Transient analysis of reliability with and without repair for K-out-of-N :G systems with M failure modes

This paper represents Markov models for transient analysis of reliability with and without repair for K-out-of-N :G systems subject to M failure modes. The reliability and the mean time between failures of repairable systems can be calculated as a result of numerical solution of simultaneous set of linear differential equations. Closed form solutions of the transient probabilities are used to obtain the reliability and the mean time to failure for nonrepairable systems.     

Transient analysis of reliability with and without repair for K-out-of-N:G systems with two failure modes

This paper presents Markov models for transient analysis of reliability with and without repair for K-out-of-N:G systems subject to two failure modes. The reliability of repairable systems can be calculated as a result of the numerical solution of a simultaneous set of linear differential equations. Closed form solutions of the transient probabilities are used to obtain the reliability for nonrepairable systems.     

The failure intensity process and the formulation of reliability and maintenance models

A unified approach to the formulation of failure event models is presented. This provides a common framework for the analysis of both repairable and nonrepairable items, preventive as well as corrective maintenance, and it also applies for items with dormant failures. The suggested procedure is supported by a set of graphs, thereby identifying the significance both of the inherent reliability (i.e., hazard rate) and of the maintenance/repair policy. The definition/interpretation of various failure intensity concepts is fundamental for this approach. Thus, interrelations between these intensities are reviewed, thereby also contributing to a clarification of these concepts. The most basic of these; concepts, the failure intensity process, is used in counting processes (Martingales), and is the rate of failures at time t, given the history of the item up to that time. The suggested approach is illustrated by considering some standard reliability and maintenance models.     

Uptime of Systems Subject to Repairable and Nonrepayable Failures

Expressions are derived for the distribution and expected value of uptime for systems subject to both repairable and nonrepairable failures. The results are applicable to a wide range of situations, including the analysis of systems subject to major structural failure, product or process obsolescence, or failure of critical nonrepairable subsystems. Several examples are investigated, including multiple component series systems, systems containing standby redundant nonrepairable subsystems and systems containing standby redundant repairable subsystems.     

Simple bounds for counting processes with monotone rate of occurrence of failures

The article discusses some aspects of analogy between certain classes of distributions used as models for time to failure of nonrepairable objects, and the counting processes used as models for failure process for repairable objects. The notion of quantiles for the counting processes with strictly increasing cumulative intensity function is introduced. The classes of counting processes with increasing (decreasing) rate of occurrence of failures are considered. For these classes, the useful nonparametric bounds for cumulative intensity function based on one known quantile are obtained. These bounds, which can be used for repairable objects, are similar to the bounds introduced by Barlow and Marshall [Barlow, R. Marshall, A. Bounds for distributions with monotone hazard rate, I and II. Ann Math Stat 1964; 35: 1234–74] for IFRA (DFRA) time to failure distributions applicable to nonrepairable objects.     

On analysing warranty data from repairable items

Fitting models to failure data is an important topic in reliability. The resulting models can be useful both for manufacturers as well as for end‐users. In this paper we provide details of some methods from the literature which can be used as a starting point when analysing and fitting models to failure data from repairable items. In particular we focus on obtaining analytical estimates of the intensity of a non‐homogeneous Poisson process. We illustrate some of these methods on failure data from the warranty database of a major car manufacturer. Copyright © 2009 John Wiley & Sons, Ltd.     

Some flexible families of intensities for non‐homogeneous Poisson process models and their Bayes inference

Non‐homogeneous Poisson processes are useful for modeling repairable system reliability. An NHPP is specified in terms of a non‐negative failure rate or intensity function. Standard parametric forms such as the well‐known power law process intensity are constant, increasing without bound or decreasing to zero. These provide limited flexibility in modeling. For example, under them the failure rate of a system cannot increase or decrease to a positive, finite constant. In this article we consider a variety of more flexible (and yet tractable) families of intensities built on the notion of switching in time between two simple constituent intensities. We consider the problem of Bayesian inference in these families based on Markov chain Monte Carlo posterior samples. Examples are provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Extended block diagram method for a multi-state system reliability assessment

The presented method extends the classical reliability block diagram method to a repairable multi-state system. It is very suitable for engineering applications since the procedure is well formalized and based on the natural decomposition of the entire multi-state system (the system is represented as a collection of its elements). Until now, the classical block diagram method did not provide the reliability assessment for the repairable multi-state system. The straightforward stochastic process methods are very difficult for engineering application in such cases due to the “dimension damnation”—huge number of system states. The suggested method is based on the combined random processes and the universal generating function technique and drastically reduces the number of states in the multi-state model.     

