Inter-failure Times Research Articles

A bivariate two-state Markov modulated Poisson process for failure modeling

Motivated by a real failure dataset in a two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for the modeling of dependent and non-exponential inter-failure times (in contexts as queuing, risk or reliability, among others). The novel two-dimensional MMPP allows for dependence between the two sequences of inter-failure times, while at the same time preserves the MMPP properties, marginally. The generalization is based on the Marshall–Olkin exponential distribution. Inference is undertaken for the new model through a method combining a matching moments approach with an Approximate Bayesian Computation (ABC) algorithm. The performance of the method is shown on simulated and real datasets representing times and distances covered between consecutive failures in a public transport company. For the real dataset, some quantities of importance associated with the reliability of the system are estimated as the probabilities and expected number of failures at different times and distances covered by trains until the occurrence of a failure.

Monitoring reliability for a gamma distribution with a double progressive mean control chart

AbstractControl charting technique for time between events (TBE) is very important in high‐yield processes for monitoring reliability. For a regularly maintained system, the interfailure times can be modeled by a gamma distribution. This article proposes a new control chart based on the double progressive mean statistic for monitoring the time between k (≥1) failures of a maintained gamma distributed system (referred as DPM‐TBE chart). The performance of the proposed scheme is measured in terms of the average run‐length (ARL) for the case when the scale parameter is known as well as when it is unknown and is estimated from an in‐control (IC) reference sample. A comparison study with other TBE charts shows that the DPM‐TBE chart is more effective. In addition, the proposed chart is shown to be very robust for large shifts when the true distribution of time between failures is a Weibull or a lognormal. Finally, an illustrative example is given to demonstrate the implementation of the proposed chart.

Reliability analysis of underground rock bolters using the renewal process, the non-homogeneous Poisson process and the Bayesian approach

PurposeReliability plays an important role in the execution of the maintenance improvement and the understanding of its concepts is essential to predict the type of maintenance according to the equipment state. Thereby, a computational tool was developed and programming with VBA in Excel® for reliability and failure analysis in a mining context. The paper aims to discuss these issues.Design/methodology/approachThe developed approach use the modeling of stochastic processes, such as the renewal process, the non-homogeneous Poisson process and less conventional method as the Bayesian approach, by considering Jeffreys non-informative prior. The resolution gives the best associated model, the parameters estimation, the mean time between failure and the reliability estimate. This approach is validated with the reliability analysis of inter-failure times from underground rock bolters subsystems, over a two-year period.FindingsResults show that Weibull and lognormal probability distribution fit to the most subsystems inter-failure times. The study revealed that the bolting head, the rock drill, the screen handler, the electric/electronic system, the hydraulic system, the drilling feeder and the structural consume the most repair frequency. The hydraulic and electric/electronic subsystems represent the lowest reliability after 50 operation hours.Originality/valueFor the first time, this case study defines practical failures and reliability information for rock bolter subsystems based on real operation data. This paper is useful to the comparative evaluation of rock bolter by detecting the weakest elements and understanding failure patterns in the individual observation subsystems on the overall machine performance.

Reliability Prediction of Computing Network with Software and Hardware Failures

In this paper, we investigate the reliability and queueing performance indices for the fault-tolerant computing network having a finite number of unreliable operating components with the provision of warm standby components. Operating and standby components are governed by dedicated software which is also prone to random failure. On failure of operating components, available standby component(s) may switch from the standby state to operating state with negligible switchover time. The switchover process may also fail due to some automation hindrance. The computing network is also subjected to common cause failure in lieu of external cause. The studied redundant fault-tolerant computing network is framed as a Markovian machine interference model with exponentially distributed inter-failure times and service times. For the reliability prediction of the computing network, various performance measures, namely, mean-time-to-failure (MTTF), reliability/availability, failure frequency, etc., have been formulated in terms of transient-state probabilities which we have obtained using the spectral method. To show the practicability of the developed model, numerical simulation has been done. Sensitivity analysis of reliability and other indices of the computing network with respect to different network parameters has been presented, and results are summarized in the tables and graphs. Finally, future scope and concluding remarks have been included.

