scholarly journals Some conditional reliability properties of k-out-of-n system composed of different types of components with discrete independent lifetimes

Metrika ◽  
2021 ◽  
Author(s):  
Krzysztof Jasiński
Keyword(s):  
Failure Probability ◽  
Conditional Survival ◽  
Survival Functions ◽  
Different Types ◽  
Failure Probabilities

AbstractIn this paper, we study reliability properties of k-out-of-n system consisting of l$$(1\le l\le n)$$ ( 1 ≤ l ≤ n ) different types of components with discrete, independent lifetimes. We obtain some conditional survival functions of lifetime of a used system. Next, we use them to calculate two conditional failure probabilities of k-out-of-n systems and show that they are equal to unconditional failure probability of a k-out-of-$$(n-r)$$ ( n - r ) system, $$r<n-k+1$$ r < n - k + 1 . These results are extended versions of the respective ones existing in the literature.

scholarly journals A note on random intensities and conditional survival functions

1988 ◽  
Vol 25 (03) ◽  
pp. 630-635 ◽  
Author(s):  
Anatoli Yashin ◽  
Elja Arjas
Keyword(s):  
Survival Analysis ◽  
Random Process ◽  
Failure Probability ◽  
Counting Process ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conditional Survival ◽  
Survival Functions ◽  
Exponential Formula ◽  
Necessary And Sufficient

Failure intensities in which the evaluation of hazard is based on the observation of an auxiliary random process have become very popular in survival analysis. While their definition is well known, either as the derivative of a conditional failure probability or in the counting process and martingale framework, their relationship to conditional survival functions does not seem to be equally well understood. This paper gives a set of necessary and sufficient conditions for the so-called exponential formula in this context.

scholarly journals A note on random intensities and conditional survival functions

1988 ◽  
Vol 25 (3) ◽  
pp. 630-635 ◽  
Author(s):  
Anatoli Yashin ◽  
Elja Arjas
Keyword(s):  
Survival Analysis ◽  
Random Process ◽  
Failure Probability ◽  
Counting Process ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conditional Survival ◽  
Survival Functions ◽  
Exponential Formula ◽  
Necessary And Sufficient

Failure intensities in which the evaluation of hazard is based on the observation of an auxiliary random process have become very popular in survival analysis. While their definition is well known, either as the derivative of a conditional failure probability or in the counting process and martingale framework, their relationship to conditional survival functions does not seem to be equally well understood. This paper gives a set of necessary and sufficient conditions for the so-called exponential formula in this context.

FORWARD APPORTIONMENT OF CENSORED COUNTS FOR DISCRETE NONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF FAILURE PROBABILITIES

2009 ◽  
Vol 16 (03) ◽  
pp. 213-234
Author(s):  
MINNIE H. PATEL ◽  
H.-S. JACOB TSAO
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Closed Form ◽  
Failure Probability ◽  
Likelihood Estimation ◽  
Lifetime Distribution ◽  
Nonparametric Maximum Likelihood ◽  
Kaplan Meier ◽  
Probability Estimates ◽  
Failure Probabilities

Empirical cumulative lifetime distribution function is often required for selecting lifetime distribution. When some test items are censored from testing before failure, this function needs to be estimated, often via the approach of discrete nonparametric maximum likelihood estimation (DN-MLE). In this approach, this empirical function is expressed as a discrete set of failure-probability estimates. Kaplan and Meier used this approach and obtained a product-limit estimate for the survivor function, in terms exclusively of the hazard probabilities, and the equivalent failure-probability estimates. They cleverly expressed the likelihood function as the product of terms each of which involves only one hazard probability ease of derivation, but the estimates for failure probabilities are complex functions of hazard probabilities. Because there are no closed-form expressions for the failure probabilities, the estimates have been calculated numerically. More importantly, it has been difficult to study the behavior of the failure probability estimates, e.g., the standard errors, particularly when the sample size is not very large. This paper first derives closed-form expressions for the failure probabilities. For the special case of no censoring, the DN-MLE estimates for the failure probabilities are in closed forms and have an obvious, intuitive interpretation. However, the Kaplan–Meier failure-probability estimates for cases involving censored data defy interpretation and intuition. This paper then develops a simple algorithm that not only produces these estimates but also provides a clear, intuitive justification for the estimates. We prove that the algorithm indeed produces the DN-MLE estimates and demonstrate numerically their equivalence to the Kaplan–Meier-based estimates. We also provide an alternative algorithm.