Modeling the failure data of a repairable equipment with bathtub type failure intensity

The paper deals with the reliability modeling of the failure process of large and complex repairable equipment whose failure intensity shows a bathtub type non-monotonic behavior. A non-homogeneous Poisson process arising from the superposition of two power law processes is proposed, and the characteristics and mathematical details of the proposed model are illustrated. A graphical approach is also presented, which allows to determine whether the proposed model can adequately describe a given failure data. A graphical method for obtaining crude but easy estimates of the model parameters is then illustrated, as well as more accurate estimates based on the maximum likelihood method are provided. Finally, two numerical applications are given to illustrate the proposed model and the estimation procedures.     

Reliability analysis for a circular consecutive-2-out-of-n:F repairable system with priority in repair

A circular consecutive-2-out-of-n:F repairable system with one repairman is studied in this paper. When there are more than one failed component, priorities are assigned to the failed components. Both the working time and the repair time of each component is assumed to be exponentially distributed. Every component after repair is as good as new. By using the definition of generalized transition probability and the concept of critical component, we derive the state transition probability matrix of the system. Methodologies are then presented for the derivation of system reliability indexes such as availability, rate of occurrence of failure, mean time between failures, reliability, and mean time to first failure.     

Rare events probabilities estimation by “ Russian Roulette and Splitting ” simulation technique

An advanced Monte Carlo Simulation (MCS) technique—namely, “Russian Roulette and Splitting” (RR & S) technique is applied for the reliability assessment of mechanical systems under stochastic excitations. The basic features of the algorithm are described and discussed. As a numerical example the technique is used for the numerical solution of the first passage problem in the low probability range. Results are compared with available solutions, obtained by another variance reduction technique—“Double and Clump”(D & C) procedure.     

Mincut-based fault tree analysis revisited and extended for calculating MTBF

It is shown that, with the mincuts given, the Shannon approach is strongly challenged by an approach resulting in subproduct inversions, based on a simple partitioning of the system faults. A simple heuristic is given for an almost optimal determination of i) system unavailability ii)—after a little addendum—system mean failure frequency; the latter for s-independent repairable components. In order to speed up calculations, optimal approximations with prescribed accuracy are possible, both for unavailability and mean failure frequency.     

Modeling repair events under intermittent failures and failures subject to unsuccessful repair

Intermittent failures are sometimes observed for a repairable system, such as an automobile. Such failures often lead to a series of unsuccessful repair attempts before the source of the failure has been identified and removed. Unsuccessful repair is also observed in cases where the failures are not intermittent. In order to model data involving repeated repair attempts related to the same failure, repair times cannot usually be assumed negligible and the model must be designed or modified to account for these. In this paper, we propose a modified version of the branching Poisson process model introduced by Lewis (1964). We discuss statistical inference procedures for this model and demonstrate these procedures using the service history of a new automobile. Copyright © 2002 John Wiley & Sons, Ltd.     

Generalized renewal process for analysis of repairable systems with limited failure experience

Repairable systems can be brought to one of possible states following a repair. These states are: ‘as good as new’, ‘as bad as old’, ‘better than old but worse than new’, ‘better than new’, and ‘worse than old’. 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 three, which are more realistic in practice. In this paper, a robust solution to a probabilistic model that is applicable to all of the five after repair states, called generalized renewal process (GRP), is presented. This research demonstrates that the GRP offers a general approach to modeling repairable systems and discusses application of the classical maximum likelihood and Bayesian approaches to estimation of the GRP parameters. This paper also presents a review of the traditional approaches to the analysis of repairable systems as well as some applications of the GRP and shows that they are subsets of the GRP approach. It is shown that the proposed GRP solution accurately describes the failure data, even when a small amount of failure data is available.Recent emphasis in the use of performance-based analysis in operation and regulation of complex engineering systems (such as those in space and process industries) require use of sound models for predicting failures based on the past performance of the systems. The GRP solution in this paper is a promising and efficient approach for such performance-based applications.     

