Universal Generating Function Approach Research Articles

Performability of Service Chains with Rejuvenation: A Multidimensional Universal Generating Function Approach

Performability of Service Chains with Rejuvenation: A Multidimensional Universal Generating Function Approach

Signature reliability scrutiny of domestic refrigerator

PurposeThe purpose of this paper is to evaluate the reliability and structure function of refrigeration complex system consisted of four components in complex manner.Design/methodology/approachAlthough, a variety of methodologies have been used to assess the refrigeration system's reliability function that has proven to be effective, the universal generating function approach is the basis of this research study, which is used in the calculation of a domestic refrigeration system with four separate components that are related in series and parallel with a corresponding sample to form a complex machine.FindingsIn this paper, signature reliability of the refrigeration system has been evaluated with the universal generating function technique. There are four components present in the proposed system in complex (series and parallel) manner. The tail signature, signature, Barlow–Proschan index, expected lifetime and expected cost of independent identically distributed are all computed.Originality/valueThis is the first study of domestic refrigeration system to examine the signature reliability with the help of universal generating function techniques with various measures. Refrigeration systems are an essential process in industries and home applications as they perform cooling or the maintain temperature at the desired value. A cycle of refrigeration consists of four main components such as, heat exchange, compression and expansion with a refrigerant flowing through the units within the cycle.

Definitions of generalized multi-performance weighted multi-state K¯-out-of-n system and its reliability evaluations

The k-out-of-n system model is widely applied for the reliability evaluation of many technical systems. Multi-state system modelling is also widely used for representing real systems, whose components can have different levels of performance. For these researches, recently multi-state k-out-of-n systems have been comprehensively studied. In these studies, it is usually assumed that the system has a single task function to complete in a given environment. Moreover, the system or component performance is characterised by one measure, for example “electric power” in generation systems or “flow-rate” in transmission systems. However, this can be a simplification for some real-life engineering systems. For example, an intertwined district heating and electricity system consists of combined heat and power generating units, which can produce both electricity and heat. In this paper, definitions of multi-performance weighted multi-state components are provided and two generalized multi-performance multi-state K¯-out-of-n system models are proposed. Universal generating function approach is developed for the evaluation of such systems, with two numerical examples.

A universal generating function-based multi-state system performance model subject to correlated failures

Multi-state system (MSS) reliability modeling is a paradigm that allows both systems and components to exhibit more than two performance levels. While several researchers have introduced correlation or dependence into MSS models to assess its negative influence on performance and associated measures, these methods exhibit complexity that is exponential or worse in the worst case. To overcome this limitation, this paper proposes an extension to the discrete universal generating function approach for MSS to allow correlation between the elements comprising a multi-state component. We subsequently generalize to the continuous case and allow failures to follow any life distribution. The approach possesses an analytical form and therefore enables efficient performance and reliability assessment as well as sensitivity analysis on the impact of correlation. This sensitivity analysis can be applied to a wide range of measures including performance, reliability, the density function, hazard rate, mean time to failure, availability, and mean residual life. The approach is illustrated through a series of examples, demonstrating the efficiency of the approach to assess performance and reliability as well as to conduct sensitivity analysis. The results indicate that the approach can identify the impact of correlation on performance, reliability, and the many measures of interest.

Random Fuzzy Extension of the Universal Generating Function Approach for the Reliability Assessment of Multi-State Systems Under Aleatory and Epistemic Uncertainties

Many engineering systems can perform their intended tasks with various levels of performance, which are modeled as multi-state systems (MSS) for system availability and reliability assessment problems. Uncertainty is an unavoidable factor in MSS modeling, and it must be effectively handled. In this work, we extend the traditional universal generating function (UGF) approach for multi-state system (MSS) availability and reliability assessment to account for both aleatory and epistemic uncertainties. First, a theoretical extension, named hybrid UGF (HUGF), is made to introduce the use of random fuzzy variables (RFVs) in the approach. Second, the composition operator of HUGF is defined by considering simultaneously the probabilistic convolution and the fuzzy extension principle. Finally, an efficient algorithm is designed to extract probability boxes ( p-boxes) from the system HUGF, which allow quantifying different levels of imprecision in system availability and reliability estimation. The HUGF approach is demonstrated with a numerical example, and applied to study a distributed generation system, with a comparison to the widely used Monte Carlo simulation method.

Reliability of Series-Parallel Systems With Random Failure Propagation Time

This paper presents an algorithm for evaluating the reliability and performance distribution of complex non-repairable series-parallel multi-state systems with common cause failures caused by propagation of failures in system elements. The failure propagation can have a selective effect, which means that the failures originating from different elements can cause failures of different subsets of system elements. The failure propagation time is assumed to be a random value with a given distribution. The suggested algorithm is based on the universal generating function approach, and a generalized reliability block diagram method (recursive aggregation of pairs of elements and their replacement by an equivalent one). The evaluation procedure is repeated for each combination of elements affected by the common cause failures. Illustrative examples are provided.