An extended geometric process and its application in replacement policy

In this article, we develop an extended geometric process model with a recovery factor and propose a two-dimensional evaluation function for each maintenance effect. The developed model can describe the mean inter-failure time which can be improved by the first or several former repairs in some repairable systems. We also propose parameter estimation methods for the developed geometric process model and use some real failure datum to prove the model’s application. Focused on the developed geometric process model, two novel replacement policies and their optimizations are also presented in detail. Then, two real case studies are discussed to illustrate the modelling and optimizing process. Modelling results show that each recovery factor is related to the effect of each repair, and the developed geometric process model has a good-fitting property for some real cases. Optimization results display that the optimal ( N, m) replacement policy is applicable for some small-sized manufacturing systems, whereas the proposed ( N) replacement policy is suitable for some expensive systems.

Joint planning of service engineers and spare parts

We analyze the joint optimization of spare parts inventories and workforce allocation in a single-site maintenance system. In this system, for each failure, a service engineer with a necessary replacement part has to be allocated. If one of the required resources is not available, the incoming failure request is routed to an external provider, such as a centralized repair facility or a sub-contractor. We study multiple failure types (related to failing components) with exponentially distributed inter-failure times. The system repair times and the replenishment times of the spare parts inventory are also exponentially distributed. The inventory replenishment is done according to a Base-Stock policy. The objective is to minimize the total system cost consisting of annual holding costs of the spare parts and the service engineers, and incidental outsourcing costs. For the joint optimization of the resources, we propose a Mixed-Integer Programming (MIP) formulation using the balance equations of the Markov Chain representation of the system. Furthermore, we provide a simple and efficient heuristic that produces close-to-optimal (< 0.3% difference) results, for solving larger instances. Using the proposed optimization methods and real-life data, we analyze the optimal balance between the costs of the resources and the outsourcing costs and show how the outsourcing rates and the total costs behave for different system parameters.

Modeling dependence in the inter-failure times. An analysis in Reliability models by Markovian Arrival Processes

The most common assumptions in reliability studies are that failures occur independently and with the same distribution. However, these two assumptions are unrealistic in practice since inter-failure times are usually correlated and not identically distributed. In this sense the Markov Arrival Process (MAP) is an active research field for managing these features. We study two versions of the MAP approach. The first one is a model which we developed in previous works. The second one is based on a non-stationary M A P of second order. We compare the results of both models with simulated data.

Stochastic comparisons of interfailure times under a relevation replacement policy

AbstractWe provide some results for the comparison of the failure times and interfailure times of two systems based on a replacement policy proposed by Kapodistria and Psarrakos (2012). In particular, we show that when the first failure times are ordered in terms of the dispersive order (or, the excess wealth order), then the successive interfailure times are ordered in terms of the usual stochastic order (respectively, the increasing convex order). As a consequence, we provide comparison results for the cumulative residual entropies of the systems and their dynamic versions.

On parameter estimation of software reliability models

ABSTRACTMost software reliability models use the maximum likelihood method to estimate the parameters of the model. The maximum likelihood method assumes that the inter-failure time distributions contribute equally to the likelihood function. Since software reliability is expected to exhibit growth, a weighted likelihood function that gives higher weights to latter inter-failure times compared to earlier ones is suggested. The accuracy of the predictions obtained using the weighted likelihood method is compared with the predictions obtained when the parameters are estimated by the maximum likelihood method on three real datasets. A simulation study is also conducted.

Reliability parameters estimation for parallel systems under imperfect repair

We consider in this paper a parallel system consisting of \(\eta \) identical components. Each component works independently of the others and has a Weibull distributed inter-failure time. When the system fails, we assume that the repair maintenance is imperfect according to the Arithmetic Reduction of Age models (\(ARA_{m}\)) proposed by Doyen and Gaudoin. The purpose of this paper is to generate a simulated failure data of the whole system in order to forecast the behavior of the failure process. Besides, we estimate the maintenance efficiency and the reliability parameters of an imperfect repair following \(ARA_{m}\) models using maximum likelihood estimation method. Our method is tested with several data sets available from related sources. The real data set corresponds to the time between failures of a compressor which is tested by Likelihood Ratio Test (LR). An analysis of the importance and the effect of the memory order of imperfect repair classes (\(ARA_{m}\)) will be discussed using LR test.

Analytical properties of an imperfect repair model and application in preventive maintenance scheduling

The paper considers repairable systems under imperfect repair. The failure rate of a new system is assumed to follow a Weibull distribution and the repair efficiency is characterized by a Kijima type II virtual age model named Arithmetic Reduction of Age with infinite memory. An analytical approach to obtain the distribution of the inter-failure times is presented. The existence of a stationary regime is highlighted and the limiting distributions are explicitly derived. In this context, an optimal age-based preventive maintenance policy can be implemented. Three approaches are proposed, considering a static, a dynamic or a failure limit policy. Numerical simulations are presented to illustrate the policies.

