scholarly journals Evaluation Of The Safety Integrity Level (SIL) Due To The Guidelines Of EN 61508 And With The Use Of Markov Processes

2015 ◽  
Vol 35 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Stanisław Młynarski ◽  
Robert Pilch ◽  
Maksymilian Smolnik ◽  
Maciej Szkoda ◽  
Jan Szybka
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Renewal Process ◽  
Probability Of Failure ◽  
On Demand ◽  
Safety Integrity Level ◽  
Methods Of Evaluation ◽  
Safety Systems

Abstract The methods of evaluation of the Probability of Failure on Demand (PFD) of safety systems were presented in the paper, assuming that the safety systems may be represented by the k out of n reliability structures. The results of the calculations obtained according to EN 61508 were compared with another results, this time obtained from the calculations done for these systems assuming that their failure-and-renewal process is a Markov process.

Probability of failure on demand of safety systems: impact of partial test distribution

2012 ◽  
Vol 226 (4) ◽  
pp. 426-436 ◽  
Author(s):  
Florent Brissaud ◽  
Anne Barros ◽  
Christophe Bérenguer
Keyword(s):  
Probability Of Failure ◽  
Test Time ◽  
Time Interval ◽  
System Failures ◽  
On Demand ◽  
Component Failure Rates ◽  
Safety Systems ◽  
The Impact ◽  
Architecture Component ◽  
Approximate Equations

In accordance with the IEC  61508 functional safety standard, safety-related systems operating in a low demand mode need to be proof tested to reveal any ‘dangerous undetected failures’. Proof tests may be full (i.e. complete) or partial (i.e. incomplete), depending on their ability to detect all the system failures or only a part of them. Following a partial test, some failures may then be left latent until the full test, whereas after a full test (and overhaul), the system is restored to an as-good-as-new condition. A partial-test policy is defined by the efficiency of the partial tests, and the number and distribution (periodic or non-periodic) of the partial tests in the full test time interval. Non-approximate equations are introduced for probability of failure on demand (PFD) assessment of a Moo N architecture (i.e. k-out-of- n: G) systems subject to partial and full tests. Partial tests may occur at different time instants (periodic or not) until the full test. The time-dependent, average, and maximum system unavailability (PFD(t), PFDavg, and PFDmax) are investigated, and the impact of the partial test distribution on average and maximum system unavailability are analysed, according to system architecture, component failure rates, and partial test efficiency.

The Effects of Maintenance Actions on the Average Probability of Failure on Demand of Spring Operated Pressure Relief Valves

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Julia V. Bukowski ◽  
William M. Goble ◽  
Robert E. Gross ◽  
Stephen P. Harris
Keyword(s):  
Probability Of Failure ◽  
Pressure Relief ◽  
Periodic Inspection ◽  
On Demand ◽  
Plant Safety ◽  
Safety Integrity Level ◽  
Proof Testing ◽  
Average Probability ◽  
Pressure Relief Valves ◽  
Inspection And Maintenance

The safety integrity level (SIL) of equipment used in safety instrumented functions is determined by the average probability of failure on demand (PFDavg) computed at the time of periodic inspection and maintenance, i.e., the time of proof testing. The computation of PFDavg is generally based solely on predictions or estimates of the assumed constant failure rate of the equipment. However, PFDavg is also affected by maintenance actions (or lack thereof) taken by the end user. This paper shows how maintenance actions can affect the PFDavg of spring operated pressure relief valves (SOPRV) and how these maintenance actions may be accounted for in the computation of the PFDavg metric. The method provides a means for quantifying the effects of changes in maintenance practices and shows how these changes impact plant safety.

scholarly journals CLASSICAL MARKOV PROCESSES FROM QUANTUM LÉVY PROCESSES

1999 ◽  
Vol 02 (01) ◽  
pp. 105-129 ◽  
Author(s):  
UWE FRANZ
Keyword(s):  
Markov Process ◽  
Hopf Algebra ◽  
Markov Processes ◽  
Lévy Processes ◽  
Sufficient Conditions ◽  
Markov Property ◽  
Vacuum State ◽  
Levy Processes ◽  
Quantum Process ◽  
Quantum Markov Processes

We show how classical Markov processes can be obtained from quantum Lévy processes. It is shown that quantum Lévy processes are quantum Markov processes, and sufficient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can restrict to a commutative subalgebra without losing the quantum Markov property.8 Several examples, including the Azéma martingale, with explicit calculations are presented. In particular, the action of the generator of the classical Markov processes on polynomials or their moments are calculated using Hopf algebra duality.

