Optimal Maintenance Time for Repairable Systems Under Two Types of Failures

Determination of preventive maintenance is an important issue for systems under degradation. A typical maintenance policy calls for complete preventive repair actions at pre-scheduled times and minimal repair actions whenever a failure occurs. Under minimal repair, failures are modeled according to a non homogeneous Poisson process. A perfect preventive maintenance restores the system to the as good as new condition. The motivation for this article was a maintenance data set related to power switch disconnectors. Two different types of failures could be observed for these systems according to their causes. The major difference between these types of failures is their costs. Assuming that the system will be in operation for an infinite time, we find the expected cost per unit of time for each preventive maintenance policy and hence obtain the optimal strategy as a function of the processes intensities. Assuming a parametrical form for the intensity function, large sample estimates for the optimal maintenance check points are obtained and discussed.     

Optimal Age Policy for a Used System with Imperfect Preventive Maintenance and Cumulative Damage Model

In this article, the concept of imperfect preventive maintenance is discussed and an age maintenance policy is developed based on the cumulative damage model for a used system with initial variable damage. The deterioration of the system is assumed to suffer the non-homogeneous Poisson shocks which can be divided into two types with stochastic probability: Type-I shock (minor) yields a random amount of additive damage of the system, or Type-II shock (catastrophic) causes the system to fail. An age preventive maintenance policy T is presented in which the system undergoes preventive maintenance at a scheduled lifetime T, or corrective maintenance at first Type-II shock and the total damage exceeds a threshold level, whichever occurs first. The objective is to determine the optimal preventive maintenance schedule such that the expected cost rate is minimized. The optimal solution is derived analytically and discussed numerically.     

Optimal design and maintenance of a repairable multi-state system with standby components

The configuration of a repairable system directly influences its performance measures, such as mean time between failures and steady state availability. Additionally, maintenance strategies such as corrective, preventive, and condition-based can affect the performance of the system. The objective of this work is to investigate the trade-offs between the configuration of a repairable multi-state system with binary components and its maintenance strategy. The corresponding stochastic process for the proposed model is formulated using the continuous-time Markov process and important performance measures of such a multi-state system are derived. An optimization model is introduced for the cost-effective design of this repairable multi-state system. The results are demonstrated using a numerical example for a power generation system.     

Optimization of continuous and discrete scheduled times for a cumulative damage system with age-dependent maintenance

Abstract

This paper presents a preventive replacement problem when a system is operating successive works with random times and suffering stochastic shocks. The works cause random amount additive damage to the system, and the system fails whenever the cumulative damage reaches a failure level threshold. As an external shock occurs, the system experiences one of the two types of shocks with age-dependent maintenance mechanism: type-I (minor) shock is rectified by a minimal repair, or type-II (catastrophic) shock causes the system to fail. To control the deterioration process, preventive replacement is scheduled to replace the system at a continuous age T or at a discrete number N of working cycles, whichever occurs first, and corrective replacement is performed immediately whenever the system fails due to either shock or damage. The optimal preventive replacement schedule that minimizes the expected cost rate is discussed analytically and computed numerically. The proposed model provides a general framework for analyzing maintenance policies and extends several existing results.     

Condition-based maintenance policy for linear consecutive-k-out-of-n: F system

In the article, a condition-based maintenance policy is proposed for a linear consecutive-k-out-of-n: F system. The failure times of components are assumed to be independent and identically distributed. It is assumed that the component states in the system can be known at any time and the system failure can be detected immediately. The preventive maintenance action is based on the number of working components in minimal cut sets of the system. If there is at least one minimal cut set consisting of only one working component, the system is maintained preventively after a certain time interval. The proposed policy is compared with corrective maintenance and age-based maintenance policies. As an extended case, it is assumed that the component states can only be known by inspection, but the system failure can be detected immediately. In this case, the system is inspected periodically and is also maintained preventively based on the system state at inspection. Numerical examples are studied to evaluate the performance of the proposed policy and investigate the effects of cost parameters on the expected cost rate.     

An Extended Sequential Imperfect Preventive Maintenance Model with Improvement Factors

This article presents a generalization of the imperfect sequential preventive maintenance (PM) policy with minimal repair. As failures occur, the system experiences one of two types of failures: a Type-I failure (minor), rectified by a minimal repair; or a Type-II failure (catastrophic) that calls for an unplanned maintenance. In each maintenance period, the system is maintained following the occurrence of a Type-II failure or at age, whichever takes place first. At the Nth maintenance, the system is replaced rather than maintained. The imperfect PM model adopted in this study incorporates with improvement factors in the hazard-rate function. Taking age-dependent minimal repair costs into consideration, the objective consists of finding the optimal PM and replacement schedule that minimize the expected cost per unit time over an infinite time-horizon.     

