Abstract. 1 Introduction

Transcription

1 RAM requirements optimal apportionment in guided transport systems G. Cosulich, P. Firpo, S. Savio Dipartimento di Ingegneria Elettrica, Universita degli Studi di Genova, Via all'operapia 11 a, Genova, Italy Abstract In railway applications, as in other industrialfields,the design of any subsystem has to face Reliability, Availability and Maintainability (RAM) analysis, if Product Assurance requirements are specified. For this reason, the first step in the design process is to translate the overall system RAM requirements into requirements for each subsystem, equipment or component. Starting from the different approaches usually adopted, the authors present in this paper the characteristics of a software tool able to automatically optimize RAM parameters (failure and repair rates) allocation, once known system dependability targets. 1 Introduction In a Guided Transport System (GTS) aim of the companies which realize any subsystem with Product Assurance requirements, is to furnish competitive products accomplishing the required RAM (Reliability, Availability and Maintainability) targets; as a consequence, mandatory is a quality design procedure, able to reduce both the design cost itself and the cost related to the final product realization. Existing european project standard provides common definitions of the RAM concepts, grouped together with Safety in the term dependability, and it defines common procedures for the analysis of a GTS along the whole life cycle. The standard shows a structured process for specifying the requirements of each element or subsystem and demonstrating that these requirements are achieved, and it defines a RAM organisation, establishing the roles and the responsibilities of the involved personnel; therefore, it is well defined what has to be done and who is meant to do that, but it is not defined how the standard procedures may be performed from an operative point of view.

2 484 Software for Electrical Engineering To this aim, the GTS designer may utilize the know-how coming from other industrial fields and the operative procedures usually adopted for military, nuclear or aeronautic applications, obviously customized for the specific purpose; in any case, whatever is the RAM analysis to be performed, the extreme complexity of a Guided Transport System makes mandatory the use of simulation packages. In this paper the authors show the characteristics of a software tool useful for the designer during thefirstphases of the design process when it is necessary, as it will be described in the next paragraph, to translate the overall system RAM requirements into requirements for each subsystem, equipment or component. In particular, the proposed tool is able to automatically perform RAM targets optimal allocation, thanks to a general purpose modelling of the system based on Reliability Block Diagram theory. 2 Apportionment of RAM targets The apportionment of RAM targets is one of thefirstphases of the system life cycle and it is fundamental to translate the overall system RAM requirements into RAM requirements for each of the subsystems. In particular, the apportionment is a process whereby the dependability elements for a system are subdivided among the various items which comprise the system to provide, for example, adequate individual targets to be imposed to subcontractors and suppliers. Once established, the overall RAM requirements shall be apportioned to lower levels in order to provide targets for the development of detail design, taking into account technical specification, costs, maintenance facilities, that shall be compliant with the allocated values. The apportionment of system RAM targets involves solving the basic inequality: where: Xj = RAM parameter for the i-th subsystem; T = system RAM requirement parameter; g = functional relationship among subsystem and system RAM parameters. Equation (1), due to the particular structure which the function g may assume in reliability models, has an infinite number of solutions, assuming no restrictions on the allocation. The problem is to establish a procedure that yields a unique or limited number of solutions by which consistent and reasonable RAM targets may be allocated. Using the traditional approximate apportionment process, if the allocated RAM values for a specific subsystem cannot be achieved at the current state of the technology, then the system design must be modified and the allocations reassigned. This procedure is repeated until an allocation is achieved that satisfies the system RAM requirement and all constraints, and results in subsystems that can be designed within the state of the art.

