Decline and repair, and covariate effects

The failure processes of repairable systems may be impacted by operational and environmental stress factors. To accommodate such factors, reliability can be modelled using a multiplicative intensity function. In the proportional intensity model, the failure intensity is the product of the failure intensity function of the baseline system that quantifies intrinsic factors and a function of covariates that quantify extrinsic factors. The existing literature has extensively studied the failure processes of repairable systems using general repair concepts such as age-reduction when no covariate effects are considered. This paper investigates different approaches for modelling the failure and repair process of repairable systems in the presence of time-dependent covariates. We derive statistical properties of the failure processes for such systems

Virtual series-system models of imperfect repair

Novel models of imperfect repair are fitted to classic reliability datasets. The models suppose that a virtual system comprises a component and a remainder in series. On failure of the component, the component is renewed, and on failure of the remainder, the component is renewed and the remainder is minimally repaired. It follows that the repair process is a counting process that is the superposition of a renewal process and a Poisson process. The repair effect, that is, the extent to the system is repaired by renewal of the component, depends on the relative intensities of the superposed processes. The repair effect may be negative, when the intensity of the part that is a renewal process is a decreasing function. Other special cases of the model exist (renewal process, Poisson process, superposed renewal process and homogeneous Poisson process). Model fit is important because the nature of the model and corresponding parameter values determine the effectiveness of maintenance, which we also consider. A cost-minimizing repair policy may be determined provided the cost of preventive-repair is less than the cost of corrective-repair and the repairable part is ageing. If the remainder is ageing, then policy needs to be adapted as it ages

Semiparametric estimate of the efficiency of imperfect maintenance actions for a gamma deteriorating system

International audienceA system is considered, which is deteriorating over time according to a non homogeneous gamma process with unknown parameters. The system is subject to periodic and instantaneous imperfect maintenance actions (repairs). Each imperfect repair removes a proportion ρ of the accumulated degradation since the previous repair. The parameter ρ hence appears as a measure for the maintenance efficiency. This model is called arithmetic reduction of degradation of order 1. The system is inspected right before each maintenance action, thus providing some multivariate measurement of the successively observed deterioration levels. Based on these data, a semiparametric estimator of ρ is proposed, considering the parameters of the underlying gamma process as nuisance parameters. This estimator is mainly based on the range of admissible ρ's, which depends on the data. Under technical assumptions, consistency results are obtained, with surprisingly high convergence rates (up to exponential). The case where several i.i.d. systems are observed is next envisioned. Consistency results are obtained for the efficiency estimator, as the number of systems tends to infinity, with a convergence rate that can be higher or lower than the classical square root rate. Finally, the performances of the estimators are illustrated on a few numerical examples

Imperfect Preventive Maintenance Policies With Unpunctual Execution.

Traditional maintenance planning problems usually presume that preventive maintenance (PM) policies will be executed exactly as planned. In reality, however, maintainers often deviate from the intended PM policy, resulting in unpunctual PM executions that may reduce maintenance effectiveness. This article studies two imperfect PM policies with unpunctual executions for infinite and finite planning horizons, respectively. Under the former policy, imperfect PM actions are periodically performed and the system is preventively replaced at the last PM instant. The objective is to determine the optimal number of PM actions and associated PM interval so as to minimize the long-run average cost rate. While the latter policy specifies that a system is subject to periodic PM activities within a finite planning horizon and there is no PM activity at the end of the horizon. The aim is then to identify the optimal number of PM activities to minimize the expected total maintenance cost. We discuss the modeling and optimization of the two unpunctual PM policies, and then explore the impact of unpunctual executions on the optimal PM decisions and corresponding maintenance expenses in an analytical or numerical way. The resulting insights are helpful for practitioners to adjust their PM plans when unpunctual executions are anticipated

The Theorem of Proportionality in Mainstream Capital Theory: An Assessment of its Applicability

This paper surveys and assesses the empirical literature that bears on the applicability of the theorem of proportionality, which asserts that depreciation is proportional to the outstanding capital stock. All available evidence shows that: a) the rates of depreciation and retirements vary from year to year in response to changes in conventional economic forces like utilization, maintenance and repair, the prices of new capital goods, etc., and b) while the approximation of the distribution of depreciation rates by a single parameter may be characterized by simplicity and ease of use, at the same time it thwarts the advances that can be achieved by returning to a general equilibrium model centered on the time structure of capital and the useful lives of its components. For this reason, it is concluded that, the sooner this theorem is replaced by an endogenous theory of depreciation and replacement, the better for economic theory and policy.Capital longevity, replacement, depreciation, scrappage, maintenance, utilization, obsolescence

Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair

We analyze the optimal replacement policy for a system subject to a general failure and repair model. Failures can be of one of two types: catastrophic or minor. The former leads to the replacement of the system, whereas minor failures are followed by repairs. The novelty of the proposed model is that, after repair, the system recovers the operational state but its condition is worse than that just prior to failure (worse than old). Undertrained operators or low quality spare parts explain this deficient maintenance. The corresponding failure process is based on the Generalized Pólya Process which presents both the minimal repair and the perfect repair as special cases. The system is replaced by a new one after the first catastrophic failure, and also undergoes two sorts of preventive maintenance based on age and after a predetermined number of minor failures whichever comes first. We derive the long-run average cost rate and study the optimal replacement policy. Some numerical examples illustrate the comparison between the as bad-as-old and the worse than old conditions

A model for availability growth with application to new generation offshore wind farms

A model for availability growth is developed to capture the effect of systemic risk prior to construction of a complex system. The model has been motivated by new generation offshore wind farms where investment decisions need to be taken before test and operational data are available. We develop a generic model to capture the systemic risks arising from innovation in evolutionary system designs. By modelling the impact of major and minor interventions to mitigate weaknesses and to improve the failure and restoration processes of subassemblies, we are able to measure the growth in availability performance of the system. We describe the choices made in modelling our particular industrial setting using an example for a typical UK Round III offshore wind farm. We obtain point estimates of the expected availability having populated the simulated model using appropriate judgemental and empirical data. We show the relative impact of modelling systemic risk on system availability performance in comparison with estimates obtained (Lesley Walls) from typical system availability modelling assumptions used in offshore wind applications. While modelling growth in availability is necessary for meaningful decision support in developing complex systems such as offshore wind farms, we also discuss the relative value of explicitly articulating epistemic uncertainties

Performance Implications of Diversification in Professional Service Firms: The Role of Synergies

There is growing interest in the Professional service firms because they are seen as archetype of the knowledge-based economy. In this study we look at under researched area of exploitation of synergies in professional service firms and its implications for performance. Overcoming the uni-dimensional nature of extant studies, we examine the performance implications of diversification along the twin dimensions of services they offer and the knowledge of the industry domain of their clients. We hypothesize that moderate levels of coherence in these dimensions lead to improved performance while excess coherence in these domains lead to diminished performance. These predictions are tested and supported by data from the Indian IT industry which is synonymous with emergence of knowledge economy in India. Our study thus contributes to the theory of diversification of professional service firms.

A unified methodology of maintenance management for repairable systems based on optimal stopping theory

This dissertation focuses on the study of maintenance management for repairable systems based on optimal stopping theory. From reliability engineering’s point of view, all systems are subject to deterioration with age and usage. System deterioration can take various forms, including wear, fatigue, fracture, cracking, breaking, corrosion, erosion and instability, any of which may ultimately cause the system to fail to perform its required function. Consequently, controlling system deterioration through maintenance and thus controlling the risk of system failure becomes beneficial or even necessary. Decision makers constantly face two fundamental problems with respect to system maintenance. One is whether or when preventive maintenance should be performed in order to avoid costly failures. The other problem is how to make the choice among different maintenance actions in response to a system failure. The whole purpose of maintenance management is to keep the system in good working condition at a reasonably low cost, thus the tradeoff between cost and condition plays a central role in the study of maintenance management, which demands rigorous optimization. The agenda of this research is to develop a unified methodology for modeling and optimization of maintenance systems. A general modeling framework with six classifying criteria is to be developed to formulate and analyze a wide range of maintenance systems which include many existing models in the literature. A unified optimization procedure is developed based on optimal stopping, semi-martingale, and lambda-maximization techniques to solve these models contained in the framework. A comprehensive model is proposed and solved in this general framework using the developed procedure which incorporates many other models as special cases. Policy comparison and policy optimality are studied to offer further insights. Along the theoretical development, numerical examples are provided to illustrate the applicability of the methodology. The main contribution of this research is that the unified modeling framework and systematic optimization procedure structurize the pool of models and policies, weed out non-optimal policies, and establish a theoretical foundation for further development

How did the introduction of managed care for the uninsured in Iowa affect the use of substance abuse services?

Concerns about access under managed care have been raised for vulnerable populations such as publicly funded patients with substance abuse problems. To estimate the effects of the Iowa Managed Substance Abuse Care Plan (IMSACP) on substance abuse service use by publicly funded patients, service use before and after IMSACP was compared; adjustments were made for changes in population sociodemographic and clinical characteristics. Between fiscal years 1994 and 1997, patient case mix was marked by a higher burden of illness and the use of inpatient, residential nondetox, outpatient counseling, and assessment services declined, while use of intensive outpatient and residential detox services increased. Findings were similar among women, children, and homeless persons. Thus, care moved away from high-cost inpatient settings to less costly venues. Without knowing the impact on treatment outcomes, these changes cannot be interpreted as improved provider efficiency versus simply cost containment and profit maximization