Barlow Proschan Research Articles

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.

A copula‐based approach on optimal allocation of hot standbys in series systems

AbstractIn this paper, we propose a copula‐based approach to study the allocation problem of hot standbys in series systems composed of two heterogeneous and dependent components. By assuming that the lifetimes of components and spares are dependent and linked via a general survival copula, optimal allocation strategies are presented for the case of one and two redundancies at the component level. Further, redundancies allocation mechanisms are also compared between the allocations at the component level and the system level. For the case of one hot standby, we find that the performance of the redundant system at the component level is always worse than that at the system level. For the case of two hot standbys, the reversed allocation principle (i.e., Barlow–Proschan principle) is valid. Numerical examples and applications are also provided as illustrations. A real application on improving tensile strength of cables in high voltage electricity transmission network systems is presented for showing the applicability of our results.

Path Tracing Method to Evaluate the Signature Reliability Function of a Complex System

This paper aims to compute the efficiency of a complex communication system (double-bridge). In this model, which applies the Path Tracing Method for evaluating the reliability function of the complex communication system, the process of analyzing the system’s reliability has been used to lower the failure rate of the complex system in order to optimize its competence. The illustrative system is subdivided into nine minimal paths that are arranged in series-parallel combinations. Using the Path Tracing Method, the system’s reliability, minimal signature, tail signature, signature, Barlow–Proschan index, expected time, expected cost, and sensitivity were determined. The results assist in the creation of a probabilistic approach to analyze and probabilistic method to evaluate the system signature and reliability in a way that is highly useful.

Analysis of signature reliability of ring-shaped network system

PurposeThe purpose of this paper is to design a ring network topology system and alter it into a series–parallel type framework. Then, reliability of the framework is analysed and authors also discussed the signature to analyse the most sensitive component.Design/methodology/approachThis study presents a ring-shaped network system where this type of topology forms a single continuous pathway for signals through every node. In this study, a system consists of ring network topology is generalized in the series–parallel mixed configuration and reliability characteristics are evaluated with the assistance of universal generating function (UGF) technique. The system consists of wires, repeaters, components or computers and power supply. The wires and repeaters are in series, so, if they fail the whole system will fail and the signals will not go further. The components or computers are connected to each other in parallel configuration. So, the whole system will not fail until the last computer is working. There is also a two-unit power supply system which has one unit in a standby mode. On the failure of first power supply, the second one will start functioning and the whole system fails on the failure of both power supply.FindingsBy the assistance of UGF technique, reliability function of the framework is evaluated. Also, Barlow–Proschan index and expected lifetime for the designed system is estimated by considering a numerical example for the general ring-shaped network system.Originality/valueUGF technique is very effective for estimating the reliability of a system with complex structure and having two performance rates, i.e. completely failed and perfectly working, or more than two, i.e. multi-state performance. This technique enables to estimate every components contribution in the working and failure of the whole system. A general model of ring-shaped network system is taken and generalized algorithm is drawn for the system. Then a particular numerical example is solved for illustrating the use of this technique.

Signature of bridge structure using universal generating function

The present paper deals with real-life bridge structure and evaluates the reliability function with the help of the universal generating function technique where the components of the system have different performance states. The bridge system (complex) is known as the combination of series and the parallel system where the system cannot be simplified into pure series or pure parallel structure. Universal generating function technique can find the performance of the system as a whole depends upon the overall performance of the components where these components are independent and identically distributed. Also, expected time Barlow–Proschan index, tail signature and signature of the proposed complex system using Owen’s and Boland methods have been calculated.

Signature reliability of linear multi-state sliding window system

PurposeThe purpose of this paper is to deal with a linear multi-state sliding window coherent system which generalizes the consecutive k-out-of-r-from-n:F system in the multi-state case. The system has n linearly ordered multi-state elements consisting of m parallel independent and identically distributed elements. Every element of the system can have two states: completely working or totally failed. The system fails if the sum of performance rate is lower than the given weight.Design/methodology/approachThe authors proposed to compute the signature, MTTF and Barlow–Proschan index with the help of UGF technique of multi-state SWS which consists of m parallel i.i.d. components in each multi-state window.FindingsIn the present study, the authors have evaluated the signature reliability, expected lifetime, cost analysis and Barlow–Proschan index.Originality/valueIn this study, the authors have studied a linear multi-state sliding window system which consists of n ordered multi-state element, and each multi-state element also consists of m parallel windows. The focus of the present paper is to evaluate reliability metrices of the considered system with the help of signature from using the universal generating function.

