scholarly journals Inspection and maintenance optimisation of multicomponent systems

2021 ◽  
Author(s):  
Vladimir Oleg Babishin
Keyword(s):  
Monte Carlo Simulation ◽  
Planning Horizon ◽  
Multicomponent Systems ◽  
Minimal Repair ◽  
Expected Number ◽  
System Failures ◽  
Inspection And Maintenance ◽  
Periodic Inspections ◽  
Component Failures ◽  
Hard Type

The present research proposes methodology and mathematical models for optimisation of inspection and maintenance in complex multicomponent systems with finite planning horizon. Components are classified by failure types: hard-type and soft-type. The systems analysed are composed of either multiple identical hidden soft-type components in k-out-of-n redundant configuration, or a combination of hard-type and hidden soft-type components. Failures of hard-type components cause system failures. Failures of components in k-out-of-n systems and soft-type component failures are hidden and not discoverable until an inspection, but reduce the system’s reliability and performance. The systems are inspected either periodically, or non-periodically. They are also inspected opportunistically at the times of system failure (occurring at (k – n + 1)st component failures in k-out-of-n systems, or at hard failures in the systems composed of hard-type and soft-type components). Inspections have negligible duration. All components may undergo minimal repair, or corrective replacement, with hard-type components also having a possibility of preventive replacement under periodic inspections. We only consider minimal repair and corrective replacement under non-periodic inspections. We propose several models for joint optimisation of inspection and maintenance policies that result in the lowest total expected cost. Since soft failures are hidden, we generate expected values for the number of minimal repairs, number of replacements and downtime recursively. Due to multiple component interactions and system complexity, Monte Carlo simulation and genetic algorithms (GA) are used for optimisation. Using GA for optimisation allows to consider quasi-continuous inspection intervals due to improved computational efficiency compared to Monte Carlo simulation. Some of proposed models feature preventive component replacements and are applicable even for systems with hidden component failures. For k-out-of-n systems, we apply periodic model to series and parallel systems and compare the results. We provide expressions for expected number of system failures in terms of cost ratio and component failure intensity. We also provide a simplified expression for system reliability. In addition, we derive a formula for finding the planning horizon length based on expected number of system failures. It may be useful for planning the system’s operating horizon, at the system design stage and when analysing its performance.

scholarly journals Inspection and maintenance optimisation of multicomponent systems

2021 ◽  
Author(s):  
Vladimir Oleg Babishin
Keyword(s):  
Monte Carlo Simulation ◽  
Planning Horizon ◽  
Multicomponent Systems ◽  
Minimal Repair ◽  
Expected Number ◽  
System Failures ◽  
Inspection And Maintenance ◽  
Periodic Inspections ◽  
Component Failures ◽  
Hard Type

The present research proposes methodology and mathematical models for optimisation of inspection and maintenance in complex multicomponent systems with finite planning horizon. Components are classified by failure types: hard-type and soft-type. The systems analysed are composed of either multiple identical hidden soft-type components in k-out-of-n redundant configuration, or a combination of hard-type and hidden soft-type components. Failures of hard-type components cause system failures. Failures of components in k-out-of-n systems and soft-type component failures are hidden and not discoverable until an inspection, but reduce the system’s reliability and performance. The systems are inspected either periodically, or non-periodically. They are also inspected opportunistically at the times of system failure (occurring at (k – n + 1)st component failures in k-out-of-n systems, or at hard failures in the systems composed of hard-type and soft-type components). Inspections have negligible duration. All components may undergo minimal repair, or corrective replacement, with hard-type components also having a possibility of preventive replacement under periodic inspections. We only consider minimal repair and corrective replacement under non-periodic inspections. We propose several models for joint optimisation of inspection and maintenance policies that result in the lowest total expected cost. Since soft failures are hidden, we generate expected values for the number of minimal repairs, number of replacements and downtime recursively. Due to multiple component interactions and system complexity, Monte Carlo simulation and genetic algorithms (GA) are used for optimisation. Using GA for optimisation allows to consider quasi-continuous inspection intervals due to improved computational efficiency compared to Monte Carlo simulation. Some of proposed models feature preventive component replacements and are applicable even for systems with hidden component failures. For k-out-of-n systems, we apply periodic model to series and parallel systems and compare the results. We provide expressions for expected number of system failures in terms of cost ratio and component failure intensity. We also provide a simplified expression for system reliability. In addition, we derive a formula for finding the planning horizon length based on expected number of system failures. It may be useful for planning the system’s operating horizon, at the system design stage and when analysing its performance.

scholarly journals Average Number of Nucleotide Differences in a Sample From a Single Subpopulation: A Test for Population Subdivision

