Nasser Fard

A maintenance policy for repairable systems based on opportunistic failure-rate tolerance

An opportunistic hazard rate replacement policy for a repairable system with several types of units is presented. A unit is repaired at failure when the hazard rate falls in (0, L-u). A unit is replaced at failure when the hazard rate falls in (L-u, L). An operating unit is replaced when its hazard rate reaches L. When a unit is replaced because its hazard rate reaches L, all operating units with their hazard rates falling in (L-u, L) are replaced. The long-run mean cost rate as a function of L and u is derived. Optimal L and u are obtained to minimize the total maintenance cost rate. Application and analysis of results are demonstrated through a numerical example. The maintenance model is designed for a system with multitype units. Each type has its own increasing hazard rate. Units are repaired or replaced depending on their hazard rate at a failure or active replacement of another unit. The repair interval, replacement limit, and replacement tolerance are determined to yield the optimal total maintenance cost rate. >

Cutset enumeration of network systems with link and node failures

Abstract Network reliability analysis has received considerable attention and is thus widely studied to predict and prevent any network failure. However, most of such works presume perfectly reliable nodes. Although a few studies have considered both link and node failures, none of these methods has utilized the minimal paths or cuts, which are considered as fundamental approaches in the network reliability evaluation. An efficient method for deducing the minimal cutsets of a system subject to both link and node failures from the minimal cutsets of the system, which assumes perfect node reliability, is presented. The proposed method does not require re-enumeration of minimal cutsets for the additional consideration of the node failures. For a simple extension of such a method, the proposed approach can be embedded in any exact or approximate algorithm to account for link failures as well as node failures. As a result, the application of this method would be more realistic and valuable in practice for the reliability evaluation of networks with unreliable nodes.

Optimum Bivariate Step-Stress Accelerated Life Test for Censored Data

A step-stress accelerated life test for two stress variables is developed. The time to failure follows the Weibull distribution, and the test is subject to termination at a predetermined time, leading to censored failure data. An optimum test plan is developed to determine the test interval for each combination of stress levels. The scale parameter of the Weibull distribution for each combination of stress levels is defined as a log linear function of the stress levels. The optimal criterion is defined to minimize the asymptotic variance of the maximum likelihood estimator of the life for a specified reliability

A Bayes Reliability Growth Model for A Development Testing Program

The problem of estimating the reliability of a system during development is considered. The development process has several stages at each stage binomial test data are obtained by testing a number of such systems on a success/fail basis. Marginal posterior distributions are derived under the assumption that the development process constrains the reliabilities to be nondecreasing and that the prior distribution for reliability at each stage is uniform. Simulation models are designed to facilitate testing for the validity and computation of the Bayesian model with ordered reliabilities as well as to compare results with other reliability growth models.

Reliability Bounds for Large Multistage Interconnection Networks

To derive the exact reliability expressions for large Multi-stage Interconnection Networks (MINs) can become rather complex. As network size increases, the reliability bounds could be used to estimate the reliability of the networks. In this paper, terminal, broadcast, lower and upper bounds network reliability will be determined. Lower bound reliability is the minimum probability that the system will be operational for a specified time. Upper bound reliability presents an optimistic view of probability that the system will work at some specified time, which is not the center of attention in terms of reliability point of view. If the lower bound reliability provides sufficient assurance that the system will be operational at some specified time, then no further effort for obtaining the exact reliability expression is necessary. As examples, the derivation of terminal, broadcast, lower and upper bounds network reliability expressions of the extra-stage cube network will be demonstrated.

Determination of minimal cut sets of a complex fault tree

Minimum cut sets are commonly obtained for evaluation of large fault trees. The number of minimum cut sets usually increases with the size of trees and this leads to a complexity in the evaluation of a fault tree. Modules of fault trees could be developed to reduce the size of trees and simplify the quantitative analysis. This paper will discuss procedures for developing modules, and methods for finding the minimum cut sets of a fault tree.

An approximate method for non-repairable systems based on oppurtunistic replacement policy

Abstract An opportunistic replacement policy for a multi-unit system with various failure rates is developed. The objective function is to minimize the total maintenance cost due to preventive and failure replacement. Failure rate is used as replacement criterion for each unit. Units are replaced at failure or at a failure rate limit, L, whichever occurs first. A unit is also replaced at replacement time of another unit if its failure rate falls in a preventive replacement interval, (L-u, L). A solution method to obtain the value of and u is presented. The solution procedure is demonstrated through an algorithm followed by a numerical example.

TERMINAL RELIABILITY IMPROVEMENT OF SHUFFLE-EXCHANGE NETWORK SYSTEMS

Multistage Interconnection Networks (MINs) are communication network systems that provide fast and efficient information transitions among N processors and N memory modules of systems. A typical MIN consists of layers of switching elements that are connected together in a predefined topology. The routing capability of a network depends on its specific topology. A shuffle-exchange network (SEN), a specific type of MIN that consists of 2 × 2 switching elements, has been widely considered a practical interconnection system. In this paper, a modified shuffle-exchange network with 1 × 2 switching elements at the input (source) stage, 2 × 2 switching elements at the intermediate stages, and 2 × 1 switching elements at the output (terminal) stage is proposed. The proposed network shows an improvement in the terminal reliability of SEN. The terminal reliability evaluation of the SEN and the modified SEN are demonstrated through numerical examples for different sizes of networks. The reliability evaluation of MINs is important, as it determines the usability and efficiency of the network to provide services. It is shown that the proposed modified SEN provides higher terminal reliability for network sizes larger than 4 inputs and 4 outputs (4 × 4).

Terminal Reliability Assessment of Gamma and Extra‐Stage Gamma Networks

Purpose – Multistage Interconnection Networks (MINs) are a class of network systems designed to improve communication in large‐scale parallel processing systems. These networks facilitate the communications to perform a single overall task in a parallel processing system consisting of a large number of processors that are working together. The purpose of this paper is to discuss two types of MINs: gamma networks and extra‐stage gamma networks. It is shown that a specific modification in the structure of a standard gamma network will add multiple paths from a specific source to a specific destination.Design/methodology/approach – The terminal reliability of these networks are evaluated and analyzed in terms of the number of their paths connecting a source i, i=1, 2, … , N to any terminal. Numerical examples are also given to demonstrate each networks performance.Findings – In this paper, terminal reliability as a function of the reliability of a switching element of MINs is analyzed. Terminal reliability,...

Nonparametric data reduction approach for large-scale survival data analysis

In the era of big data, analysis of complex and huge data expends time and money, may cause errors and misinterpretations. Consequently, inaccurate and erroneous reasoning could lead to poor inference and decision making, sometimes irreversible and catastrophic events. On the other hand, proper management and utilization of valuable data could significantly increase knowledge and reduce cost by preventive actions. In this field, time-to-event and survival data analysis is a kernel of risk assessment and have an inevitable role in predicting the probability of many events occurrence such as failure of a device or component. Thus, in the presence of large-scale, massive and complex data, specifically in terms of variables, applying proper methods to efficiently simplify such data before any analysis process is desired. In this paper we propose an applied data reduction approach which enables us to obtain appropriate variable selection in high dimensional and large-scale data in order to avoid aforementioned difficulties in decision making and facilitate survival data and failure analysis. This paper present applied data reduction and variable selection approach for risk assessment and decision making in complex large-scale survival data analysis.