Showing papers in "IEEE Transactions on Reliability in 1982"
TL;DR: This paper provides, in the i.i.d.f. case, recursive formulas and bounds for computing system reliability and questions of optimal system design in the linear k-of-n:F system.
Abstract: The linear (circular) k-of-n:F system has n linearly (circularly) ordered components. Each component either functions or fails. The system fails i.f.f.k consecutive components fail. This paper provides, in the i.i.d. case, recursive formulas and bounds for computing system reliability. It considers properties of system life distributions and, in the non i.i.d. case, questions of optimal system design.
240 citations
TL;DR: In this article, the authors give recursive equations for the more general case when the component reliabilities can be different from each other, which can be computed more quickly from these recursive equations than those previously given.
Abstract: The previous literature on consecutive-k-out-of-n: F systems gives recursive equations for the system reliability only for the special case when all component reliabilities are equal. This paper gives recursive equations for the more general case when the component reliabilities can be different from each other. Furthermore, reliabilities can be computed more quickly from these recursive equations than those previously given.
164 citations
TL;DR: A recursive algorithm computes the reliability of a consecutive-k-out-of-n:F system with unequal component failure probabilities.
Abstract: A recursive algorithm computes the reliability of a consecutive-k-out-of-n:F system with unequal component failure probabilities.
127 citations
TL;DR: A simple method for deriving a symbolic reliability expression of some practical systems such as a communication system having fixed channel capacities of its links, a power distribution system having limited power ratings of its power lines, a transport system which might not allow traffic more than a particular value, or a chemical system in which oil or gas flow through pipes is permissible only up to some safe limits.
Abstract: This paper presents a simple method for deriving a symbolic reliability expression of some practical systems such as a communication system having fixed channel capacities of its links, a power distribution system having limited power ratings of its power lines, a transport system which might not allow traffic more than a particular value, or a chemical system in which oil or gas flow through pipes is permissible only up to some safe limits. A system is good if and only if it is possible to transmit successfully the required capacity from source node to the sink node. This paper defines a group as a set of branches such that success of these branches ensures system success, as defined above. All such groups are obtained from a knowledge of the minimal paths of the system graph. The method is computerized and implemented on DEC-20 computer. Two examples are considered and their solutions presented to illustrate the technique.
126 citations
TL;DR: In this paper, a topological formula for vertex-to-vertex communication from a source to a terminal was derived for solving a variety of network reliability problems such as vertices to vertices communication.
Abstract: A topological formula is derived for solving a variety of network reliability problems such as vertex-to-vertex communication from a source to a terminal; from a source to some specified subset of the vertices or else all vertices; between any given vertex-pair; between all vertex-pairs within a given subset of the vertices; or else between all vertex-pairs. The formula applies to networks consisting of imperfect (unreliable) vertices and/or links, and with failure events s-independent or not. The formula explicitly characterizes the structure of both cancelling and noncancelling terms in the reliability expression obtained by Inclusion-Exclusion, and involves only noncancelling terms. Earlier topological formulas for the source-to-terminal problem and the source-to-all-vertices problem are shown to be special cases of this new one.
124 citations
TL;DR: A counting scheme for determining the reliability of a consecutive-k-out-of-n:F network is developed and an example of such a network, a set of tables, and a comparative example are provided.
Abstract: This paper develops a counting scheme for determining the reliability of a consecutive-k-out-of-n:F network. An example of such a network, a set of tables, and a comparative example are provided.
101 citations
TL;DR: The assumption of a common underlying failure process leads to both the inverse Gaussian distribution and the fatigue life distribution of Birnbaum & Saunders as discussed by the authors, which is obtained by an exact derivation while the second involves certain approximations.
Abstract: The assumption of a common underlying failure process leads to both the inverse Gaussian distribution and the fatigue life distribution of Birnbaum & Saunders. The first is obtained by an exact derivation while the second involves certain approximations. Although both of these distributions fit many failure data well, the inverse Gaussian distribution enjoys a distinct advantage in regard to the availability of procedures for a sound statistical analysis and tractability of the sampling distributions.
