Letter to the Editor—A Note on Conditional Probability of Failure When Hazards are Proportional

Reliability assessment is an important procedure in engineering design in which the probability of failure or equivalently the probability of survival is computed based on appropriate design criteria and model behavior. In this paper, a new approximate and efficient reliability assessment method is proposed: the conditional probability method (CPM). Focus is set on computational efficiency and the proposed method is applied to classical load-strength structural reliability problems. The core of the approach is in the computation of the probability of failure starting from the conditional probability of failure given the load. The number of function evaluations to compute the probability of failure is a priori known to be 3n + 2 in CPM, where n is the number of stochastic design variables excluding the strength. The necessary number of function evaluations for the reliability assessment, which may correspond to expensive computations, is therefore substantially lower in CPM than in the existing structural reliability methods such as the widely used first-order reliability method (FORM).

Download Full-text

Optimal Control of Performance Risk for Large Potentially Dangerous Systems (LPDS)

Selected Topics on Aging Management, Reliability, Safety and License Renewal ◽

10.1115/pvp2002-1389 ◽

2002 ◽

Author(s):

Sviatoslav A. Timashev

Keyword(s):

Optimal Control ◽

Risk Analysis ◽

Conditional Probability ◽

Structural Reliability ◽

Process Analysis ◽

Probability Of Failure ◽

Simultaneous Optimization ◽

Normal Operation ◽

Residual Lifetime ◽

Parameter Problem

The paper considers the safety problem for large potentially dangerous systems (LPDS). Disruption of their normal operations may lead to casualties, ecological and property damage. Solution to the above problem is sought in the framework of risk control of LPDS during their normal operation, based on the principle of preventive actions. Risk is described as the product of conditional probability of failure and the overall consequences of such failure. Methods of brining down risk analysis problems to reliability problems are presented. They are based on the following: assessments of “cost of life” (as economic equivalent of casualty); simultaneous optimization of the LPDS and its safety subsystem (expansion of the object of optimization). Such an approach allows unification and merging of structural reliability theory and probabilistic risk analysis. A quantitative method of damage size (the first component of risk) assessment is described, based on computer modeling of a full group of scenarios of a structural failure developing into a full blown LPDS catastrophe. As a result of modeling, the destruction zones and the character, size and probabilities of all kinds of damage (casualties, ecological damage, loss of property) are assessed. It is proposed, as the main method of securing LPDS integrity and safety, to equip each LPDS with suitable monitoring/inspection/maintenance systems, designed as an instrument for controlling the second component of risk (conditional probability of failure), on the basis of a three-level (warning-alarm-failure) control policy. In the outlined format maintenance/repair is considered as optimal control of random degradation and renewal functions, interaction of which forms a certain regeneration process. Analysis of this process allows defining the optimal triggering levels of deterioration parameters or risk that minimize total expenditures of LPDS performance while ensuring its safety. The problem formulated above naturally embodies all existing maintenance methods (based on admissible performance time, rate of failure and on actual and prognosed system condition). Further, the problem of optimal cessation of performance is solved. It allows convoluting a multi-parameter problem into a one-parameter problem and defining the ultimate permissible level of conditional probability of failure. The described methods of risk analysis and control were used in residual lifetime monitoring systems for oil pumping aggregates and for main oil pipe line segments repair prioritization.

Download Full-text

Markov Description of Corrosion Defects Growth and Its Application to Reliability Based Inspection and Maintenance of Pipelines

2008 7th International Pipeline Conference, Volume 4 ◽

10.1115/ipc2008-64546 ◽

2008 ◽

Cited By ~ 14

Author(s):

S. A. Timashev ◽

M. G. Malyukova ◽

L. V. Poluian ◽

A. V. Bushinskaya

Keyword(s):

Markov Model ◽

Conditional Probability ◽

Limit State ◽

Simulation Method ◽

Probability Of Failure ◽

State Function ◽

Main Concern ◽

Defect Parameter ◽

Pipeline Failure ◽

Pressurized Pipelines

The paper describes a Markov model of corrosion growth of pipe wall defects and its implementation for assessing the conditional probability of pipeline failure and optimizing pipeline repair and maintenance. This pure growth Markov model is of the continuous time, discrete states type. This model is used in conjunction with the geometrical limit state function (LSF) to assess the conditional probability of failure of pressurized pipelines when the main concern is loss of containment. It is shown how to build an empirical Markov model for the length, depth and width of defects, using field data gathered by In-line inspection (ILI) or direct assessment (DA) or by using a combination of a differential equation (DE) that describes defect parameter growth with the Monte Carlo simulation method. As a result of implementation of this approach the probability for the defect parameters being in a given state (analog of a histogram) and the transition intensities (from state to state) are easily derived for any given moment of time. This approach automatically gives an assessment of the probability of failure of a pipeline segment, as it is derived using the data from a specific pipeline length. This model also allows accounting for the pipeline failure pressure LSF. On the basis of this model an algorithm is constructed for optimizing the time of the next inspection/repair. This methodology is implemented to a specific operating pipeline which was several times inspected by a MFL inspection tool. The expected number and volume of repairs depend on the value of the ultimate permissible pipeline failure probability. Sensitivity of pipeline conditional failure rate and optimal repair time to actual growth rate is investigated. A brief description of the software that implements the described above technology is given.

