Models For Repairable Systems Research Articles

Frailty model for multiple repairable systems hierarchically represented subject to competing risks

In this paper, we propose a statistical model to describe the behaviour of failure times associated with groups of repairable systems hierarchically represented, under a competing risks framework, considering the existence of unobserved heterogeneity that acts individually on systems of each group, as well as the possibility of imperfect repairs whose initial failure rate is in the form of the power law. In this context for the unobserved heterogeneity in the groups, we consider the multiplicative frailty. To illustrate the use of the proposed model, we consider a database with the failures of 38 agricultural machines categorized into five different groups. We understand that the tractor fleet corresponds to the farm's agricultural system, therefore the need for intervention in this system occurs with the failure of any unit, individually, in a serial structure, of competing risks.e On the other hand, the understanding of the time in which all the machinery that makes up the fleet will have required some intervention is obtained by analysing the results under a parallel structure.

Stochastic modeling and optimization of discrete-time cold standby repairable systems with unreliable repair facility and retrial mechanism

This study develops novel reliability models for discrete-time cold standby repairable systems with unreliable repair facility and retrial mechanism. In view of the situation that the state of some engineering systems cannot be continuously monitored, discrete distribution is used to describe the distribution of random variables involved in this paper. For the case that multiple events can occur simultaneously in the discrete-time system model, the priority order of multiple events occurring simultaneously is defined. Two different models are proposed based on two types of priority rules. The retrial mechanism of the components is considered in the case that the failure information of the system components cannot be successfully transmitted to the repair facility. The preventive maintenance (PM) and repair after the breakdown of the repair facility are considered. The key reliability indices are derived by using the iterative algorithm of the difference equation and the generative function method. The algorithms for calculating system state probability, key reliability indices and cost–benefit ratio (CBR) are designed. To demonstrate the impact of each parameter on the system reliability indices, numerical results are provided. The optimal repair rate configuration scheme is chosen using the Particle Swarm Optimization (PSO) algorithm to achieve the lowest possible CBR. The impact of the system model with or without PM on stationary availability and CBR is shown. In addition, the impact of the number of system components on a series of system performance indices is analyzed, and the optimal number of components of the system corresponding to the minimum value of CBR is obtained.

Reliability analysis of multiple repairable systems under imperfect repair and unobserved heterogeneity

AbstractImperfect repairs (IRs) are widely applicable in reliability engineering since most equipment is not completely replaced after failure. In this sense, it is necessary to develop methodologies that can describe failure processes and predict the reliability of systems under this type of repair. One of the challenges in this context is to establish reliability models for multiple repairable systems considering unobserved heterogeneity associated with systems failure times and their failure intensity after performing IRs. Thus, in this work, frailty models are proposed to identify unobserved heterogeneity in these failure processes. In this context, we consider the arithmetic reduction of age (ARA) and arithmetic reduction of intensity (ARI) classes of IR models, with constant repair efficiency and a power‐law process distribution to model failure times and a univariate Gamma distributed frailty by all systems failure times. Classical inferential methods are used to estimate the parameters and reliability predictors of systems under IRs. An extensive simulation study is carried out under different scenarios to investigate the suitability of the models and the asymptotic consistency and efficiency properties of the maximum likelihood estimators. Finally, we illustrate the practical relevance of the proposed models on two real data sets.

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.

Statistical Modeling of the Effectiveness of Preventive Maintenance for Repairable Systems

Preventive maintenance (PM) is commonly adopted in practice to improve a system’s health condition and reduce the risk of unexpected failures. When a PM action is poorly performed, however, it is likely to have adverse effects on system reliability. We observe this phenomenon when evaluating the effectiveness of a PM program for a fleet of service vehicles based on their four-year operating data. This phenomenon is also commonly reported in the maintenance of vehicles and aircraft. Motivated by this observation, we propose a statistical model for repairable systems by taking potential PM adverse effects into account. In the formulation, the baseline failure process without PM effects is modeled by a nonhomogeneous Poisson process. When a PM action is performed, its effect on the failure process is modeled as a multiplicative random effect on the system rate of occurrence of failures. Statistical inference under the proposed model is discussed, and we further develop goodness-of-fit test procedures to validate the adequacy of this model. The above-mentioned service vehicle operating data are used to demonstrate the proposed methods.