92 citations
TL;DR: An algorithm for performing certain parts of the fault tree construction process is described and a systematic approach to component model construction is presented.
Abstract: An algorithm for performing certain parts of the fault tree construction process is described. Its input is a flow sheet of the plant, a piping and instrumentation diagram, or a wiring diagram of the circuits, to be analysed, together with a standard library of component functional and failure models. A systematic approach to component model construction is also presented.
79 citations
TL;DR: In this paper, basic results about discrete hazard functions are described and several of these results have parallels in the continuous case, and several open questions are posed in Section 4.1.
Abstract: This paper describes basic results about discrete hazard functions. Several of these results have parallels in the continuous case. Two theorems in section three are presented. The first provides a basis for selecting hazard functions; the cumulative hazard must become infinite. The second describes the limiting behavior of residual lifetime. Several open questions are posed in section four.
77 citations
TL;DR: A simple, direct combinatorial method for determining the system failure probability in a consecutive-k-out-of-n F system.
Abstract: A consecutive-k-out-of-n: F system has n i.i.d. components; the system fails if any k consecutive components fail. This paper gives a simple, direct combinatorial method for determining the system failure probability.
64 citations
TL;DR: An efficient enumeration algorithm generates all minimal cut-sets separating a special vertex pair in an undirected graph based on a blocking mechanism that guarantees that every minimalcut-set between the two specified vertices is generated exactly once.
Abstract: An efficient enumeration algorithm generates all minimal cut-sets separating a special vertex pair in an undirected graph. The algorithm is based on a blocking mechanism that guarantees that every minimal cut-set between the two specified vertices is generated exactly once. The algorithm is intended for computer implementation, and computational times are provided.
TL;DR: The technique is based on analysing and modifying the Boolean expression prior to the conversion process, originally developed as an aid to fault-tree analysis but it applies to general problems of reliability assessment.
Abstract: A reliability block diagram for complex systems is often analyzed by applying the series/parallel product laws or, where this is not possible, by using a conditional probability result (Bayes theorem). In both cases, the analysis is conducted in the probabilistic domain and, for complex systems, is lengthy. An alternative method is to consider the component reliability parameters to be Boolean variables rather than probabilistic variables and to treat the whole problem as if it were Boolean. This has the advantage of allowing the use of powerful Boolean reduction theorems to contain the size of the problem. Unfortunately, much of this advantage is lost when conversion back into the probabilistic domain takes place. This paper presents a technique for overcoming this disadvantage; the technique is based on analysing and modifying the Boolean expression prior to the conversion process. The technique was originally developed as an aid to fault-tree analysis but it applies to general problems of reliability assessment. I claim no originality for the procedure. The motivation to write the paper is quite simple: the procedure is not as well-known as it should be either amongst practising reliability engineers or amongst those who teach the subject. The purpose of the paper is therefore tutorial.
TL;DR: Disjoint Products applied to 2-terminal system reliability recursively partitions the logic polynomial into nonintersecting terms and develops the theory common to all three algorithms.
Abstract: Disjoint Products (DP) applied to 2-terminal system reliability recursively partitions the logic polynomial into nonintersecting terms. Each step represents the incremental contribution of one minimal state. Three different DP algorithms for s-coherent systems were published. This paper develops the theory common to all three algorithms, and also shows those respects in which they differ from one another. Proofs are sketched.
TL;DR: In this article, a new Bayes estimator for the 2-parameter Weibull model is proposed when both parameters are unknown, which can be reasonably quantified in terms of the range of the shape parameter and the anticipated value of a quantile (reliable life) of the sampling distribution.