3 Software for Electrical Engineering 485 If even with reallocation some of the individual subsystem requirements cannot be met within the current state of the art, then the designer must use one of the following approaches: find more dependable component parts to use; simplify the design by using fewer components parts, if this is possible without degrading performance; apply component derating techniques to reduces the failure rates below the averages; use redundancy. 3 Optimal apportionment technique The authors propose an optimization approach to solve the problem of RAM targets apportionment, in order to obtain an exact solution which takes into account the system constraints. The optimization procedure is related to the solution of the following problem: with the constraints: 0 (3) Parametric optimization is used to find a set of design parameters, X = [xy, r?, --, * ], which can in some way be defined as optimal. In the case analyzed by the authors, the design parameters agree with the system components RAM parameters to be allocated, it is to say the failure rates A/ and the repair rates ///, /=7,2,...,w assuming n the number of the elements of the system. f(x) is the objective function (/" : %n=>%) to be minimized, which may be subject to the inequality constraints g/qo, i=l,2,...,m. G(X) is the vector of inequality constraints (G : 9?n=>9? ) which agree with the system Reliability Block Diagram constraints and with the system components constraints. Two different types of constraints have been considered: constraints which take into account the system Reliability Block Diagram structure and define a relationship between the target T to be apportioned, the failure rates and the repair rates of the system components (4); constraints which are fixed by the current state of the technology, the physical parameters of the components, the cost and complexity, the maintenance facilities and so on (5). (4)

4 486 Software for Electrical Engineering Different objective functions may be defined according to the requirements of the designer: in fact, the structure of the objective function allows the optimization procedure to manipulate the RAM parameters which may be more suitable to solve the problem, on the basis of considerations related, for instance, to the system life cycle cost or to the mission profile. Equation (6) is an example of objective function for a long life system; this function allows the minimization of the component failure rates and the maximization of the repair rates in order to reduce the system maintenance cost: with this solution the system is characterized by a low number of failures and reduced man-hours are needed to perform the maintenance operations. 2 + "+an'an+ + + ' + (6) /4 /"2 /4, Equation (7) is another example of objective function for a system where the costs related to hardware acquisition may be not negligible if compared with maintenance cost; in this case the function allows, in particular, the minimization of hardware acquisition through the maximization of the relevant failure rate. In equations (6) and (7), a,, bj and c\ are coefficients able to penalize the related RAM parameters; for instance, in equation (6), thanks to a\ and bj it is possible, once the objective function has been defined, to favour, during the minimization process, the manipulation of the RAM parameters characterized by high values of the above mentioned coefficients. In this context would be useful to have at disposal, during thefirstphases of the design, a software tool able to solve non linear constrained optimization problems, in order to support the allocation process, providing targets for the development of the design. 4 The software tool The software tool proposed by the authors and under development at the Electrical Engineering Department of the University of Genova, is able to give an exact solution to the problem, taking into account the system Reliability Block Diagram structure and defining the exact relationship among subsystem RAM parameters to be allocated and the overall RAM requirements: in particular, starting from a set of elementary configurations which will be described in the following, the tool is able to define the MTTF (Mean Time To Failure), the MTTR (Mean Time To Reapair) and the steady-state availability of the overall system as a mathematical function of the RAM parameters of the system components. Starting from the real structure of the system, the software tool is able to analyze any cost function defined by the designer to penalize the variables to be apportioned, taking automatically into account the state of the technology, physical parameters, such as weight and dimension, the subsystem cost and complexity, the maintenance facilities and so on.

5 Software for Electrical Engineering 487 As previously mentioned, the software tool is based on the implementation of the system Reliability Block Diagram (RED): a RED may be considered a logic chart which, by means of the arrangement of blocks and lines, depicts the effect of components failure on the system functional capability. Different reliability model configurations, as it will be shown in the following, may be represented in a Reliability Block Diagram and, in particular, items whose failure causes system failure are shown in series with other items; items whose failure causes system failure only when some other items have also failed are drawn in parallel with the other items. For a complex system it is often convenient to have several block diagrams, as depicted in Figure 1. The first diagram (Level I) is a simple diagram showing thefirst-ordersubdivision breakdown of the system. Separate block diagrams (Level II) are then constructed for each of the first order subdivisions. This process of diagramming goes on until individual blocks represent an order complexity such that their failure rates can be readily estimated from part level data. Levels I and II diagrams may be derived from the information available in the system planning phases. Level III diagram may be defined in the early design step and Level IV diagram is usually drawn once defined the detail structure of the system by design reviews. Level I System Level H Sub system Level m Module Level IV Equipment Figure 1: Progressive expansion of RBD