The repair alert models with fixed and random effects

This article extends a random preventive maintenance scheme, called repair alert model, when there exist environmental variables that effect on system lifetimes. It can be used for implementing age-dependent maintenance policies on engineering devices. In other words, consider a device that works for a job and is subject to failure at a random time X, and the maintenance crew can avoid the failure by a possible replacement at some random time Z. The new model is flexible to including covariates with both fixed and random effects. The problem of estimating parameters is also investigated in details. Here, the observations are in the form of random signs censoring data (RSCD) with covariates. Therefore, this article generalizes derived statistical inferences on the basis of RSCD albeit without covariates in past literature. To do this, it is assumed that the system lifetime distribution belongs to the log-location-scale family of distributions. A real dataset is also analyzed on basis of the results obtained.     

The alert-delay competing risks model for maintenance analysis

The paper considers the modelling of the dependency between corrective maintenance and condition-based preventive maintenance of complex repairable systems. A new model of dependent competing risks is proposed, called the alert-delay (AD) model. This model has different properties from that of the delay-time, repair-alert and proportional warning constant inspection models and happens to fit some data sets which could not be fitted by the previous models. The main features of the AD model are derived: probabilistic properties and statistical analysis. Simulation results and an application to real data are presented.     

Failure and maintenance data extraction from power plant maintenance management databases

Reliability analysis is plagued by a lack of accurate data, leading to suboptimal parameter estimates and inaccurate decisions about replacement intervals and preventive maintenance activities. This paper discusses some of the problems associated with failure and maintenance data extraction from coal-fired power plant maintenance databases. Data from four generating units were observed for over 5 years and a reasonable number of equipment classes reviewed. The coal mills are identified as significant equipment that affects the availability of the generating units. This paper describes the interplay of events which includes failure modes, failure, repair and operating time. We investigate a database showing operation of coal mills, and give an exploratory data analysis in which we investigate engineering hypotheses related to mill operation. A competing risk probability model is proposed which captures some of the observed features of the systems under study.     

Bayesian inference for power law processes with applications in repairable systems

Statistical models for recurrent events are of great interest in repairable systems reliability and maintenance. The adopted model under minimal repair maintenance is frequently a nonhomogeneous Poisson process with the power law process (PLP) intensity function. Although inference for the PLP is generally based on maximum likelihood theory, some advantages of the Bayesian approach have been reported in the literature. In this paper it is proposed that the PLP intensity be reparametrized in terms of (β,η), where β is the elasticity of the mean number of events with respect to time and η is the mean number of events for the period in which the system was actually observed. It is shown that β and η are orthogonal and that the likelihood becomes proportional to a product of gamma densities. Therefore, the family of natural conjugate priors is also a product of gammas. The idea is extended to the case that several realizations of the same PLP are observed along overlapping periods of time. Some Monte Carlo simulations are provided to study the frequentist behavior of the Bayesian estimates and to compare them with the maximum likelihood estimates. The results are applied to a real problem concerning the determination of the optimal periodicity of preventive maintenance for a set of power transformers. Prior distributions are elicited for β and η based on their operational interpretation and engineering expertise.     

Optimal preventive policies for imperfect maintenance models with replacement first and last

ABSTRACT

This paper proposes preventive replacement policies for an operating system which may continuously works for N jobs with random working times and is imperfectly maintained upon failure. As a failure occurs, the system suffers one of the two types of failures based on some random mechanism: type-I (repairable or minor) failure is rectified by a minimal repair, or type-II (non repairable or catastrophic) failure is removed by a corrective replacement. A notation of preventive replacement last model is considered in which the system is replaced before any type-II failure at an operating time T or at number N of working times, whichever occurs last. Comparisons between such a preventive replacement last and the conventional replacement first are discussed in detail. For each model, the optimal schedule of preventive replacement that minimizes the mean cost rate is presented theoretically and determined numerically. Because the framework and analysis are general, the proposed models extend several existing results.     

Optimal scheduling replacement policies for a system with multiple random works

From the economical viewpoint in reliability theory, this paper addresses a scheduling replacement problem for a single operating system which works at random times for multiple jobs. The system is subject to stochastic failure which results the imperfect maintenance activity based on some random failure mechanism: minimal repair due to type-I (repairable) failure, or corrective replacement due to type-II (non-repairable) failure. Three scheduling models for the system with multiple jobs are considered: a single work, N tandem works, and N parallel works. To control the deterioration process, the preventive replacement is planned to undergo at a scheduling time T or the job's completion time of for each model. The objective is to determine the optimal scheduling parameters (T^* or N^*) that minimizes the mean cost rate function in a finite time horizon for each model. A numerical example is provided to illustrate the proposed analytical model. Because the framework and analysis are general, the proposed models extend several existing results.     