Abstract: New Bayes estimators for the 2-parameter Weibull model are proposed when both parameters are unknown. In many life testing situations there is prior information which can be reasonably quantified in terms of: 1) range of the shape parameter, and 2) anticipated value of a quantile (reliable life) of the sampling distribution. This paper directly incorporates such information into the estimation process, using a new (not completely specified) prior distribution. Since analytic tractability is not possible, the estimates are obtained with easy numerical integration. A Monte Carlo simulation (carried out each time on 1000 samples and also using very poor priors) has shown that these estimators are quite s-unbiased and s-efficient for a large range of parameter values of poor priors.
TL;DR: In this article, the authors describe the approach and progress on a 1981 study of photovoltaic (PV) system reliability being conducted by Battelle-Columbus for Sandia Laboratories as part of DOE's PV Systems Definition Project.
Abstract: This paper describes the approach and progress on a 1981 study of photovoltaic (PV) system reliability being conducted by Battelle-Columbus for Sandia Laboratories as part of DOE's PV Systems Definition Project. Initially, the study is concerned with the functional modeling of reliability and maintenance of a PV system. We begin with relatively general, but simple, system level reliability models that can be expanded to more detailed, lower-level forms as input data justify. Corrective maintenance is Included to permit estimates of system availability. The output of these models will be coupled with life-cycle energy cost models and applied to PV system designs.
TL;DR: A tree construction technique to compute a reliability expression of a network is derived that gives mutually disjoint success branches and involves fewer multiplications than other known techniques.
Abstract: A tree construction technique to compute a reliability expression of a network is derived. The technique is straight forward and good for both directed and undirected graphs. It gives mutually disjoint success branches. The reliability expression of each branch can be directly written by a set of rules. The reliability of the network can then be obtained by taking the direct sum of the reliabilities of the branches. It involves fewer multiplications than other known techniques. For a moderately complex network it is very easy to use this technique for evaluating reliability.
TL;DR: In this article, simple approximations for s-bias and mean square error of the maximum likelihood estimator of Pr{Y < X} for two cases: 1) both? and s are unknown; 2) only s is unknown.
Abstract: Let X and Y be s-independent exponentially distributed random variables with mean s and ? respectively. This work povides simple approximations for s-bias and mean square error of the maximum likelihood estimator of Pr{Y < X} for two cases: 1) both ? and s are unknown; 2) only s is unknown. When ? is known, the mean square error is compared with that of the minimum variance s-unbiased estimator and a preference relationship between them is established using the mean square error criterion.
TL;DR: In this article, a method with a new criterion of local optimality is proposed to solve reliability optimization problems of complex systems, where the structure need not be series and the proposed algorithm yields a solution which is optimal in 2-neighborhood.
Abstract: A method with a new criterion of local optimality is proposed to solve reliability optimization problems of complex systems, where the structure need not be series. Unlike previous methods, the proposed algorithm yields a solution which is optimal in 2-neighborhood. The effectiveness of the method is shown through examples.
TL;DR: A simple technique is presented for evaluating NR in symbolic form based on cutsets and is computationally advantageous with respect to the spanning tree approach because it requires fewer cutsets to be manipulated in the process of determining the NR expression.
Abstract: A global reliability measure called 'network reliability' (NR) is the probability that a call entering a probabilistic network at any originating node can reach every other node. This concept is quite useful in multiterminal networks such as computer networks and parallel processors, etc. A simple technique is presented for evaluating NR in symbolic form. The method is based on cutsets and is computationally advantageous with respect to the spanning tree approach. It requires fewer cutsets to be manipulated in the process of determining the NR expression. The number of cutsets is approximately half that of spanning trees even for a small sized computer communication network and there is a further improvement in the situation for larger networks.
TL;DR: In this article, the reliability of large computer communication systems is evaluated by systematic decomposition of the probabilistic graph of the system into two parts using an appropriate cutset, and a technique is evolved for determining the conditional success events using both the node removal and connection multiplication methods for path enumeration.
