Repair Assumption Research Articles

Reliability evaluation of repairable systems considering component heterogeneity using frailty model

The failure processes of heterogeneous repairable systems with minimal repair assumption can be modelled by nonhomogeneous Poisson processes. One approach to describe an unobserved heterogeneity between systems is to multiply the intensity function by a positive random variable (frailty term) with a gamma distribution. This approach assumes that the relative frailty distribution among survivors is independent of age. Where systems are being continuously repaired and modified, the frailty distribution may be dependent on the system’s age. This paper investigates the application of the inverse Gaussian (IG) frailty model for modelling the failure processes of heterogeneous repairable systems. The IG frailty model, which combines the power law model and inverse Gaussian distribution, assumes that the relative frailty distribution among survivors becomes increasingly homogeneous over time. We develop the maximum likelihood for the IG frailty model, a method for event prediction, and investigate the effect of accuracy of the IG estimator and mis-specification of the frailty distribution through a simulation study. The mean estimates of the scale and shape parameters of the intensity function are examined for bias and efficiency loss. We find that the developed estimator is robust to changes in the input parameters for a relatively large sample sizes. We investigate the robustness of selecting an IG compared with a gamma frailty model. The developed IG model is applied to real data for illustration showing an improvement on existing models.

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.

Dynamic maintenance strategy with iteratively updated group information

Maintenance grouping methods such as the rolling horizon approach are effective in reducing maintenance costs of multi-component systems. Despite the theoretical advancements of this approach, it still faces three challenges. First, the extensively adopted minimal repair assumption upon failures limits its application. Second, opportunistic maintenance upon corrective maintenance is overlooked, unable to fully take advantage of economic dependence. Third, maintenance plans are not based on actual maintenance history and health information, which may increase failure risks. To address these challenges, this paper formulates a novel dynamic planning framework that captures economic dependence in both preventive and opportunistic replacement. Unlike conventional approaches that restrict all maintenance activities into a finite planning horizon, our proposal focuses on activity-to-activity scheduling without specifying the horizon. As such, the subsequent maintenance schedule is dynamically updated once a system maintenance is executed. A flexible dynamic programming algorithm is developed to optimize the maintenance grouping, and the strategy framework is further extended to condition-based maintenance scenarios. The effectiveness and generality of the proposed maintenance strategy are demonstrated by numerical experiments.

Optimal periodic replacement policy for a GPP repairable product under the free-repair warranty

This article provides an extension study on the optimal periodic replacement policy for repairable products under the free-repair warranty. A new and more general type of repair, called the ‘GPP repair’, is applied in this study, which is defined based on the Generalized Polya Process and which is more close to practical situations than the ‘minimal repair’. Under the GPP repair assumption, the future reliability performance of a product becomes worse as the number of system failures that occurred in the past increases. Cost models from the user’s perspective are developed for both a GPP repairable product with free-repair warranty and without warranty, and the corresponding optimal replacement periods are derived such that the long-run expected cost rate is minimized. The difference and relationship between GPP repairable and minimal repairable products on the optimal replacement policies are analytically presented. Numerical examples are demonstrated for illustration and verification. Finally, a practical case is provided to explain the potential application areas of this study, and managerial implications and insights are addressed.

Extending minimal repair models for repairable systems: A comparison of dynamic and heterogeneous extensions of a nonhomogeneous Poisson process

For many applications of repairable systems, the minimal repair assumption, which leads to nonhomogeneous Poisson processes (NHPP), is not adequate. We review and study two extensions of the NHPP, the dynamic NHPP and the heterogeneous NHPP. Both extensions are motivated by specific aspects of potential applications. It has long been known, however, that the two paradigms are essentially indistinguishable in an analysis of failure data. We investigate the connection between the two approaches for extending NHPP models, both theoretically and numerically in a data example and a simulation study.

A Bayesian Nonparametric Test for Minimal Repair

The article develops a Bayesian nonparametric reliability model for recurrent events where failure and truncated time-to-failure density shape is regressed on past maintenance decisions: perfect repair and minimal repair. By comparing the system interfailure lifetime distributions after minimal and perfect repair, we are able to test the minimal repair assumption of “good as old.” Interfailure hazard functions after perfect and minimal repairs are estimated, shedding light on departures from minimal repair. The method is illustrated both on simulated data as well as failure time data from air-conditioning units at the South Texas Nuclear Operating Company near Bay City, Texas. This article has supplementary material online.