A temporal factorization at the maximum for certain positive self-similar Markov processes

2020 ◽  
Vol 57 (4) ◽  
pp. 1045-1069
Author(s):  
Matija Vidmar
Keyword(s):  
Markov Process ◽  
Laplace Transform ◽  
Markov Processes ◽  
Absorption Time ◽  
The Laplace Transform ◽  
Self Similar

AbstractFor a spectrally negative self-similar Markov process on $[0,\infty)$ with an a.s. finite overall supremum, we provide, in tractable detail, a kind of conditional Wiener–Hopf factorization at the maximum of the absorption time at zero, the conditioning being on the overall supremum and the jump at the overall supremum. In a companion result the Laplace transform of this absorption time (on the event that the process does not go above a given level) is identified under no other assumptions (such as the process admitting a recurrent extension and/or hitting zero continuously), generalizing some existing results in the literature.

Review of Technological Advancements and HSE-Based Safety Model for Deep-Water Human Occupied Vehicles

2014 ◽  
Vol 48 (3) ◽  
pp. 25-42 ◽  
Author(s):  
Narayanaswamy Vedachalam ◽  
Gidugu Ananada Ramadass ◽  
Malayath Aravindakshan Atmanand
Keyword(s):  
Deep Water ◽  
Capital Expenditure ◽  
Mean Time Between Failures ◽  
Safety Integrity Level ◽  
Geological Surveys ◽  
Time Between Failures ◽  
High Resolution Bathymetry ◽  
Safety Systems ◽  
Mean Time ◽  
Safety And Environment

AbstractThis paper reviews the latest advancements in subsea technologies associated with the safety of deep-water human occupied vehicles. Human occupied submersible operations are required for deep-water activities, such as high-resolution bathymetry, biological and geological surveys, search activities, salvage operations, and engineering support for underwater operations. As this involves direct human presence, the system has to be extremely safe and reliable. Based on applicable IEC 61508 Standards for health, safety, and environment (HSE), the safety integrity level requirements for the submersible safety systems are estimated. Safety analyses are done on 10 critical submersible safety systems with the assumption that the submersible is utilized for 10 deep-water missions per year. The results of the analyses are compared with the estimated target HSE requirements, and it is found that, with the present technological maturity and safety-centered design, it is possible to meet the required safety integrity levels. By proper maintenance, it is possible to keep the mean time between failures to more than 9 years. The results presented shall serve as a model for designers to arrive at the required trade-off between the capital expenditure, operating expenditure, and required safety levels.

Extension of Wald's first lemma to Markov processes

1999 ◽  
Vol 36 (01) ◽  
pp. 48-59 ◽  
Author(s):  
George V. Moustakides
Keyword(s):  
Integral Equation ◽  
Markov Process ◽  
Markov Processes ◽  
Correction Term ◽  
Stopping Time ◽  
Poisson Integral ◽  
Homogeneous Markov Process ◽  
Partial Sum ◽  
Poisson Integral Equation ◽  
Scalar Nonlinearity

Let ξ0,ξ1,ξ2,… be a homogeneous Markov process and let S n denote the partial sum S n = θ(ξ1) + … + θ(ξ n ), where θ(ξ) is a scalar nonlinearity. If N is a stopping time with 𝔼N < ∞ and the Markov process satisfies certain ergodicity properties, we then show that 𝔼S N = [lim n→∞𝔼θ(ξ n )]𝔼N + 𝔼ω(ξ0) − 𝔼ω(ξ N ). The function ω(ξ) is a well defined scalar nonlinearity directly related to θ(ξ) through a Poisson integral equation, with the characteristic that ω(ξ) becomes zero in the i.i.d. case. Consequently our result constitutes an extension to Wald's first lemma for the case of Markov processes. We also show that, when 𝔼N → ∞, the correction term is negligible as compared to 𝔼N in the sense that 𝔼ω(ξ0) − 𝔼ω(ξ N ) = o(𝔼N).