Abstract: The method evaluates the reliability of large computer communication systems by systematic decomposition of the probabilistic graph of the system into two parts using an appropriate cutset. A technique is evolved for determining the conditional success events using both the node removal and connection multiplication methods for path enumeration. An example is solved to show the versatility of the method. The results of the example are verified by using an existing algorithm. The suggested method is general and computationally economical.
TL;DR: In this article, a modified block replacement policy was proposed in which a unit is replaced at failure during (0, T0) and at scheduled replacement time T. The model with two variables was transformed into one variable and the optimum policy was discussed.
Abstract: This paper considers a modified block replacement policy in which a unit is replaced at failure during (0, T0) and at scheduled replacement time T. If a failure occurs in an interval (T0, T), then the unit remains as it is until T. The mean cost rate is obtained, using the results of renewal theory. The model with two variables is transformed into one variable and the optimum policy is discussed. An example shows how to compute the optimum T0* and T* when the failure time of the unit has a gamma distribution.
TL;DR: In this article, the reliability analysis of k-out-of-n systems was improved to use only noncancelling terms in evaluating bounds on the reliability of K-out of n systems, which converge to the exact system reliability in at most n? k + 1 steps.
Abstract: The method of inclusion-exclusion is represented in general form for reliability analysis. Applying it to the reliability of k-out-of-n system causes many cancelling terms. The method is improved to use only noncancelling terms in evaluating bounds on the reliability of k-out-of-n systems. These bounds are appreciably better, and converge to the exact system reliability in at most n ? k + 1 steps. In conclusion some numerical considerations suggest the quality of the bounds. Similar results for the reliability analysis of networks were derived by Satyanaraynna & Prabhakar.
TL;DR: In this paper, a generalization of the Total Time on Test (TTT) concept, the TTT-transform, defined as a certain function of the survivor function, can be used when analyzing different types of age-replacement problems.
Abstract: The Total Time on Test (TTT) concept has proven to be a very useful tool in several reliability contexts. The objective of this note is to illustrate how a generalization of the TTT-concept, the TTT-transform, defined as a certain function of the survivor function, can be used when analyzing different types of age-replacement problems.
TL;DR: In this paper, an analytic method for uncertainty analysis of the output of a complex model is described, where model inputs are s-independent random variables and model output is given as an analytic though possibly nonlinear function of the inputs.
Abstract: An analytic method for uncertainty analysis of the output of a complex model is described. It is assumed that model inputs are s-independent random variables and that model output is given as an analytic though possibly nonlinear function of the inputs. Using conditional s-expectations as a tool, a theoretical basis is developed for a method of partitioning the variance of the output among contributing causes. Such a partitioning helps the system analyst to identify the most important contributors to output uncertainty and, hence, to find effective ways of reducing that uncertainty. The method is illustrated by application to the uncertainty analysis of fault trees. There is no reason, in principle, why the method should not be applied to large computer codes where output cannot be represented as an analytic function of input. However, the evaluation of the required conditional s-expectations in such cases would be likely to involve considerable computation. It would be very desirable to extend the method to handle the case of s-correlated input variables. However, the partitioning of output variance in the presence of s-dependent inputs is difficult. The difficulties involved have not yet been resolved except in simple cases of s-dependence which can be reduced to the s-independent case by transformations of variables or other devices.
TL;DR: In this paper, the authors consider the problem of nonparametric accelerated life testing by extending the results of Shaked & Singpurwalla in two directions: first, they solve the case of censored data, and then they extend the methods to the cases of competing risks.
Abstract: This paper considers the problem of nonparametric accelerated life testing by extending the results of Shaked & Singpurwalla in two directions. First we solve the case of censored data. Next we extend the methods to the case of competing risks. A s-consistent estimate of the failure distribution at use-stress is given for both cases.
