System Availability and Optimum Spare Units

Sasaki, Masafumi; Kaburaki, Shigeru; Yanagi, Shigeru

doi:10.1109/tr.1977.5220110

Cited by 28 publications

(7 citation statements)

References 6 publications

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“…It was shown by Henley and Kumamoto − that the conditional probabilities of the FS and FD failures of the alarm subsystem can be written as left P FS AL = Pr false{ f false( boldy false) = 1 | ξ = 0 false} = ∑ y f ( y ) Pr false{ y | ξ = 0 false} P FD AL = Pr false{ f false( boldy false) = 0 | ξ = 1 false} = ∑ y [ 1 − f ( y ) ] Pr false{ y | ξ = 1 false} If the shutdown subsystem is always functional, the expected loss of operating the given process in this situation can be formulated as L AL = C normala Pr { normalξ = 0 } P FS AL + C …”

Section: Total Expected Loss Of Protective Systemmentioning

confidence: 99%

“…It was shown by Henley and Kumamoto [13][14][15] that the conditional probabilities of the FS and FD failures of the alarm subsystem can be written as If the shutdown subsystem is always functional, the expected loss of operating the given process in this situation can be formulated as where In eqs 28 and 29, C a and C b denote the financial losses incurred from FS and FD failures, respectively, of the protective system. If the outputs of alarm channels are statistically independent, the conditional probabilities in the above equations (i.e., Pr{y|ξ ) 0} and Pr{y|ξ ) 1}) can be transformed into functions of Α i and Β i , respectively, that is To facilitate comprehensive protective system designs, let us consider all possible failure scenarios (see Figure 8).…”

Section: Total Expected Loss Of Protective Systemmentioning

confidence: 99%

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Design and Maintenance of Multichannel Protective Systems

Liao¹,

Chang²

2010

Ind. Eng. Chem. Res.

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To mitigate the undesirable effects caused by accidents in chemical plants, it is a common practice to install protective systems on processing units operated under hazardous conditions. Because hardware failures are basically random events, the availability of the protective system is highly dependent on its structural properties and also the maintenance programs. The aim of this study is to improve and generalize the current practice 1 for generating the design specifications and maintenance policies. Specifically, instead of monitoring only a single condition, in this work, the emergency system status is detected according to the measurements of several different process variables (or "alarm channels") so as to optimize alarm performance. Because each of these channels can be consist of more than one online sensor, a modified version of the spare-supported corrective maintenance policy is also devised in this study to enhance availability. By solving the corresponding mathematical programming model, the optimal configurations of sensors and shutdown units, the best corrective and preventive maintenance procedures, and alarm/shutdown logic can all be identified automatically. Two examples are provided in this article to demonstrate the feasibility and effectiveness of the proposed approach.

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Section: Total Expected Loss Of Protective Systemmentioning

confidence: 99%

Section: Total Expected Loss Of Protective Systemmentioning

confidence: 99%

Design and Maintenance of Multichannel Protective Systems

Liao¹,

Chang²

2010

Ind. Eng. Chem. Res.

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“…These probabilities can be related with a set of state equations derived according to the Markov diagram in Figure 1. 6,15,16 For the sake of brevity, the detailed derivations are again omitted and only the resulting formulas are given below:…”

Section: R(t) ) E -λTmentioning

confidence: 99%

A Simultaneous Optimization Approach To Generate Design Specifications and Maintenance Policies for the Multilayer Protective Systems in Chemical Processes

Liang

Chang

2008

Ind. Eng. Chem. Res.

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Generally speaking, a protective system is adopted to perform two basic functions, i.e., alarm and shutdown. The subsystem to perform the former function is equipped with one or more independent sensors. On the basis of the online measurements of these sensors, Boolean logic is applied to determine whether or not alarm signal(s) should be issued. The subsystem for the latter task is usually configured with solenoid valves. In response to the aforementioned signal(s), these valves are energized (or de-energized) to carry out the required shutdown operation. Since the hardware failures are basically random events, the reliability (or availability) of a protective system is highly dependent upon its structural characteristics and also maintenance policies. Traditionally, the alarm logic and shutdown configuration are synthesized according to experience and the maintenance scheme is also established on an ad hoc basis. The aim of this study is to develop an integrated mathematical programming model to minimize the total expected expenditure, i.e., the sum of the capital investments, the expected maintenance costs, and the expected losses due to system failures. From the optimal solution, one should be able to produce the design specifications for every protection layer, i.e., (1) the number of sensors and the corresponding alarm logic, (2) the number of valves and the corresponding shutdown configuration, and (3) the needed repair/replacement policies. In this work, the sensors and valves are assumed to be maintained respectively with the corrective and preventive strategies. Thus, the optimal number of spare sensors stored offline and the best inspection interval for each valve can also be determined by solving this model. Extensive case studies have been carried out to demonstrate the feasibility and effectiveness of the proposed approach.

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“…Both these algorithms experience intrinsic limitations associated to computational complexity. Sasaki et al [41] developed a method for finding the global optimum between specified upper and lower bounds of the allocation vector for classes of problems where both the objective function and the constraints are monotonically non-decreasing. Several additional methods to find the global optimum are discussed in the Handbook of global optimization edited by Pardalos and Romeijn [33].…”

Section: Introductionmentioning

confidence: 99%

A Two-Phase Combined Gradient-Tunneling Based Algorithm for Constrained Integer Programming Problems

Srivastava

Spinello

2015

Journal of Information and Optimization Sciences

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We propose a gradient-based optimization procedure consisting of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In the first phase a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to a feasible region. In the second phase a tunneling function is constructed at this local minimum in order to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle the search for the global optimum commences again using this new found point as the starting state. The search continues until no improvement in function the result is found. Results from the proposed optimization method are presented and compared with those from the gradient method involving 3 n enumeration proposed earlier, as well as with other published results.

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System Availability and Optimum Spare Units

Cited by 28 publications

References 6 publications

Design and Maintenance of Multichannel Protective Systems

Design and Maintenance of Multichannel Protective Systems

A Simultaneous Optimization Approach To Generate Design Specifications and Maintenance Policies for the Multilayer Protective Systems in Chemical Processes

A Two-Phase Combined Gradient-Tunneling Based Algorithm for Constrained Integer Programming Problems

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