Composable Markov processes

1970 ◽  
Vol 7 (2) ◽  
pp. 400-410 ◽  
Author(s):  
Tore Schweder
Keyword(s):  
Social Sciences ◽  
Markov Process ◽  
Markov Processes ◽  
Infinitesimal Generator ◽  
A Priori ◽  
The Social

Many phenomena studied in the social sciences and elsewhere are complexes of more or less independent characteristics which develop simultaneously. Such phenomena may often be realistically described by time-continuous finite Markov processes. In order to define such a model which will take care of all the relevant a priori information, there ought to be a way of defining a Markov process as a vector of components representing the various characteristics constituting the phenomenon such that the dependences between the characteristics are represented by explicit requirements on the Markov process, preferably on its infinitesimal generator.

scholarly journals On invariant measures of nonlinear Markov processes

1993 ◽  
Vol 6 (4) ◽  
pp. 385-406 ◽  
Author(s):  
N. U. Ahmed ◽  
Xinhong Ding
Keyword(s):  
Markov Process ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Invariant Measures ◽  
Nonlinear Markov Processes

We consider a nonlinear (in the sense of McKean) Markov process described by a stochastic differential equations in Rd. We prove the existence and uniqueness of invariant measures of such process.

scholarly journals Genetic Algorithm Optimization Model for Determining the Probability of Failure on Demand of the Safety Instrumented System

2019 ◽  
Vol 1 (2) ◽  
Author(s):  
Ahmed H. Aburawwash ◽  
Moustafa Mohammed Eissa ◽  
Azza F. Barakat ◽  
Hossam M. Hafez
Keyword(s):  
Genetic Algorithm ◽  
Accurate Determination ◽  
Probability Of Failure ◽  
System Structure ◽  
Control Element ◽  
Algorithm Optimization ◽  
On Demand ◽  
Uncertainty Sources ◽  
Iec 61508 ◽  
Proposed Model

A more accurate determination for the Probability of Failure on Demand (PFD) of the Safety Instrumented System (SIS) contributes to more SIS realiability, thereby ensuring more safety and lower cost. IEC 61508 and ISA TR.84.02 provide the PFD detemination formulas. However, these formulas suffer from an uncertaity issue due to the inclusion of uncertainty sources, which, including high redundant systems architectures, cannot be assessed, have perfect proof test assumption, and are neglegted in partial stroke testing (PST) of impact on the system PFD. On the other hand, determining the values of PFD variables to achieve the target risk reduction involves daunting efforts and consumes time. This paper proposes a new approach for system PFD determination and PFD variables optimization that contributes to reduce the uncertainty problem. A higher redundant system can be assessed by generalizing the PFD formula into KooN architecture without neglecting the diagnostic coverage factor (DC) and common cause failures (CCF). In order to simulate the proof test effectiveness, the Proof Test Coverage (PTC) factor has been incorporated into the formula. Additionally, the system PFD value has been improved by incorporating PST for the final control element into the formula. The new developed formula is modelled using the Genetic Algorithm (GA) artificial technique. The GA model saves time and effort to examine system PFD and estimate near optimal values for PFD variables. The proposed model has been applicated on SIS design for crude oil test separator using MATLAB. The comparison between the proposed model and PFD formulas provided by IEC 61508 and ISA TR.84.02 showed that the proposed GA model can assess any system structure and simulate industrial reality. Furthermore, the cost and associated implementation testing activities are reduced.

Sign in / Sign up

Export Citation Format

Share Document