Computing subsignatures of systems with exchangeable component lifetimes

The subsignatures of a system with continuous and exchangeable component lifetimes form a class of indexes ranging from the Samaniego signature to the Barlow–Proschan importance index. These indexes can be computed through explicit linear expressions involving the values of the structure function of the system. We show how the subsignatures can be computed more efficiently from the reliability function of the system via identifications of variables, differentiations, and integrations.

Computing marginal and joint Birnbaum, and Barlow–Proschan importances in weighted-k-out-of-n:G systems

A weighted-k-out-of-n:G system is a system that consists of n binary components, each with its own positive weight, and operates only when the total weight of working components is at least k. Such a structure is useful when the components have different contributions to the performance of the entire system. This paper is concerned with both marginal and joint Birnbaum, and Barlow–Proschan (BP) importances of the components in weighted- k-out-of-n:G systems. The method of universal generating function is used for computing marginal and joint Birnbaum importances. The method for computing BP-importance is based on a direct probabilistic approach. Extensive numerical calculations are presented. By the help of these calculations and illustrations, it is possible to observe how the marginal and joint importances change with respect to the weights of components.

Subsignatures of systems

We introduce the concept of subsignature for semicoherent systems as a class of indexes that range from the system signature to the Barlow–Proschan importance index. Specifically, given a nonempty subset M of the set of components of a system, we define the M-signature of the system as the |M|-tuple whose kth coordinate is the probability that the kth failure among the components in M causes the system to fail. We give various explicit linear expressions for this probability in terms of the structure function and the distribution of the component lifetimes. We also examine the case of exchangeable lifetimes and the special case when M is a modular set.

Discrete event simulation methods applied to advanced importance measures of repairable components in multistate network flow systems

Discrete event models are frequently used in simulation studies to model and analyze pure jump processes. A discrete event model can be viewed as a system consisting of a collection of stochastic processes, where the states of the individual processes change as results of various kinds of events occurring at random points of time. We always assume that each event only affects one of the processes. Between these events the states of the processes are considered to be constant. In the present paper we use discrete event simulation in order to analyze a multistate network flow system of repairable components. In order to study how the different components contribute to the system, it is necessary to describe the often complicated interaction between component processes and processes at the system level. While analytical considerations may throw some light on this, a simulation study often allows the analyst to explore more details. By producing stable curve estimates for the development of the various processes, one gets a much better insight in how such systems develop over time. These methods are particulary useful in the study of advanced importancez measures of repairable components. Such measures can be very complicated, and thus impossible to calculate analytically. By using discrete event simulations, however, this can be done in a very natural and intuitive way. In particular significant differences between the Barlow–Proschan measure and the Natvig measure in multistate network flow systems can be explored.

On the extensions of Barlow–Proschan importance index and system signature to dependent lifetimes

For a coherent system the Barlow–Proschan importance index, defined when the component lifetimes are independent, measures the probability that the failure of a given component causes the system to fail. Iyer (1992) [3] extended this concept to the more general case when the component lifetimes are jointly absolutely continuous but not necessarily independent. Assuming only that the joint distribution of component lifetimes has no ties, we give an explicit expression for this extended index in terms of the discrete derivatives of the structure function and provide an interpretation of it as a probabilistic value, a concept introduced in game theory. This enables us to interpret Iyer’s formula in this more general setting. We also discuss the analogy between this concept and that of system signature and show how it can be used to define a symmetry index for systems.

Measures of component importance in repairable multistate systems—a numerical study

Dynamic and stationary measures of importance of a component in a repairable multistate system are an important part of reliability. For multistate systems little has been published until now on such measures even in the nonrepairable case. According to the Barlow–Proschan type measures a component is important if there is a high probability that a change in the component state causes a change in whether or not the system state is above a given state. On the other hand, the Natvig type measures focus on how a change in the component state affects the expected system uptime and downtime relative to the given system state. In the present paper we first review these measures which can be estimated using advanced simulation methods. Extending earlier work from the binary to the multistate case, a numerical study of these measures is then given for two three component systems, a bridge system and also applied to an offshore oil and gas production system. In the multistate case the importance of a component is calculated separately for each component state. Thus it may happen that a component is very important at one state, and less important, or even irrelevant at another. Unified measures combining the importances for all component states can be obtained by adding up the importance measures for each individual state. According to these unified measures a component can be important relative to a given system state but not to another. It can be seen that if the distributions of the total component times spent in the non-complete failure states for the multistate system and the component lifetimes for the binary system are identical, the Barlow–Proschan measure to the lowest system state simply reduces to the binary version of the measure. The extended Natvig measure, however, does not have this property. This indicates that the latter measure captures more information about the system.