Imperfect maintenance modeling and assessment of repairable multi-component systems

Industrial systems are subject to several maintenance tasks during their operational life. To ensure optimal performance of these systems, it is crucial to build maintenance models that describe the real behavior of the system. In this scope, the herein paper provides an original approach for maintenance efficiency modeling of multi-component systems. The proposed approach seeks to model the behavior of multi-component system after the replacement of one or more of its components and evaluate this effect. As a matter of fact, from maintenance efficiency point of view, the replacement of one component can be considered as perfect maintenance for the component itself but imperfect for the whole system. To this end, a hybrid model, which considers geometric adjustment of failure intensity, proportional adjustment of failure intensity and proportional adjustment of age is provided. Then, an efficient procedure based on Bayesian networks is provided for the assessment of the imperfect maintenance model parameters. Finally, the proposed model is compared to the most common imperfect maintenance models.

수리 가능한 체계에 대한 Upside-Down 욕조 곡선 형태의 삼분할된 고장 강도 모형

Purpose: This study proposes an upside-down bathtub-shaped three-segmented failure intensity model for repairable systems. The procedure for estimating the parameters for the proposed model is presented under certain assumptions regarding the change points of the model.BRMethods: The proposed model comprises three failure intensity functions - one for each of the three model segments. The model is therefore a P-H-P model, with the power law process model, the homogeneous Poisson process model, and the power law process model that follows the non-homogeneous Poisson process as the failure intensity functions. The change points and the parameters of each failure intensity function were determined using maximum likelihood estimation and least squares estimation.BRResults: The case study shows that compared with other extant models, the proposed P-H-P model is more suitable in terms of log-likelihood function value, Akaike information criterion corrected, and mean squared error.BRConclusion: The proposed P-H-P model is expected to better explain the failure intensities of similar systems and to allow for more accurate reliability analysis.

Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure

In this paper, a three components repairable system under K-mixed redundancy strategy with unreliable switching failure is proposed, in which the lifetimes of components, the repair time of failure components and the vacation time are distributed with different phase-type (PH) distributions. The multiple vacation policy of the repairman is adopted so that the human resources can be fully utilized. The proposed repairable system model is studied in both transient and stationary regimes with matrix-analytic method. Some reliability indexes are obtained by employing Kronecker operator theory and aggregated stochastic theory. Finally, a numerical example and a comparison analysis between K-mixed redundancy strategy model and mixed redundancy strategy model are implemented to illustrate the results obtained in the paper.

Statistical modeling and reliability analysis of multiple repairable systems with dependent failure times under perfect repair

In repairable systems, a fundamental aspect to be considered is to predict the reliability of the systems under study. Establishing reliability models for multiple repairable systems, however, is still a challenging problem when considering the dependency or unobserved heterogeneity of component failures. This paper focuses on a special repair assumption, called perfect repair, for repairable systems with dependent failures, where only the failed component is restored to as good as new condition. A frailty model is proposed to capture the statistical dependency and unobserved heterogeneity. The classical inferential method for estimating parameters and the reliability predictors will be shown for models in repairable systems under the assumption of perfect repair. An extensive simulation study is conducted under different scenarios to verify the suitability of the model and the asymptotic consistency and efficiency properties of the maximum likelihood estimators. The proposed methodology can be especially useful for industries that operate with repairable systems subjected to the replacement of parts after failures and to non-quantifiable factors that can interfere with the failure times of these parts. We illustrate the practical relevance of the proposed model on two real data sets. The first deals with a set of 9 sugarcane harvesters, observed during a fixed period of time, whose cutting blades failed several times in this interval. The other deals with a set of 5 dump trucks whose diesel engines also had recurring failures during the observation period. Parametric inference is carried out under the power-law process model that has found significant attention in industrial applications.

Efficient semiparametric estimation of time‐censored intensity‐reduction models for repairable systems

AbstractThe rate reduction models have been widely used to model the recurrent failure data for their capabilities in quantifying the repair effects. Despite the widespread popularity, there have been limited studies on statistical inference of most failure rate reduction models. In view of this fact, this study proposes a semiparametric estimation framework for a general class of such models, called extended geometric failure rate reduction (EGFRR) models. Covariates are considered in our analysis and their effects are modeled as a log‐linear factor on the baseline failure rate. Unlike the existing inference methods for the EGFRR models that assume the failure data are censored at a fixed number of failures, our study considers covariates and time‐censoring, which are more common in practice. The semiparametric maximum likelihood (ML) estimators are obtained by carefully constructing the likelihood function. Asymptotic properties including consistency and weak convergence of the ML estimators are established by using the properties of the martingale process. In addition, we show that the semiparametric estimators are asymptotically efficient. A real example from the automobile industry illustrates the usefulness of the proposed framework and extensive simulations show its outstanding performance when comparing with the existing methods.