Business Cycle Asymmetries

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment and consumption growth. The robustness of the tests to model misspecification, and the effects of regime-dependent heteroscedasticity, are investigated.     

A parametric multistate model for the analysis of carcinogenicity experiments

A fully parametric multistate model is explored for the analysis of animal carcinogenicity experiments in which the time of tumour onset is not known. This model does not require assumptions about tumour lethality or cause of death judgements and can be fitted in the absence of sacrifice data. The model is constructed as a three-state model with simple parametric forms for the transition rates. Maximum likelihood methods are used to estimate the transition rates and different treatment groups are compared using likelihood ratio tests. Selection of an appropriate model and methods to assess the fit of the model are illustrated with data from animal experiments. Comparisons with standard methods are made.     

Some remarks on the physical models concerning two different approaches to inference in statistical process control

Summary For technological applications it can be useful to identify some simple physical mechanisms, which, on the basis of the available knowledge of the production process, may suggest the most appropriate approach to statistical control of the random quantities of interest. For this purpose the notion of rupture point is introduced firstly. A rupture point is characterized bym randomly arising out of control states, assumed to be mutually exclusive and stochastically independent. Shewhart's control charts seem to represent the natural statistical tool for controlling a rupture point; however it is shown that they are fully justified only when the hazard rates attached to the causes of failure are constant. Otherwise, typically in the presence of time increasing hazard rates, Shewhart's control charts should be completed by a preventive intervention rule (preventive maintenance). In the second place, the notion of dynamic instability point is introduced, which is specifically characterized by assuming that the random quantity of interest is ruled by a stochastic differential equation with constant coefficients. By discretization, developed according to a possibly new approach, it is shown that the former model reduces to an equation error model, which is among the simplest used in adaptive control, and thus particularly easy to deal with in regard to parameter estimation and the definition of the optimum control rule.     

Copulas,degenerate distributions and quantile tests in competing risk problems

It is well known that, given observable data for a competing risk problem, there is always an independent model consistent with the data. It has been pointed out, however, that this independent model does not necessarily have to be one with proper marginals. One purpose of this paper is to explore the extent to which one might try to use the non-parametric assumption that the marginals are proper in order to test whether or not independence holds. This will lead us naturally to a closely related estimation problem—how we estimate the marginals given that a certain quantile of one variable is reached at the same time as a given quantile of the other variable. The problem will be considered using the copula-based approach of Zheng and Klein. Two different methods are discussed. One is a non-parametric maximum likelihood method. The other is a consistent estimator, called the bilinear adjustment estimator, that can be computed quickly and which thus lends itself more readily to simulation methods such as bootstrapping.The ultimate objective of the work in this paper is to provide an additional analytical tool to understand the effectiveness of preventive maintenance. Preventive maintenance censors component failure data and thus provides an important example of competing risk within the reliability area.     

Using Markov Chains for Non-perennial Daily Streamflow Data Generation

The use of Markov chains to simulate non-perennial streamflow data is considered. A non-perennial stream may be thought as having three states, namely zero flow, increasing flow and decreasing flow, for which a three-state Markov chain can be constructed. Alternatively, two two-state Markov chains can be used, the first of which represents the existence and non-existence of flow, whereas the second deals with the increment and decrement in the flow for periods with flow. Probabilistic relationships between the two alternatives are derived. Their performances in simulating the state of the stream are compared on the basis of data from two different geographical regions in Turkey. It is concluded that both alternatives are capable of simulating the state of the stream.     

An alternative approach to reliability analysis of cold standby systems

ABSTRACT

An alternative approach is applied for reliability analysis of standby systems on the basis of matrix renewal function. In this regard, a single-server, two identical unit cold standby systems with an imperfect switch is considered as a three-state semi-Markov process. Several important reliability measures such as availability, mean time to failure, expected number of failures, etc., are obtained for general lifetime distributions. Also, the main results have been treated to the case of exponential lifetimes and explicit formulas obtained for this case in addition of some numerical illustrations. This approach can easily be extended to more general standby systems with different configurations.     

Modelling of dependence between critical failure and preventive maintenance: The repair alert model

We consider the competing risks problem for a repairable unit which at each sojourn may be subject to either a critical failure, or a preventive maintenance (PM) action, where the latter will prevent the failure. It is reasonable to expect a dependence between the failure mechanism and the PM regime. The paper presents a new model, called the repair alert model, for handling such cases. This model is a special case of random signs censoring, which was introduced by Roger Cooke [1993. The total time on test statistic and age-dependent censoring. Statist. Probab. Lett., 18, 307–312]. The pleasant feature of random signs censoring is that the marginal distribution of the failure time is identifiable. The repair alert model introduces the so-called repair alert function, which characterizes the “alertness” of the maintenance crew, and which is shown to be uniquely identifiable from field data. Statistical estimation is considered both nonparametrically and parametrically.