Bounds on uptime distribution based on aging for systems with finite lifetimes

Consider a system which is subject to occasional failures over its lifetime. Under general stochastic assumptions concerning the occurrence of these failures, the duration of the repair times, and the length of the system’s lifetime, the distribution of the total uptime the system accumulates over its lifetime may be determined. While the distribution is unfortunately complicated except in certain circumstances, it is possible to derive useful bounds based on the aging characteristics of the distributions of interfailure times, repair times, and system life. Bounds are developed for the cases where the system lifetime follows (1) a degenerate distribution (or constant mission duration), (2) an exponential distribution, and (3) a general distribution. These bounds may be interpreted as extensions of well-known bounds based on aging notions from renewal theory. Conditions are identified for when the bounds are sharp, and examples are used to show the computational tractability and usefulness of the results.

Prediction of software inter-failure times using artificial neural network and particle swarm optimisation models

Knowledge of time between failures is required for achieving certain reliability goal in a given amount of testing to determine release time of a software. In practice, existing artificial neural network (ANN) models to predict time between failures utilise complex and variable architecture. In this paper, an ANN model and an ANN-PSO model with fixed and simple architecture are proposed to predict time between failures. Effects of scaling time between failures data have been analysed using logarithmic function. In ANN model, the scaling parameter of logarithmic function is determined by varying maximum scaled value in a certain range. In ANN-PSO model, the scaling parameter is determined automatically during ANN training using particle swarm optimisation (PSO) algorithm. Proposed models are applied on literature reported datasets and found that ANN-PSO model provides better performance than ANN model trained using back propagation algorithm in terms of normalised mean square error.

로그형 관측고장시간에 근거한 결함 발생률을 고려한 소프트웨어 비용 모형에 관한 비교 연구

Abstract In this study, reliability software cost model considering logarithmic fault detection rate based on observations from the process of software product testing was studied. Adding new fault probability using the Goel-Okumoto model that is widely used in the field of reliability problems presented. When correcting or modifying the software, finite failure non-homogeneous Poisson process model. For analysis of software cost model considering the time-dependent fault detection rate, the parameters estimation using maximum likelihood estimation of inter-failure time data was made. In this research, Software developers to identify the best time to release some extent be able to help is considered. Key Words : Logarithmic Fault Detection Rate, Software Release Policy, NHPP, Cost Model, Goel-Okumoto Model Received 2 September 2013, Revised 25 September 2013Accepted 20 November 2013Corresponding Author: Hee-Cheul Kim(Namseoul University) Email: kim1458@nsu.ac.krⒸ The Society of Digital Policy & Management. All rights reserved. This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License(http://creativecommons.otg/licenses/by-nc/3.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is ISSN: 1738-1916 properly cited.

Consistent Single- and Multi-Step Sampling of Multivariate Arrival Times: A Characterization of Self-Chaining Copulas

This paper deals with dependence across marginally exponentially distributed arrival times, such as default times in financial modeling or inter-failure times in reliability theory. We explore the relationship between dependence and the possibility to sample final multivariate survival in a long time-interval as a sequence of iterations of local multivariate survivals along a partition of the total time interval. We find that this is possible under a form of multivariate lack of memory that is linked to a property of the survival times copula. This property defines a self-chaining-copula, and we show that this coincides with the extreme value copulas characterization. The self-chaining condition is satisfied by the Gumbel-Hougaard copula, a full characterization of self chaining copulas in the Archimedean family, and by the Marshall-Olkin copula. The result has important practical implications for consistent single-step and multi-step simulation of multivariate arrival times in a way that does not destroy dependency through iterations, as happens when inconsistently iterating a Gaussian copula.

Characterisation of router and link failure processes in UNINETT's IP backbone network

Backbone networks must be highly reliable. The offered availability can be predicted prior to operation if the stochastic behaviour of network components is known. The aim of this paper is provide information about failures and repairs processes in an operational network. Operational logs from UNINETT's core network were analysed to obtain distributions of the time between failures and downtimes of routers and links. The network components were classified according to their role in the network. The measured processes were fit with well-known distributions. The inter-failure times of routers and short distance links may be characterised by a Weibull distribution, but for the long distance links the gamma distribution yielded a better characterisation. The difference is discussed based on the hazard function. The parameters of each network component are made available and provide a detailed insight that may be used for dependability predictions and research.