Genetics ◽  
1987 ◽  
Vol 117 (1) ◽  
pp. 149-153
Author(s):  
Curtis Strobeck
Keyword(s):  
Monte Carlo Simulation ◽  
Population Structure ◽  
Random Mating ◽  
Population Subdivision ◽  
Expected Number ◽  
Migration Rates ◽  
Mating Population ◽  
Unbiased Estimates ◽  
Increasing Function ◽  
Stepping Stone Model

ABSTRACT Unbiased estimates of θ = 4Nµ in a random mating population can be based on either the number of alleles or the average number of nucleotide differences in a sample. However, if there is population structure and the sample is drawn from a single subpopulation, these two estimates of θ behave differently. The expected number of alleles in a sample is an increasing function of the migration rates, whereas the expected average number of nucleotide differences is shown to be independent of the migration rates and equal to 4N  Tµ for a general model of population structure which includes both the island model and the circular stepping-stone model. This contrast in the behavior of these two estimates of θ is used as the basis of a test for population subdivision. Using a Monte-Carlo simulation developed so that independent samples from a single subpopulation could be obtained quickly, this test is shown to be a useful method to determine if there is population subdivision.

Using Rio-Paris Flight 447 Crash to Assess Human Error and Failure Propagation Analysis Early in Design

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Lukman Irshad ◽  
H. Onan Demirel ◽  
Irem Y. Tumer ◽  
Guillaume Brat
Keyword(s):  
Human Error ◽  
Prediction Algorithm ◽  
Engineering System ◽  
Human Errors ◽  
System Failures ◽  
Propagation Analysis ◽  
Failure Propagation ◽  
Complex Engineering ◽  
Component Failures ◽  
Complex Engineering System

Abstract While a majority of system vulnerabilities such as performance losses and accidents are attributed to human errors, a closer inspection would reveal that often times the accumulation of unforeseen events that include both component failures and human errors contribute to such system failures. Human error and functional failure reasoning (HEFFR) is a framework to identify potential human errors, functional failures, and their propagation paths early in design so that systems can be designed to be less prone to vulnerabilities. In this paper, the application of HEFFR within the complex engineering system domain is demonstrated through the modeling of the Air France 447 crash. Then, the failure prediction algorithm is validated by comparing the outputs from HEFFR and what happened in the actual crash. Also, two additional fault scenarios are executed within HEFFR and in a commercially available flight simulator separately, and the outcomes are compared as a supplementary validation.

A general formula for the downtime distribution of a parallel system

1996 ◽  
Vol 33 (03) ◽  
pp. 772-785
Author(s):  
Harald Haukås ◽  
Terje Aven
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Time Distribution ◽  
Life Time ◽  
Exact Formula ◽  
Parallel System ◽  
System Failure ◽  
System Failures ◽  
Failure Scenario ◽  
Common Situation

In this paper we study the problem of computing the downtime distribution of a parallel system comprising stochastically identical components. It is assumed that the components are independent, with an exponential life-time distribution and an arbitrary repair time distribution. An exact formula is established for the distribution of the system downtime given a specific type of system failure scenario. It is shown by performing a Monte Carlo simulation that the portion of the system failures that occur as described by this scenario is close to one when we consider a system with quite available components, the most common situation in practice. Thus we can use the established formula as an approximation of the downtime distribution given system failure. The formula is compared with standard Markov expressions. Some possible extensions of the formula are presented.

A general formula for the downtime distribution of a parallel system

1996 ◽  
Vol 33 (3) ◽  
pp. 772-785 ◽  
Author(s):  
Harald Haukås ◽  
Terje Aven
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Time Distribution ◽  
Life Time ◽  
Exact Formula ◽  
Parallel System ◽  
System Failure ◽  
System Failures ◽  
Failure Scenario ◽  
Common Situation

In this paper we study the problem of computing the downtime distribution of a parallel system comprising stochastically identical components. It is assumed that the components are independent, with an exponential life-time distribution and an arbitrary repair time distribution. An exact formula is established for the distribution of the system downtime given a specific type of system failure scenario. It is shown by performing a Monte Carlo simulation that the portion of the system failures that occur as described by this scenario is close to one when we consider a system with quite available components, the most common situation in practice. Thus we can use the established formula as an approximation of the downtime distribution given system failure. The formula is compared with standard Markov expressions. Some possible extensions of the formula are presented.

scholarly journals The identifiability problem for repairable systems subject to competing risks

2004 ◽  
Vol 36 (03) ◽  
pp. 774-790 ◽  
Author(s):  
Tim Bedford ◽  
Bo H. Lindqvist
Keyword(s):  
Competing Risks ◽  
Probabilistic Models ◽  
Failure Time ◽  
Repairable Systems ◽  
Minimal Repair ◽  
Partial Repair ◽  
Observable Data ◽  
Identifiability Problems ◽  
Component Failures ◽  
Identifiability Problem

Within reliability theory, identifiability problems arise through competing risks. If we have a series system of several components, and if that system is replaced or repaired to as good as new on failure, then the different component failures represent competing risks for the system. It is well known that the underlying component failure distributions cannot be estimated from the observable data (failure time and identity of failed component) without nontestable assumptions such as independence. In practice many systems are not subject to the ‘as good as new’ repair regime. Hence, the objective of this paper is to contrast the identifiability issues arising for different repair regimes. We consider the problem of identifying a model within a given class of probabilistic models for the system. Different models corresponding to different repair strategies are considered: a partial-repair model, where only the failing component is repaired; perfect repair, where all components are as good as new after a failure; and minimal repair, where components are only minimally repaired at failures. We show that on the basis of observing a single socket, the partial-repair model is identifiable, while the perfect- and minimal-repair models are not.