Geometric imperfect preventive maintenance and replacement (GIPMAR) model for aging repairable systems

PurposeThis work seeks to develop a geometric imperfect preventive maintenance (PM) and replacement model (GIPMAR) for aging repairable systems due to age and prolong usage that would meet users need in three phases: within average life span, beyond average life span and beyond initial replacement age of system.Design/methodology/approachThe authors utilized the geometric process (GP) as the hazard function to characterize the increasing failure rate (IFR) of the system. The GP hazard function was incorporated into the hybridized preventive and replacement model of Lin et al. (2000). The resultant expected cost rate function was optimized to obtain optimum intervals for PM/replacement and required numbers of PM per cycle. The proposed GIPMAR model was applied to repairable systems characterized by Weibull life function and the results yielded PM/replacement schedules for three different phases of system operation.FindingsThe proposed GIPMAR model is a generalization of Lin et al. (2000) PM model that were comparable with results of earlier models and is adaptive to situations in developing countries where systems are used across the three phases of operation depicted in this work. This may be due to economic hardship and operating environment.Practical implicationsThe proposed model has provided PM/Replacement schedules for different phases of operation which was never considered. This would provide a useful guide to maintenance engineers and end-users in developing countries with a view to minimizing the average cost of maintenance as well as reducing the number of down times of systems.Social implicationsA duly implemented GIPMAR model would ensure efficient operation of systems, optimum man-hour need in the organization and guarantee customer's goodwill in a competitive environment.Originality/valueIn this work, the authors have extended Lin et al. (2000) PM model to provide PM/replacement schedules for aging repairable systems which was not provided for in earlier existing models and literature.

A study on stochastic modelling of the repairable system

All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible.When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.

Optimizing imperfect preventive maintenance in multi-component repairable systems under [formula omitted]-dependent competing risks

Existing maintenance optimization models for single-component repairable systems are extensively studied. However, maintenance optimization in multicomponent reparable systems (MCRS) is still a challenging problem, especially when dealing with stochastic dependent (s-dependent) competing risks between components. This paper develops a novel reliability-centered maintenance optimization model for MCRS operating under s-dependent competing risks. The s-dependency is captured by the joint reliability function constructed using Copula method and unknown parameters are estimated by maximum likelihood estimations (MLE). Maintenance strategies are carried out both at components and system levels. At components level, a preventive maintenance (PM) is performed whenever the reliability of the MCRS reaches a given threshold. PM actions are imperfect and modeled using the hybrid hazard rate approach. At system level, the whole system is preventively replaced after a certain number of PM cycles. The objective of the proposed maintenance strategies is to determine the optimal reliability threshold together with the optimal number of PM cycles that minimize the total expected maintenance cost rate in the infinite time horizon. The optimality conditions of the resulting maintenance optimization problem are formally discussed via two propositions. A case study that investigates a ball screw mechanism with multiple components is provided to validate the proposed approaches.

Failure modes based censored data analysis for repairable systems and its industrial perspective

Reliability analysis of repairable systems (RS) has always been a challenging task for the industries especially when the collected data is censored. In real-world situation, the industries, generally preserve all the system’s related information such as the number of failures, time between failures and their respective failure modes (FMs) for future reliability analysis. The problem arises when FM wise analysis is required to be done for RS along with other censoring criteria such as test termination, removing the operating system from the study etc. The literature provides various models to deal with different types of censored data but lacks in providing FM based censored data analysis technique for RS, when both preventive and corrective maintenances (PM and CM) are treated as imperfect. To bridge this gap, the paper develops a technique and virtual age models for RS which can simultaneously address FM wise analysis with right and multiply censoring data considering both the PM and CM as imperfect. The paper also develops likelihood function using proposed models for parameter estimation. The proposed technique and models are demonstrated with the help of a case study selected from aviation industry. The paper then highlights the applicability of proposed models to industries dealing with complex and critical RS in conducting failure modes and effects analysis (FMEA) and remaining useful life (RUL) estimation. The paper also brings out as to how the proposed models can be converted to the existing models with some modifications.

