariates, which include time-invariant system attributes such as nominal operating conditions, geo-locations, etc., the recent advances of sensing technologies have also made it possible to obtain dynamic sensor measurement of system operating and environmental conditions. As a common practice in the Big Data environment, the massive reliability data are typically stored in some distributed storage systems. Leveraging the power of modern statistical learning, this article investigates a statistical approach which integrates the random forests algorithm and the classical data analysis methodologies for repairable system reliability, such as the nonparametric estimator for the mean cumulative function and the parametric models based on the nonhomogeneous Poisson process. We show that the proposed approach effectively addresses some common challenges arising from practice, including system heterogeneity, covariate selection, model specification and data locality due to the distributed data storage. The large sample properties as well as the uniform consistency of the proposed estimator are established. Two numerical examples and a case study are presented to illustrate the application of the proposed approach. The strengths of the proposed approach are demonstrated by comparison studies. Datasets and computer code have been made available on GitHub.

Modelling and evaluation of multi-state reliability of repairable non-series manufacturing system with finite buffers

The capacity and capability of flexible manufacturing system varies with different market demands. To satisfy the requirements of performance expressions, avoid the problem of combinatorial explosion and consider the influence of intermediate buffer stations, a new reliability modelling and evaluating methodology for repairable non-series hybrid flexible manufacturing systems with finite buffers is proposed using an extended vector universal generating function technique. For repairable modular machines, the Markov models of modular machines are established using stochastic process analysis and the corresponding theoretical steady-state probability in various states is obtained. Furthermore, the original system in combination with multi-state reliability measures of buffer stations is equivalent to a system with independent machines which can be expressed by vector u-functions. Based on the probability distributions of the states of subsystems, the composition operators for series connections and parallel connections are defined. Consequently, the entire system is simplified to one component represented by the polynomial universal generating function. In particular, reliability indicators and measurement models are given to assess the system’s reliability through promoting the basic ones. Finally, a practical case of engine head machining line is utilized to verify the effectiveness of the method. The results demonstrate that the use of vector universal generating functions can describe the system structure and states more appropriately while providing efficient assessment.

Numerical Estimation of Expected Number of Failures for Repairable Systems Using a Generalized Renewal Process Model

The reliability of repairable systems is important for many engineering applications such as warranty forecasting, maintenance strategies, and durability, among others. A generalized renewal process (GRP) approach, considering the effectiveness of repairs, is commonly used, modeling the concepts of minimal repair, perfect repair, and general repair. The effect of the latter is between the effects of a minimal and a perfect repair. The GRP models the sequence of recurrent failure/repair events for repairable systems by solving the so-called g-renewal equation, which has no analytical solution. This paper proposes a data-driven numerical estimation of the expected number of failures (ENF) for the GRP model without solving the complicated g-renewal equation directly. Instead, it uses an empirical relationship among the cumulative intensity function (CIF) of the GRP, ordinary renewal process (ORP), and nonhomogeneous Poisson process (NHPP). The ORP and NHPP are limiting cases of the generalized renewal process. For practical reasons, it is common to observe only a few units of a repairable system population for only a short time. Using the observed data, the proposed approach creates a reliability metamodel of a renewal process, which is then used to predict the expected number of failures, and assess the average effectiveness of each repair. This increases the usefulness of the method for many practical reliability problems where the collection of a large amount of data is not possible or economical. The good accuracy of the proposed approach is demonstrated with three examples using simulated data, and a real-life example of locomotive braking grids using actual data.

Analysis of repairable systems with severe left censoring or truncation

ABSTRACTLeft censoring or left truncation occurs when specific failure information on machines is not available before a certain age. If only the number of failures but not the actual failure times before a certain age is known, we have left censoring. If neither the number of failures nor the times of failure are known, we have left truncation. A datacenter will typically include servers and storage equipment installed on different dates. However, data collection on failures and repairs may not begin on the installation date. Often, the capture of reliability data starts only after the initiation of a service contract on a particular date. Thus, such data may exhibit severe left censoring or truncation, since machines may have operated for considerable time periods without any reliability history being recorded. This situation is quite different from the notion of left censoring in non-repairable systems, which has been dealt with extensively in the literature. Parametric modeling methods are less intuitive when the data has severe left censoring. In contrast, non-parametric methods based on the Mean Cumulative Function (MCF), recurrence rate plots, and calendar time analysis are simple to use and can provide valuable insights into the reliability of repairable systems, even under severe left censoring or truncation. The techniques shown have been successfully applied at a large server manufacturer to quantify the reliability of computer servers at customer sites. In this discussion, the techniques will be illustrated with actual field examples.