Impact of Different Repair Assumptions on Repairable System Risk Assessment

In this study risk assessment is carried out to estimate the probability and magnitude of risk due to the unexpected system failure by considering different repair assumptions for repairable system. In order to measure the risk for different repair assumptions, the probability of failures and consequences are required. The probability of failure estimated using parametric Recurrent Data Analysis (RDA) approach while the consequences of failure analyzed based on reported data. Gas Turbine (GT) system was taken as a case study to verify the model. The results indicated that perfect repair assumption leads to minimum risk compared to imperfect and minimal repair assumptions. Based on results it was concluded that the maintenance team needs to follow perfect repair to mitigate the risk each time a failure happens.

Availability-based optimal maintenance policies for repairable systems in military aviation by identification of dominant failure modes

Modeling of imperfect repair through perfect renewal process uses an “as good as new” repair assumption and nonhomogeneous Poisson process uses an “ABAO” repair assumption. In practice, repair actions do not result in such extreme situations but in a complex transitional one, that is, general repair. This article discusses generalized renewal process for an aero engine as repairable component. Maximum likelihood estimators for the reliability parameters are estimated using generalized renewal process, for field failure data of an aero engine. The current practice designates repairable components, as high failure rate components based on intuition, experience and the number of unscheduled failures at repair depots. A methodology is developed to designate high failure rate components based on availability by taking into consideration the dominant failure modes of the aero engine. Then, a comparison is made with a “Black Box” approach. The present maintenance policy is then reviewed by reducing the present time between overhauls for the high failure rate components. We observe a noteworthy enhancement in all the performance parameters in the suggested maintenance policy. We also observe that percent improvement achieved in all performance parameters on reducing the next overhaul cycle time, with failure modes analysis is more than when failure modes are not considered.

Reliability Analysis of Repairable Systems With Dependent Component Failures Under Partially Perfect Repair

Existing reliability models for repairable systems with a single component can be well applied for a range of repair actions from perfect repair to minimal repair. Establishing reliability models for multi-component repairable systems, however, is still a challenge problem when considering the dependency of component failures. This paper focuses on a special repair assumption, called partially perfect repair, for repairable systems with dependent component failures, where only the failed component is repaired to as good as new condition. A parametric reliability model is proposed to capture the statistical dependency among different component failures, in which the joint distribution of the latent component failure time is established using copula functions. The model parameters are estimated by using the maximum likelihood method, and the maximum likelihood function is calculated based on the conditional probability. Based on the proposed reliability model, statistical hypothesis testing procedures are developed to determine the dependency of component failures. The developed methods are illustrated with an application in a cylinder head assembling cell that consists of multiple stations.

Comparative Analysis of Optimal Maintenance Policies Under General Repair With Underlying Weibull Distributions

Various replacement policies under Kijima's general repair model with the underlying Weibull distribution function are studied via two efficient methods. The first one is based on our previously derived approximate formula for the g-renewal function; the second is an improved Monte Carlo method. These methods enable an in-depth, comparative analysis of the maintenance polices in question. An efficient algorithm is suggested for finding optimal preventive replacement times. The influence of restoration factor, including the deviation from a minimal repair assumption, on the optimal solution is studied. A practical study illustration is provided.

Low-dose radiation hyper-radiosensitivity in multicellular tumour spheroids

We propose and study a new model aimed at describing the low-dose hyper-radiosensitivity phenomenon appearing in the survival curves of different cell lines. The model uses the induced repair assumption, considering that the critical dose at which this mechanism begins to act varies from cell to cell in a given population. The model proposed is compared with the linear-quadratic model and the modified linear-quadratic model, which is commonly used in literature and in which the induced repair is taken into account in a heuristic way. The survival curve for the MCF-7 line of human breast cancer is measured at low absorbed doses and the uncertainties in these doses are estimated using thermoluminiscent dosemeters. It is shown that these multicellular spheroids present low-dose hyper-radiosensitivity. The new model permits an accurate description of the data of two human cell lines (previously published) and of the multicellular spheroids of the MCF-7 line here measured. The model shows enough flexibility to account for data with very different characteristics and considers in a faithful way the hypothesis of the repair induction.