Download Full-text

Boiling Water Reactor Pressure Vessel Integrity Evaluation by Probabilistic Fracture Mechanics

ASME 2010 Pressure Vessels and Piping Conference: Volume 7 ◽

10.1115/pvp2010-25195 ◽

2010 ◽

Author(s):

Bo-Yi Chen ◽

Chin-Cheng Huang ◽

Hsoung-Wei Chou ◽

Ru-Feng Liu ◽

Hsien-Chou Lin

Keyword(s):

Fracture Mechanics ◽

Conditional Probability ◽

Pressure Vessel ◽

Structural Integrity ◽

Neutron Fluence ◽

Probability Of Failure ◽

Life Extension ◽

Water Reactor ◽

License Renewal ◽

Reactor Pressure

The Chinshan boiling water reactor (BWR) units 1 and 2, owned by Taiwan Power Company (TPC), started commercial operations in 1978 and 1979, respectively. The reactor pressure vessel (RPV) welds unavoidably degrade with the long time operation because of the fast-neutron fluence exposure. This effect should be considered in the life extension and license renewal application. Thus, the structural integrity of the axial and circumferential welds at the beltline region of reactor vessel must be evaluated carefully. The probabilistic fracture mechanics (PFM) analysis code: Fracture Analysis of Vessels – Oak Ridge (FAVOR), which has been verified by USNRC, is adopted in this work to calculate the conditional probability of initiation (CPI) and the conditional probability of failure (CPF) for the welds with 32 and 64 effective full power years (EFPY) operation, respectively. The Monte Carlo technique is involved in the simulation. This is the first time that the PFM technique is adopted for evaluating the risk of nuclear power plant components in Taiwan. Actual geometries, material properties, chemistry components, neutron fluence and operation conditions are used for the plant specific analyses. Moreover, the design basis transients/accidents described in the final safety analysis report are also taken into account. The computed results show that the failure probabilities of welds are less than 10−10 per year. Only the axial weld, W-1001-08, is found to have the probability of failure. The results of this work can be used to evaluate the structural integrity of the welds located at the RPV beltline region, and provide the aging analysis results for the life extension and the license renewal applications.

Download Full-text

Boiling Water Reactor Pressure Vessel Integrity Evaluation by Probabilistic Fracture Mechanics (PVP2010-25195)

Journal of Pressure Vessel Technology ◽

10.1115/1.4007292 ◽

2012 ◽

Vol 135 (1) ◽

Cited By ~ 1

Author(s):

Bo-Yi Chen ◽

Chin-Cheng Huang ◽

Hsoung-Wei Chou ◽

Ru-Feng Liu ◽

Hsien-Chou Lin

Keyword(s):

Fracture Mechanics ◽

Conditional Probability ◽

Pressure Vessel ◽

Structural Integrity ◽

Neutron Fluence ◽

Probability Of Failure ◽

Reactor Pressure Vessel ◽

Circumferential Welds ◽

Probabilistic Fracture Mechanics ◽

Reactor Pressure

The reactor pressure vessel (RPV) welds unavoidably degrade with the long time operation because of the fast neutron fluence exposure. Thus, the structural integrity of the axial and circumferential welds at the beltline region of reactor vessel must be evaluated carefully. The probabilistic fracture mechanics (PFM) analysis code: Fracture analysis of vessels—Oak Ridge (FAVOR), which has been verified by USNRC, is adopted in this work to calculate the conditional probability of initiation (CPI) and the conditional probability of failure (CPF) for the welds with 32 and 64 effective full power years (EFPY) operation, respectively. The Monte Carlo technique is involved in the simulation. This is the first time that the PFM technique is adopted for evaluating the risk of nuclear power plant components in Taiwan. Actual geometries, material properties, alloying elements, neutron fluence, and operation conditions are used for the plant specific analyses. Moreover, the design basis transients/accidents described in the final safety analysis report are also taken into account. The computed results show that the failure probabilities of welds are less than 10−10 per year. Only the axial weld, W-1001-08 has the probability of failure. The results of this work can be used to evaluate the structural integrity of the welds located at the RPV beltline region and provide the aging analysis results for the life extension and the license renewal applications.

Download Full-text