Sensitivity Analysis of Major Parameters on Piping Failure Probabilities

2004 ◽  
Vol 261-263 ◽  
pp. 821-826
Author(s):  
Sung Gyu Jung ◽  
Chang Soon Lee ◽  
In Gyu Park ◽  
Se Hwan Lee ◽  
Tae Eun Jin
Keyword(s):  
Sensitivity Analysis ◽  
Size Distribution ◽  
Nuclear Power ◽  
Power Plants ◽  
Nuclear Power Plants ◽  
Crack Size ◽  
Deterministic Approach ◽  
Inspection Interval ◽  
Different Types ◽  
Failure Probabilities

In-service inspections (ISI) of pipes in the nuclear power plants are currently performed based on mandated requirements in the ASME Section XI, which is based on deterministic approach of the critical welds. The 20 years of ISI experience in U.S.A. has revealed less correlation between the critical welds and actual failures, and much conservatism in current ISI requirements. To reduce those problems, risk-informed ISI technology has been developed and proved to be useful. This paper presented a method for predicting piping failure probabilities in an application of risk-informed ISI, and analyzed the effect of input parameters on piping failure probabilities. Results generated using this approach revealed that the calculated failure probabilities can be sensitive to the different types of stressors, crack size distribution, inspection interval, etc..

Reliabilities of Consecutive-2 Graphs

1987 ◽  
Vol 1 (3) ◽  
pp. 293-298 ◽  
Author(s):  
D.Z. Du ◽  
F. K. Hwang
Keyword(s):  
Failure Probability ◽  
Linear Time ◽  
Time Algorithm ◽  
Polynomial Algorithms ◽  
Linear Time Algorithm ◽  
Linear Algorithms ◽  
Failure Probabilities

A consecutive-2 graph is a graph where each vertex is associated with a failure probability and the graph is considered failed if any two adjacent vertices both fail. Recently, the problem of computing reliability for general consecutive-2 graph was shown to be #P-complete while polynomial algorithms exist for trees. In this paper, we give a linear time algorithm for a class of graphs including forests and cycles.For a given set of failure probabilities qi, the assignment of qi to the vertices of a given graph is optimal if it maximizes the reliability of that graph. It is known that optimal assignments for trees require messy computations while linear algorithms exist for lines and stars. In this paper, we prove that the optimal reliability of any n−tree is bounded between those of an n−line and an n−star.

scholarly journals The Unifying Frameworks of Information Measures

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Shiwei Yu ◽  
Ting-Zhu Huang
Keyword(s):  
Similarity Measures ◽  
Random Variables ◽  
Tsallis Entropy ◽  
Density Functions ◽  
Survival Functions ◽  
Information Theoretic ◽  
Information Measures ◽  
Different Types ◽  
Types Of Information ◽  
Available Information

Information measures are capable of providing us with fundamental methodologies to analyze uncertainty and unveiling the substantive characteristics of random variables. In this paper, we address the issues of different types of entropies through q-generalized Kolmogorov-Nagumo averages, which lead to the propositions of the survival Rényi entropy and survival Tsallis entropy. Therefore, we make an inventory of eight types of entropies and then classify them into two categories: the density entropy that is defined on density functions and survival entropy that is defined on survival functions. This study demonstrates that, for each type of the density entropy, there exists a kind of the survival entropy corresponding to it. Furthermore, the similarity measures and normalized similarity measures are, respectively, proposed for each type of entropies. Generally, functionals of different types of information-theoretic metrics are equally diverse, while, simultaneously, they also exhibit some unifying features in all their manifestations. We present the unifying frameworks for entropies, similarity measures, and normalized similarity measures, which helps us deal with the available information measures as a whole and move from one functional to another in harmony with various applications.