A generalized geometric process based repairable system model with bivariate policy

The maintenance model of simple repairable system is studied. We assume that there are two types of failure, namely type I failure (repairable failure) and type II failure (irrepairable failure). As long as the type I failure occurs, the system will be repaired immediately, which is failure repair (FR). Between the (n-1)th and the nth FR, the system is supposed to be preventively repaired (PR) as the consecutive working time of the system reaches λ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-1</sup> T, where λ and T are specified values. Further, we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the Nth type I failure or the occurrence of the first type II failure, whichever occurs first. In practice, the system will degrade with the increasing number of repairs. That is, the consecutive working time of the system forms a decreasing generalized geometric process (GGP) whereas the successive repair time forms an increasing GGP. A simple bivariate policy (T,N) repairable model is introduced based on GGP. The alternative searching method is used to minimize the cost rate function C(N,T), and the optimal (T,N) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> is obtained. Finally, numerical cases are applied to demonstrate the reasonability of this model.

A Weibull-based recurrent regression model for repairable systems considering double effects of operation and maintenance: A case study of machine tools

The failure processes of repairable systems may be impacted by operational conditions and repair activities. In reliability engineering, many real-life data have a bathtub-shaped failure intensity (FI). In order to handle the relationship between the effects of operational conditions and maintenance and bathtub-shaped FI, this paper proposes a double effects regression model in the context of the Weibull-based general renewal process. The model considers the multiplicative and cumulative effects of operational conditions, indicating both scale and shape parameters of the underlying Weibull distribution can potentially change with operational covariates and virtual age. It extends a recurrent regression model to the case of a bathtub-shaped FI and further provides more flexible FI shapes by setting different ranges of effect coefficients. An efficient parameter estimation procedure is illustrated to support the application of the proposed model. The proposed model is shown to more closely describe the bathtub-shaped failure process through several simulated and real-life examples.

Mixed-Effects Nonhomogeneous Poisson Process Model for Multiple Repairable Systems

The nonhomogeneous Poisson process (NHPP) has become a useful approach for modeling failure patterns of recurrent failure data revealed by minimal repairs from an individual repairable system. Sometimes, multiple repairable systems may present system-to-system variability owing to operation environments or working intensities of individual systems. In this paper, we go over the application of generalized mixed-effects models to recurrent failure data from multiple repairable systems based on the NHPP. The generalized mixed-effects models explicitly involve between-system variation through randomeffects, along with a common baseline for all the systems through fixed-effects for non-normal data. Details on estimation of the parameters of the mixed-effects NHPP models and construction of their confidence intervals are examined. An applicative example shows prominent proof of the mixed-effects NHPP models for the purpose of reliability analysis.

On the Maintenance Modeling of a Hybrid Model with Exponential Repair Efficiency

In the reliability literature, maintenance efficiency is usually dealt with as a fixed value. Since repairable systems are subject to different degrees and types of repair, it is more convenient to regard a random variable for maintenance efficiency. This paper is devoted to the statistical study of a general hybrid model for repairable systems working under imperfect maintenance. For both failure improvement and virtual age reduction of the system, maintenance efficiency is assumed to be random, with an exponential distribution as a probability density function. The likelihood function of this model is provided, and the estimation of the model parameters is computed by considering the maximization likelihood procedure. Obtained results were tested and applied to simulated and real data sets. To construct confidence intervals, the bias-corrected accelerated bootstrap method has been used.

Modeling of Repairable Multi-State Systems with time-varying failure and repair rates using Equivalent Systems Dynamics Models

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.

Reliability parameter estimation of repairable systems with imperfect maintenance, repair and overhaul

PurposeIndustries generally require good maintenance, repair and overhaul (MRO) facilities. Maintenance activities at MRO cover the normal scheduled check-ups known as scheduled preventive maintenance (SPM) whereas an overhaul reviews and rejuvenates the complete system at a scheduled time. The literature is reasonably stocked with reliability modelling of repairable systems considering both the corrective maintenance (CM) and SPM as imperfect. However, in all these situations the overhaul is modelled as perfect repair. Thus, the purpose of this research paper is to develop a mathematical model for the estimation of reliability parameters considering the complete MRO as imperfect.Design/methodology/approachThe paper proposes arithmetic reduction of age (Kijima I) based virtual age model to estimate reliability parameters by considering the complete MRO as imperfect and provides the likelihood and log-likelihood functions for parameter estimation of the proposed model and also presents the various extensions of the proposed model.FindingsFor analysis, two real-time data sets of two components, i.e. turbostarter and plunger pump are considered. The analysis mainly focuses on intensity function and availability of components. The availability analysis of the components directly affects the cost analysis. It is very important to analyze the realistic trend of availability, and the comparative analysis shows that the assumption of perfect overhaul overestimates and minimal overhaul underestimates the performance of the components whereas assumption of imperfect overhaul portraits more sensible deteriorating and availability trend of the components.Originality/valueThe proposed methodology in this paper is a novice and not available in the literature.