Measures of Component Importance in Nonrepairable and Repairable Multistate Strongly Coherent Systems

In Natvig and Gasemyr (Methodol Comput Appl Probab 11:603–620, 2009) dynamic and stationary measures of importance of a component in a binary system were considered. To arrive at explicit results the performance processes of the components were assumed to be independent and the system to be coherent. Especially the Barlow–Proschan and the Natvig measures were treated in detail and a series of new results and approaches were given. For the case of components not undergoing repair it was shown that both measures are sensible. Reasonable measures of component importance for repairable systems represent a challenge. A basic idea here is also to take a so-called dual term into account. For a binary coherent system, according to the extended Barlow–Proschan measure a component is important if there are high probabilities both that its failure is the cause of system failure and that its repair is the cause of system repair. Even with this extension results for the stationary Barlow–Proschan measure are not satisfactory. For a binary coherent system, according to the extended Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. With this extension the results for the stationary Natvig measure seem very sensible. In the present paper most of these results are generalized to multistate strongly coherent systems. For such systems little has been published until now on measures of component importance even in the nonrepairable case.

New Results on the Barlow–Proschan and Natvig Measures of Component Importance in Nonrepairable and Repairable Systems

In this paper dynamic and stationary measures of importance of a component in a binary system are considered. To arrive at explicit results we assume the performance processes of the components to be independent and the system to be coherent. Especially, the Barlow–Proschan and the Natvig measures are treated in detail and a series of new results and approaches are given. For the case of components not undergoing repair it is shown that both measures are sensible. Reasonable measures of component importance for repairable systems represent a challenge. A basic idea here is also to take a so-called dual term into account. According to the extended Barlow–Proschan measure a component is important if there are high probabilities both that its failure is the cause of system failure and that its repair is the cause of system repair. Even with this extension results for the stationary Barlow–Proschan measure are not satisfactory. According to the extended Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. With this extension the results for the stationary Natvig measure seem very sensible.

A Combinatorial Approach for Component Importance

A number of structural importance measures like Birnbaum importance, Barlow–Proschan importance etc., are used for studying component importance in a system. A unified approach for calculating component importance in a system was introduced by Seth and Ramamurthy. It is based on the concept of structural matrix which needs to be determined from the simple form of a structure function of a system. In this article, we present a combinatorial expression for the elements of the structural matrix. Other related results and applications of this approach to different systems are considered. Results of this article is also applicable to the problem of finding power of a player in game theory.

The Barlow–Proschan importance and its generalizations with dependent components

For a coherent system the Barlow–Proschan measure of importance of component i, defined when the components are independent to be the probability that i causes system failure, will here be generalized to the case where the component lifetimes are jointly absolutely continuous but not necessarily independent. When the system has a modular decomposition, properties analogous to that of the Barlow–Proschan measure are proved. Xie has generalized the Barlow–Proschan importance using the system yield function when all components are independent. This will be extended here to dependent components.

BOOK REVIEWS

Book review in this Article Man‐Machine Engineering. By ALPHON SECH APANIS. Leaning for Leaahship. By A. K. RICE Systems of Organigation. The Control of Task and Sentient Boundaries. By E. J. MILLER and A. K. RICE Accountabilify in Government Departments, Public Corporations and Public Companies. Edited by R. W. Ennis Corporate Social Responsibilities. By CLARENCE C. WALTON Regulating Business by Independent Commission. By MARVER H. BERNSTEIN An Introduction to Management Statistics. A Grundytext. Mathematical Theory of Rcliabiliity. By RICHARD E. BARLOW and FRANK PROSCHAN with contributions by LARRY C. HUNTER Statistics for Buriness and Economics. By STEPHEN P. SHAO The Searcb for Ability. Standardized Testing in Social Perspective. By DAVID A. Goslin Training in Industry, The Management of Learning. By BERNARD M. BASS Developing Efective Managers. By T. J. ROBERTS An Approad to the Training and Development of Managers. Ministry of Labour Training for Development. By ROLF P. LYNTON and UDAE PAREEK The Eakcation of Technologists. By LURE JAHODA

Nematodes: A Review and Résumé: The Physiology of Nematodes . D. L. Lee. Freeman, San Francisco, Calif., 1965. 164 pp. Illus. Paper, $2.50.

Nematodes: A Review and Résumé: <i>The Physiology of Nematodes</i> . D. L. Lee. Freeman, San Francisco, Calif., 1965. 164 pp. Illus. Paper, $2.50.