Reliability assessment of N-version software fault tolerant system with common mode failures

Common mode failures create the major impact on the system reliability in many real time systems. In this paper, we incorporate the concept of common mode faults (CMF) for the reliability prediction of fault tolerant software system consisting of N-version with different failure characteristics. The common mode faults may occur simultaneously in two or more versions due to faults in the common communication buses or shared environmental factors, failure of common source of power, design mistake, etc.. The recursive algorithm based on universal generating function approach is presented to obtain the system probabilities. Various performance measures of the fault tolerant software system are established. Furthermore, by setting appropriate parameters, some special cases are illustrated numerically.

Multi-state systems with selective propagated failures and imperfect individual and group protections

The paper presents an algorithm for evaluating performance distribution of complex series–parallel multi-state systems with propagated failures and imperfect protections. The failure propagation can have a selective effect, which means that the failures originated from different system elements can cause failures of different subsets of elements. Individual elements or some disjoint groups of elements can be protected from propagation of failures originated outside the group. The protections can fail with given probabilities. The suggested algorithm is based on the universal generating function approach and a generalized reliability block diagram method. The performance distribution evaluation procedure is repeated for each combination of propagated failures and protection failures. Both an analytical example and a numerical example are provided to illustrate the suggested algorithm.

Reliability and performance of multi-state systems with propagated failures having selective effect

The paper presents an algorithm for evaluating performance distribution of complex series-parallel multi-state systems with common cause failures caused by propagation of failures in system elements. The failure propagation can have a selective effect, which means that the failures originated from different elements can cause failures of different subsets of system elements. The suggested algorithm is based on the universal generating function approach and a generalized reliability block diagram method (recursive aggregation of pairs of elements and their replacement by an equivalent one). The performance distribution evaluation procedure is repeated for each combination of common cause failures. Illustrative examples are provided.

Approximation algorithm for evaluating time-to-failure distribution of k-out-of- n system with shared standby elements

The paper presents an approximation algorithm for evaluating cdf of time-to-failure for k-out-of- n systems with shared spare elements. The working and spare elements can have different arbitrary distributions of time-to-failure. Different spare elements can be in different standby modes: cold, hot and warm. The algorithm is based on a universal generating function approach. It is shown that for small k the algorithm outperforms simulation.

Reliability evaluation of multi-state weighted [formula omitted]-out-of- [formula omitted] systems

The k -out-of- n systems have been extensively studied in recent years. A binary weighted k -out-of- n model has also been reported in the literature. In this paper, we first compare two approaches for reliability evaluation of binary weighted k -out-of- n systems. We then provide two models of multi-state weighted k -out-of- n system models. Recursive algorithms are presented for reliability evaluation of these new models. The universal generating function approach is also used for reliability evaluation of multi-state weighted k -out-of- n systems.

Optimization of series–parallel multi-state systems under maintenance policies

In the redundancy optimization problem, the design goal is achieved by discrete choices made from components available in the market. In this paper, the problem is to find, under reliability constraints, the minimal cost configuration of a multi-state series–parallel system, which is subject to a specified maintenance policy. The number of maintenance teams is less than the number of repairable components, and a maintenance policy specifies the priorities between the system components. To take into account the dependencies resulting from the sharing of maintenance teams, the universal generating function approach is coupled with a Markov model. The resulting optimization approach has the advantage of being mainly analytical.

A universal generating function approach for the analysis of multi-state systems with dependent elements

Abstract The paper extends the universal generating function technique used for the analysis of multi-state systems to the case when the performance distributions of some elements depend on states of another element or group of elements.

Reliability of acyclic multi-state networks with constant transmission characteristics of lines

Abstract Multi-state acyclic networks (MANs) consist of a number of independent multi-state nodes (MNs). Each network has a root MN (source), a number of intermediate MNs and a sink node. All the nodes are ordered and each node (except the sink) is connected by edges with a set of nodes with greater numbers. Each MN can have different states determined by a subset of available edges. Probability of each MN state is assumed to be known for every MN. The aim of the MAN is transmission of information or material flow from source to sink. The transmission process intensity depends on transmission characteristics (TCs) of network elements. In this paper we suggest a method for determining TC of the entire MAN based on TCs and availability of its elements. The MAN reliability is defined as probability that its TC meets some specified demand. A universal generating function approach is suggested for estimating reliability of MANs of different physical nature. In order to demonstrate the flexibility of the approach two different types of MANs are considered: minimal transmission time networks and maximal flow path networks. Illustrative examples are presented.