TL;DR: In this paper, a new replacement policy is proposed: at the moment when the repair cost rate reaches or exceeds a fixed level, the system is replaced, compared with the economic lifetime policy.
Abstract: A new replacement policy is proposed: At the moment when the repair cost rate reaches or exceeds a fixed level, the system is replaced. This policy is compared with the economic lifetime policy. An example is presented.
TL;DR: In this article, the failure modes of MOS technology are described with emphasis on recent trends in LSI. Failures are classified into short, open, degradation, and soft recoverable errors.
Abstract: The failure modes of MOS technology are described with emphasis on recent trends in LSI. Failures are classified into short, open, degradation, and soft recoverable errors. The following failure modes are covered: oxide breakdown caused by static discharge and time-dependent effects; metallization failures caused by electromigration or corrosion; threshold voltage shifts caused by ionic contamination, surface-charge spreading, and the hot-electron effect. Special attention is paid to the increasingly important alpha-particle-induced soft errors. Methods by which each of the failure modes can be detected are discussed and tabulated, together with the information on acceleration factors necessary for designing life and screen tests. Of the failure modes cited, threshold shifts due to hot electrons, and soft errors caused by ionizing radiation are likely to be increasingly important as VLSI technology progresses.
TL;DR: In this article, the causes of field failures have been analyzed with respect to environmental and operational stresses and to induced degradation mechanisms, and manufacturers have improved the reliability of later generations of modules through changes in design, material selection, and manufacturing controls.
Abstract: Field experience obtained through photovoltaic test and application experiments sponsored by the US Department of Energy has offered an opportunity for solar cell module reliability assessment and improvement. Through a formal problem/failure reporting and analysis system, field problems have been identified and characterized. The causes of field failures have been analyzed with respect to environmental and operational stresses and to induced degradation mechanisms. On the basis of these results, manufacturers have improved the reliability of later generations of modules through changes in design, material selection, and manufacturing controls. This paper summarizes field experience, describes key failure modes, and evaluates industry progress in addressing such problems.
TL;DR: In this article, a nonparametric approach to accelerated life testing by deleting the requirement that the common parametric family of life distributions under all the stresses be specified in advance is presented.
Abstract: This paper presents a nonparametric approach to accelerated life testing by deleting the requirement that the common parametric family of life distributions under all the stresses be specified in advance. The requirement that the time transformation function be specified is retained, and a version of the familiar inverse power law is considered. A s-consistent estimate of the failure distribution at use stress, and a test of the hypothesis that the underlying failure distribution belongs to a specified family are given. Approximate s-confidence bounds for the failure distribution at use stress are obtained. The approach is illustrated in an example using real data.
TL;DR: In this article, the principal causes of failure were: (1) cells cracked due to weathering or internal module stresses; (2) failed solder joints; (3) interconnects not soldered to rear sides of cells at assembly; (4) cells or wires electrically shorted to metallic substrates; and (5) broken or split connections.
Abstract: During the years 1977-1980, MIT Lincoln Laboratory (LL) placed over 11 000 photovoltaic (PV) modules at experimental PV power generating systems in a number of field test sites in the United States. Prominent among these are a 100 kW system at Natural Bridges National Monument in Utah, a 25 kW system at Mead, Nebraska, and a 15 kW system at Bryan, Ohio. The modules used in each of these systems were procured through the Jet Propulsion Laboratory's Large Scale Procurement Program as part of the US Department of Energy's National Photovoltaic Program. Through a program of periodic surveillance, measurements, and inspections at the aforementioned sites, over 320 electrically failed modules have been located, removed, and analyzed during this 4-year period. The principal causes of failure were: 1) cells cracked due to weathering or internal module stresses; 2) failed solder joints; 3) interconnects not soldered to rear sides of cells at assembly; 4) cells or interconnects electrically shorted to metallic substrates; and 5) broken or split interconnects. Details and photographs of many of the different types of failures are presented and some of the analysis techniques used to locate the failures are described.