Improvement of Probabilistic Fracture Mechanics Analysis Code PASCAL-SP With Regardto PWSCC

2019 ◽  
Vol 5 (3) ◽  
Author(s):  
Akihiro Mano ◽  
Yoshihito Yamaguchi ◽  
Jinya Katsuyama ◽  
Yinsheng Li
Keyword(s):  
Fracture Mechanics ◽  
Failure Probability ◽  
Power Plants ◽  
Crack Detection ◽  
Structural Integrity ◽  
Energy Agency ◽  
Pressurized Water ◽  
Integrity Assessment ◽  
Probabilistic Fracture Mechanics ◽  
Failure Probabilities

Probabilistic fracture mechanics (PFM) analysis is expected to be a rational method for structural integrity assessment because it can consider the uncertainties of various influence factors and evaluate the quantitative values such as failure probability of a cracked component as the solution. In the Japan Atomic Energy Agency, a PFM analysis code PASCAL-SP has been developed for structural integrity assessment of piping welds in nuclear power plants (NPP). In the past few decades, a number of cracks due to primary water stress corrosion cracking (PWSCC) have been detected in nickel-based alloy welds in the primary piping of pressurized water reactors (PWRs). Thus, structural integrity assessments considering PWSCC have become important. In this study, PASCAL-SP was improved considering PWSCC by introducing several analytical functions such as the models for evaluation of crack initiation time, crack growth rate (CGR), and probability of crack detection. By using the improved version of PASCAL-SP, the failure probabilities of pipes with a circumferential crack or an axial crack due to PWSCC were numerically evaluated. Moreover, the influence of leak detection and nondestructive examination (NDE) on failure probabilities was detected. Based on the obtained numerical results, it was concluded that the improved version of PASCAL-SP is useful for evaluating the failure probability of a pipe considering PWSCC.

Probabilistic Assessment of Pipeline Resistance to Third Party Damage: Use of Surveys to Generate Necessary Input Data

2004 ◽  
Author(s):  
Geoffray Wolvert ◽  
Mure`s Zarea ◽  
Didier Rousseau ◽  
Ce´cile Andrieux
Keyword(s):  
Failure Probability ◽  
Urban Areas ◽  
Large Scale ◽  
Western Europe ◽  
Third Party ◽  
Illustrative Case ◽  
Assessment Procedure ◽  
Key Factor ◽  
Tool Types ◽  
Failure Probabilities

A complete risk assessment procedure for pipelines relies, among other things, on the evaluation of failure probabilities. Incident reviews in western countries have identified third party damage as the main cause of failures with leaks. While some approaches already exist in order to evaluate the failure probability of transmission pipelines subject to third party damage, the issues of feeding the models with appropriate statistical data is a key factor for the success of the evaluation. We present here briefly the outline of the tool developed by Gaz de France R&D Davison to evaluate failure probabilities in the event of third party damage. Then we discuss the issue of available data, and particularly the most critical one, i.e. the population of ground working machinery, a majority of which are excavators. In order to assess as well as possible the exposure of pipelines to the threat of interference with excavators, we conducted a large scale survey in rural, semi-urban and urban areas in Western Europe in order to determine important parameter distributions of the excavators population: mass, digging depth, tool types and dimensions, soil type, type of ground works, etc. Random variables are used to describe these parameters and their influence on the failure probability is illustrated in a series of illustrative case studies. The importance of access to reliable information about the loads to which a pipeline is exposed is clearly shown in this paper, particularly due to the fact that the dispersion is a lot larger for the parameters linked with third parties working around the pipeline than for parameters of the pipeline: geometry and material properties.

Study on System Reliability of Large Tensile Structure Based on Failure of Main Cables

2013 ◽  
Vol 753-755 ◽  
pp. 1477-1482
Author(s):  
Shi Tang
Keyword(s):  
Failure Probability ◽  
System Reliability ◽  
Failure Modes ◽  
System Failure ◽  
Design Strategies ◽  
Special Design ◽  
Structure System ◽  
Main Cables ◽  
The Relationship ◽  
Failure Probabilities

In this paper, cable-membrane structure roof of a stadium was taken as a research case, a system reliability research method for large tensile structure was proposed. In the method, failure probabilities of main tensile cables were determined firstly, and main failure modes were obtained according to the relationship between the main tensile cables failure and the system failure, system reliability index would be gotten on the basis of main tensile cables failure probabilities and main failure modes accordingly. In analysis of the stadium, JC method was applied to analyze the reliability of main tensile cables, it was shown that, compared with other cables, the failure probability of lower ring cables and that of lower radial cables were higher, so the structure system failure mode caused by lower ring cables failure and that caused by lower radial cables failure were underlined, and enumeration method has been adopted to analyze the reliability of structure system. The system failure probability caused by the failure of lower ring cables was found relatively high, and the failure of lower ring cables would result in the failure of the structure system immediately, so special attention should be paid. Finally, design strategies have been put forward according to the results of reliability research, safety protection lines were added up by special design of tensile cable joints, and the reliability of the structure system has been improved.

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