Monte Carlo simulation of the renewal function

1981 ◽  
Vol 18 (2) ◽  
pp. 426-434 ◽  
Author(s):  
Mark Brown ◽  
Herbert Solomon ◽  
Michael A. Stephens
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Renewal Process ◽  
Time Distribution ◽  
Interarrival Time ◽  
Renewal Function ◽  
Expected Number ◽  
Unbiased Estimators ◽  
Monte Carlo Estimation ◽  
Naive Estimator

The problem of Monte Carlo estimation of M(t) = EN(t), the expected number of renewals in [0, t] for a renewal process with known interarrival time distribution F, is considered. Several unbiased estimators which compete favorably with the naive estimator, N(t), are presented and studied. An approach to reduce the variance of the Monte Carlo estimator is developed and illustrated.

scholarly journals Non-periodic inspection of optimization of repairable systems

2021 ◽  
Author(s):  
Yassin Hajipour
Keyword(s):  
Simulation Model ◽  
Failure Time ◽  
Planning Horizon ◽  
Repairable Systems ◽  
Expected Cost ◽  
Total Cost ◽  
Penalty Cost ◽  
Periodic Inspection ◽  
Finite Planning Horizon ◽  
Hard Type

This study proposes models to find the optimal non-periodic inspection interval over a finite planning horizon for two types of multi-component repairable systems. The first system consists of hard-type and soft-type components, and the second system is a k-out-of-m system with m identical components. The failures of components in both systems follow a non-homogeneous Poisson process. The failure of soft-type components and the failure of components in a k-out-of-m system when the number of failed components is still less than m-k+1, are soft failures. Soft failures are revealed only at scheduled inspections or when an event of opportunistic inspection or a system failure occurs. The failures of hard-type components or the failure of (m-k+1)th failed component in a k-out-of-m system are hard failures, and cause the system to stop functioning. Hard failures are revealed immediately and the failed components are fixed. In this study, a failed component is either replaced or minimally repaired according to its age at failure time. To find the optimal inspection schedules for the systems, we minimize the total expected cost of the systems over a finite planning horizon. The total cost for the first type of system includes the costs of components’ minimal repairs, replacements, downtimes, and the scheduled inspections. The total cost of a k-out-of-m system has an additional penalty cost for system failures. We consider a binary variable for a possible scheduled inspection’s time, in which 1 indicates performing a planned inspection at that time, and 0 shows no inspection to be performed. Thus, our goal is to find the optimal vector of binary decision variables which results in the minimum total cost of the system. A recursive formula is developed to calculate the expected number of minimal repairs, replacements and downtime of soft-type components. However since obtaining the expected values from the mathematical formula is cumbersome, we develop a simulation model to obtain the total expected cost for a given non-periodic inspection scheme. We then integrate the simulation model with a genetic algorithm to obtain the optimal inspection scheme.

scholarly journals The identifiability problem for repairable systems subject to competing risks

2004 ◽  
Vol 36 (3) ◽  
pp. 774-790 ◽  
Author(s):  
Tim Bedford ◽  
Bo H. Lindqvist
Keyword(s):  
Competing Risks ◽  
Probabilistic Models ◽  
Failure Time ◽  
Repairable Systems ◽  
Minimal Repair ◽  
Partial Repair ◽  
Observable Data ◽  
Identifiability Problems ◽  
Component Failures ◽  
Identifiability Problem

Within reliability theory, identifiability problems arise through competing risks. If we have a series system of several components, and if that system is replaced or repaired to as good as new on failure, then the different component failures represent competing risks for the system. It is well known that the underlying component failure distributions cannot be estimated from the observable data (failure time and identity of failed component) without nontestable assumptions such as independence. In practice many systems are not subject to the ‘as good as new’ repair regime. Hence, the objective of this paper is to contrast the identifiability issues arising for different repair regimes. We consider the problem of identifying a model within a given class of probabilistic models for the system. Different models corresponding to different repair strategies are considered: a partial-repair model, where only the failing component is repaired; perfect repair, where all components are as good as new after a failure; and minimal repair, where components are only minimally repaired at failures. We show that on the basis of observing a single socket, the partial-repair model is identifiable, while the perfect- and minimal-repair models are not.

Sign in / Sign up

Export Citation Format

Share Document