6 488 Software for Electrical Engineering The apportionment process is iteratively performed at different detail levels and corresponds to a top-down analysis, starting from the system functional representation: these different levels of analysis are related to the RED Levels of Figure 1. Figure 2 shows the reliability model elementary configurations most commonly used which are implemented in the software tool. (a) (b) I S r (c) Figure 2: Reliability model elementary configurations Figure 2a shows the simplest and perhaps most commonly occurring configuration in reliability mathematical modelling; it is to say the series configuration; in this case the successful operation of the system depends on the proper functioning of all the system components as the a component failure represents total system failure. Figure 2b shows another common redundant configuration represented by the parallel configuration; in this case, for the system to fail, all of the components have to fail. Finally Figure 2c depicts the k-out-of-n configuration which represents a system consisting of n components or subsystems, of which only k need to be

7 Software for Electrical Engineering 489 functioning for system success; obviously the parallel configuration may be modelled as a k-out-of-n configuration with k=l. Furthermore, in Figure 2c is also shown with a dashed line the block S which represents the possibility of the tool to take automatically into account the presence of a switch, able to connect or disconnect a block, for instance integrated with a comparator for blocks output majority voting. The presence of block S is particularly interesting from a conceptual point of view as it is related to the skill of the software tool to analyze system managed with different policies as far as operating conditions and maintenance are concerned. In particular the software tool is able to manage systems characterized by hot and stand-by redundant configuration in presence of repairable and not repairable elements. If the mission of the system begins at time t=0, hot redundant configuration means that all the elements are connected at t=0 while stand-by redundant configuration means that only the needed elements (primary) are connected at t=0 and a further element (secondary) is connected only when a failure occurs, it is to say no time is accumulated on a secondary element until a primary element fails. At last, as far as maintenance operations are concerned, the package can analyze repairable configurations, where the elements are repaired when they fail during the mission, and non repairable configurations, represented by elements which are repaired only when the system fails. In Figure 3 the functional block diagram of the simulation package is shown. System Reliability Block Diagram Decomposition Elementary RED System RAM parameters Mathematical definition Components RAM parameters Constraints Components RAM parameters Optimal Apportionment Figure 3: Functional block diagram of the software tool

8 490 Software for Electrical Engineering The software tool, starting from the global RED of the system, decomposes it into the reliability elementary configurations depicted in Figure 3, in order to build the mathematical expression of the RAM parameters of the overall system (MTTF, MTTR, steady-state availability) as a function of the components failure and repair rates, which are assumed exponentially distributed. The following step is represented by the optimization procedures able to allocate the RAM parameters of each component, once known the objective function and the constraints furnished by the designer, as described in the previous paragraph. 5 Conclusions The companies involved in the design, manufacturing and management of a Guided Transport System have to mandatorily perform Reliability, Availability and Maintainability analysis, if Product Assurance requirements are specified. In particular, the first step in the design process is related to the apportionment, or allocation, of the overall system RAM requirements into requirements for each subsystem, equipment or component. In this paper the authors show the features of a software package able to automatically optimize RAM parameters allocation, once known system dependability targets. The tool, based on the Reliability Block Diagram theory, allows the designer to apportion, whatever is the structure of the overall system, the failure and repair rates of each component by minimizing an objective function defined by the user and taking into account different policies, as far as operating conditions and maintenance are concerned. To this aim, the most commonly utilized reliability configurations are implemented in order to allow the management of hot and stand-by redundancy with repairable and not repairable elements. References 1. U.S.A. Department of Defense, Military Handbook MIL-HDBK-338-1A, Electronic Reliability Design Handbook, U.S.A., October CENELEC TC9X, Final Draft pren50126, Railway Applications: The Specification and Demonstration of Reliability, Availability, Maintainability and Safety (RAMS), Brussels, August Y. Nakagawa, K. Nakashima, A heuristic method for determining optimal reliability allocation, IEEE Transactions on Reliability, vol. R-26, July 1977, pp F.A. Tillman, C Hwang, W. Kuo, Determining component reliability and redundancy for optimum system reliability, IEEE Transactions on Reliability, vol. R-26, July 1977, pp Z. Xu, W. Kuo, H.H. Lin, Optimization limits in improving system reliability, IEEE Transactions on Reliability, vol. 39, April 1990, pp A.K. Dhingra, Optimizal apportionment of reliability and redundancy in series systems under multiple objectives, IEEE Transactions on Reliability, vol. 41, October 1992, pp