Generalized renewal process for repairable systems based on finite Weibull mixture

Repairable systems can be brought to one of possible states following a repair. These states are: ‘as good as new’, ‘as bad as old’ and ‘better than old but worse than new’. The probabilistic models traditionally used to estimate the expected number of failures account for the first two states, but they do not properly apply to the last one, which is more realistic in practice. In this paper, a probabilistic model that is applicable to all of the three after-repair states, called generalized renewal process (GRP), is applied. Simplistically, GRP addresses the repair assumption by introducing the concept of virtual age into the stochastic point processes to enable them to represent the full spectrum of repair assumptions. The shape of measured or design life distributions of systems can vary considerably, and therefore frequently cannot be approximated by simple distribution functions. The scope of the paper is to prove that a finite Weibull mixture, with positive component weights only, can be used as underlying distribution of the time to first failure (TTFF) of the GRP model, on condition that the unknown parameters can be estimated. To support the main idea, three examples are presented. In order to estimate the unknown parameters of the GRP model with m-fold Weibull mixture, the EM algorithm is applied. The GRP model with m mixture components distributions is compared to the standard GRP model based on two-parameter Weibull distribution by calculating the expected number of failures. It can be concluded that the suggested GRP model with Weibull mixture with an arbitrary but finite number of components is suitable for predicting failures based on the past performance of the system.

DISCONTINUOUS POINT PROCESSES FOR THE ANALYSIS OF REPAIRABLE UNITS

In this paper, a useful family of discontinuous point processes is proposed, which is able to analyze the failure pattern of repairable units subjected to repair actions that depart from the commonly assumed minimal repair policy. Maximum likelihood estimators of the parameters which index two special cases of the above family are derived, and procedures for testing the departure from the minimal repair assumption, based on asymptotic results, are discussed. An exact and unbiased testing procedure to be performed for small or moderate sample sizes is also proposed. Finally, numerical examples are given to illustrate the proposed estimation and testing procedures.

Testing the Minimal Repair Assumption in an Imperfect Repair Model

Testing the Minimal Repair Assumption in an Imperfect Repair Model

Testing the Minimal Repair Assumption in an Imperfect Repair Model

Abstract Models assuming minimal repair specify that on repair, a failed system is returned to the working state, while the effective age of the system is held constant; that is, the distribution of the time until the next failure of the repaired system is the same as for a system of the same age that has not yet failed. These models are common in the literature of operations research and reliability, and many probabilistic results as well as inferential procedures depend on the minimal repair assumption. We propose two nonparametric tests of the assumption that imperfectly repaired systems are minimally repaired in some models. The large sample theory for these tests is derived from the asymptotic joint distribution of a survival function estimator and the ordinary empirical survival function based on the initial failure times of new or perfectly repaired systems. Simulation results are also provided for the null hypothesis case and under other alternatives.

An application of a bathtub failure model to imperfectly repaired systems data

AbstractIn this paper we use an exponential power distribution to develop a bathtub failure model for repairable systems. These results are compared with those using the more familiar Weibull distribution. The analysis is extended to three types of repair scenarios: good‐as‐new repairs (in which the repair following a failure completely refreshes the failure intensity), bad‐as‐old repairs (in which the repair has no effect on the failure intensity) and imperfect repairs (in which the failure intensity is only partially reset). We apply this analysis to hydro‐electric turbine data and find that an exponential power distribution produces a well‐defined bathtub failure model when used with an imperfect repair assumption. We furthermore find that this bathtub model produces an improved fit over the equivalent Weibull model.

Periodical replacement problem without assuming minimal repair

In this paper, a periodical replacement problem with a general repair is considered where a system is replaced at only scheduled times kT (k = 0,1,…) and is repaired whenever it fails. By general repair, we mean that repair brings the state of the system to a certain better state. A stochastic model to describe the operation in time of a repairable system which is maintained by a general repair is developed. The model contains the minimal repair case in which repair restores a system to its functioning condition just prior to failure. The sensitivity of replacement policies under a general repair to derivation from the minimal repair assumption is numerically examined. It will be seen that the policies are insensitive when the deterioration of the system is not fast and the replacement cost is high relative to the repair cost. The minimal repair assumption is then justified for such situations.