The Comparative Study of Software Optimal Release Time Based on Burr Distribution

It is great practical interest to decide when to stop testing a software system in development phase and transfer it to the user. This problem is called as the optimal software release policies. In this research, it was studied about this software release problem. Because of the possibility of introducing new faults when correcting or modifying the software, infinite failure NHPP models presented and propose an optimal release policies of the life distribution applied Burr distribution which makes out efficiency application for software reliability. In this paper, discuss optimal software release policies which minimize a total software cost of development and maintenance under the constraint of satisfying a software reliability requirement. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data (Lyu, M. R. [13]), make out estimating software optimal release time.

지수 및 비지수족 분포 모형에 근거한 소프트웨어 최적방출시기에 관한 비교 연구

본 연구에서는 소프트웨어 제품을 개발하여 테스팅을 거친 후 사용자에게 인도하는 시기를 결정하는 방출문제에 대하여 연구 하였다. 방출문제의 분포는 소프트웨어의 결함을 제거하거나 수정 작업 중에도 새로운 결함이 발생될 가능성이 있는 무한고장수를 가진 비동질적인 포아송 과정에 기초하였다. 수명분포는 지수 족 분포와 비지수족 분포를 이용한 최적 방출시기에 관한 문제를 비교 제시하였다. 이러한 지수 및 비지수분포에 근거하여 소프트웨어 요구 신뢰도를 만족시키고 소프트웨어 개발 및 유지 총비용을 최소화 시키는 최적 소프트웨어 방출 정책에 대하여 논의 되었다. 본 논문의 수치적인 예에서는 고장 간격 시간 자료를 적용하고 모수추정 방법은 최우추정법을 이용하고 추세분석을 통하여 자료의 효율성을 입증한 후 최적 방출시기를 추정하였다. Decision problem called an optimal release policies, after testing a software system in development phase and transfer it to the user, is studied. The applied model of release time exploited infinite non-homogeneous Poisson process. This infinite non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The failure life-cycle distribution used exponential and non-exponential family which has various intensity. Thus, software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time.

강도함수 특성에 근거한 소프트웨어 최적 방출시기에 관한 비교 연구

Abstract In this paper, we were researched decision problem called an optimal release policies after testing a software system in development phase and transferring it to the user. The applied model of release time exploited infinite failure non-homogeneous Poisson process This infinite failure non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The intensity function used Gompertz, Preto and Log-logstic pattern which has the efficient various property. Thus, optimal software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time. Key Words : Software Release Policies, Infinite Non-Homogeneous Poisson Process, Intensity Function Property

와이블 분포 특성에 근거한 소프트웨어 최적 방출시기에 관한 비교 연구

본 연구에서는 소프트웨어 제품을 개발하여 테스팅을 거친 후 사용자에게 인도하는 시기를 결정하는 방출문제에 대하여 연구하였다. 인도시기에 관한 모형은 무한 고장수에 의존하는 비동질적인 포아송 과정을 적용하였다. 이러한 포아송 과정은 소프트웨어의 결함을 제거하거나 수정 작업 중에도 새로운 결함이 발생될 가능성을 반영하는 모형이다. 고장발생 수명분포는 여러 분포들을 적합시키는데 효율적인 특성을 가진 와이블분포를 이용하였다. 따라서 소프트웨어 요구 신뢰도를 만족시키고 소프트웨어 개발 및 유지 총비용을 최소화시키는 방출시간이 최적 소프트웨어 방출 정책이 된다. 본 논문의 수치적인 예에서는 고장 간격 시간 자료를 적용하고 모수추정 방법은 최우추정법과 추세분석을 통하여 자료의 효율성을 입증한 후 최적 방출시기를 추정하였다. In this paper, we were researched decision problem called an optimal release policies after testing a software system in development phase and transferring it to the user. The applied model of release time exploited infinite failure non-homogeneous Poisson process This infinite failure non-homogeneous Poisson process is a model which reflects the possibility of introducing new faults when correcting or modifying the software. The failure life-cycle distribution used the Weibull distribution which has the efficient various property which has the place efficient quality. Thus, optimal software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement becomes an optimal release policies. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, estimated software optimal release time.