Bayesian analysis of repairable systems showing a bounded failure intensity

The failure pattern of repairable mechanical equipment subject to deterioration phenomena sometimes shows a finite bound for the increasing failure intensity. A non-homogeneous Poisson process with bounded increasing failure intensity is then illustrated and its characteristics are discussed. A Bayesian procedure, based on prior information on model-free quantities, is developed in order to allow technical information on the failure process to be incorporated into the inferential procedure and to improve the inference accuracy. Posterior estimation of the model-free quantities and of other quantities of interest (such as the optimal replacement interval) is provided, as well as prediction on the waiting time to the next failure and on the number of failures in a future time interval is given. Finally, numerical examples are given to illustrate the proposed inferential procedure.     

Integration of computation and testing for reliability estimation

This paper develops a methodology to integrate reliability testing and computational reliability analysis for product development. The presence of information uncertainty such as statistical uncertainty and modeling error is incorporated. The integration of testing and computation leads to a more cost-efficient estimation of failure probability and life distribution than the tests-only approach currently followed by the industry. A Bayesian procedure is proposed to quantify the modeling uncertainty using random parameters, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. An adaptive method is developed to determine the number of tests needed to achieve a desired confidence level in the reliability estimates, by combining prior computational prediction and test data. Two kinds of tests — failure probability estimation and life estimation — are considered. The prior distribution and confidence interval of failure probability in both cases are estimated using computational reliability methods, and are updated using the results of tests performed during the product development phase.     

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

ABSTRACT

In 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.     

Estimation of future breakdowns to determine optimal warranty policies for products with deterioration

Warranty has been played an important role not only for safeguarding the rights and interests of consumers but also for promoting the sales and reputation of manufacturers, since a good warranty policy signifies the image of high-quality products and thus becomes a powerful weapon for marketing products in increasingly competitive markets. It is obvious that a more thoughtful warranty policy of a product will attract more customers to consume the specific product, and increase the product's market share accordingly. However, an unlimited warranty for monopolizing the market is absolutely unrealistic, since the cost will significantly increase for maintaining such a warranty policy with better offers. In this paper, a Bayesian decision model for determining the optimal warranty policy for repairable products is proposed. The successive failure times of the repairable product are assumed to be drawn from a nonhomogeneous Poisson process. Both the repair costs for restoring the product to full functionality after each breakdown and the potential sales increases due to the specific warranty policy are also considered. Finally, an application case is utilized to demonstrate the feasibility and validity of the proposed approach.     

Transient behavior of time‐between‐failures of complex repairable systems

It is well known for complex repairable systems (with as few as four components), regardless of the time‐to‐failure (TTF) distribution of each component, that the time‐between‐failures (TBFs) tends toward the exponential. This is a long‐term or ‘steady‐state’ property. Aware of this property, many of those modeling such systems tend to base spares provisioning, maintenance personnel availability and other decisions on an exponential TBFs distribution. Such a policy may suffer serious drawbacks. A non‐homogeneous Poisson process (NHPP) accounts for these intervals for some time prior to ‘steady‐state’. Using computer simulation, the nature of transient TBF behavior is examined. The number of system failures until the exponential TBF assumption is valid is of particular interest. We show, using a number of system configurations and failure and repair distributions, that the transient behavior quickly drives the TBF distribution to the exponential. We feel comfortable with achieving exponential results for the TBF with 30 system failures. This number may be smaller for configurations with more components. However, at this point, we recommend 30 as the systems failure threshold for using the exponential assumption. Copyright © 2002 John Wiley & Sons, Ltd.     

Setting reliability requirements based on minimum failure‐free operating periods

A new reliability methodology and tools have been created for setting reliability requirements. At the heart of the new methodology are reliability requirements based on specified minimum failure‐free operating (MFFOP) intervals and a maximum acceptable level of the probability of premature failure. These types of requirements are suitable to industries where the consequences of failure and the cost of intervention for maintenance are very high (e.g. deepwater offshore oil and gas industries). The methodology proposed includes models and tools for: (i) setting reliability requirements to limit the risk of premature failure below an acceptable level; (ii) setting reliability requirements to minimize the total losses; and (iii) setting reliability requirements to guarantee a set of MFFOP intervals. An advantage of the MFFOP approach is that it directly links the reliability requirements with health, safety, environmental and business risks. Another advantage is that the MFFOP requirements are suitable for non‐constant hazard rates where the mean time to failure (MTTF) reliability measure is often misleading. A solution to the important problem of determining the maximum hazard rate that guarantees with a required probability the existence of a specified set of MFFOP intervals has also been found. The reliability tools proposed also permit the extraction of useful information from data sets containing a given number of random failures, in cases where the failure times are unknown. Copyright © 2003 John Wiley & Sons, Ltd.