VALIDATION AND APPLICATION OF A RELIABILITY ALLOCATION TECHNIQUE (ADVANCED INTEGRATED FACTORS METHOD) TO AN INDUSTRIAL SYSTEM Falcone Domenico, Fabio De Felice, GianPaolo Di Bona, Vincenzo Duraccio, Antonio Forcina, Alessandro Silvestri. Department of Civil and Mechanical Engineering Università degli Studi di Cassino e del Lazio Meridionale 03043 Cassino ( FR )-Italy tel.: +39-0776-2993653; fax: +39-0776-2993886 e-mail:
[email protected] ABSTRACT The proposed work analyses and applies a new reliability and redundancy allocation procedure. Starting from a similar methodology previously developed by the authors, Integrated Factors Method (IFM), a new reliability allocation and optimization method is developed: Advanced Integrated Factors Method (AIFM). The new technique has been proposed to analyze complex systems in the pre-design phase, even if its general characteristics allow extending the method to different design and production phases. The previous method has been improved through the introduction of new indexes that help improve underperforming components in order to achieve the allocated reliability values. The method introduces a big number of factors, so it can be applied to a wide range of systems. It is characterized by a very simple mathematical formulation, that can be made more complicated for a more detailed analysis. KEY WORDS Reliability, Allocation, Redundancy, Redesign
1. Introduction Since the beginning of history, Humanity has attempted to predict the future [1]. In the past, safety factors and overabundant redundancies have been often adopted to guarantee the future reliability of a component or installation [2]. Troubles or disasters have dictated the changes in components or installations to achieve the desired system reliability [3] [4]. Fortunately, today's engineers use product life data to predict the "future" of their products, to determine the probability of failures and the capabilities of parts, components, and systems to perform required functions for desired periods of time without failures, in specified environments. Life data can be lifetimes of products in the marketplace, such as the time the product operated successfully or the time the product operated before it failed, measured in hours, miles, cycles-to-failure etc. The
subsequent analysis and prediction are called Reliability Analysis. In the last few years, some analysis methods are developing to forecast system reliability, availability, maintainability and safety (R.A.M.S.), and to point out and mitigate weak points during the planning phase [5]. The system reliability represents both the starting and the ending point of R.A.M.S. Analysis: • we are interested in the single sub-system reliability to obtain the whole system reliability (reliability research techniques); • we can fix the system reliability value and then estimate components performances, obtaining the most critical sub-systems in terms of reliability (system design). In the second case we speak of Reliability Allocation techniques; they permit to assign reliability parameters to the different system units, so that the whole system reaches the established reliability target. Reliability Analysis is based on the performance results of tests in labs and working products [6] [7]. Those data are utilized to measure and improve the reliability of the products being produced. Often, an initial cost reduction is achieved by using cheaper parts or cutting testing programs [8] [9]. Unfortunately, quick savings thanks to the use of cheaper components or few test samples, usually result in higher long-term costs in the form of warranty costs or loss of the customer confidence (see Fig. 1).
Figure 1. Reliability-Cost Trade-Off Curve
⋅
⋅
2. Reliability allocation: integrated factors method (IFM)
GIi (2.1)
Some USA standards [10] [11] [12] [13] supply the guide lines for the development of a correct allocation model. The main aspects are: • generality; • input data standardization; • cheapness; • definition of realistic and reachable requests.
GI%i = GIi/(Σi=1,…,n GIi) (2.2) GI%i: global index percentage relative to the sub-system; GIi: global index relative to the sub-systemi; n: number of units.
Starting from the above guide lines, a new methodology for the reliability allocation has been developed: “Integrated Factors Method” (IFM). The proposed reliability allocation technique has been thought-out for prototype complex systems during the pre-design phase. Subsequently, the method has been developed to permit its application to different design phases, when more and detailed information about components is available. At the beginning, the new methodology has been proposed for systems in series, prototype (this hypothesis is in favour of security, in fact the mission fails just when one unit breaks down) [14] [15]. Studying in detail the different methods, we have noticed the need to use opportune factors of influence. These factors have to permit the discrimination among the system units [16] [17]. Initially, we have supposed the same technological level for the units and the same operative severity. We have chosen the following factors and relative indexes: Criticality index (C): ratio between the number of subsystem functions that cause an undesirable event, and the number of total system functions; Complexity index (K): referring to the technological and constructive structure; possible values are: 0,10-0,30 for simple system; 0,40-0,70 for not very complex system; 0,80-1,00 for complex one; Functionality index (F): ratio between the number of unit functions, and the number of total system functions; Effectiveness index (O): referring to the unit operative time; possible values are: 1,00 for times equal to the whole mission; 0,67 for continuous and long times; 0,33 for short times. The evaluation of the above indexes, thanks to an Expert Judgement’s help, permits to calculate the Global Index (GI), useful to the system unreliability (consequently the reliability) allocation:
=
Ki
Fi
Oi
/
Ci
After the evaluation of the Global Index Percentage for each unit (GI%i), it is possible to allocate the system unreliability target (Us(t)) to the uniti (Ui(t)): Ui(t) = Us(t) · GI%i
(2.3)
Later, in a dynamical approach, we have proposed a more quantitative definition of K and O indexes: Complexity index (K): ratio between the number of parts of the unit and the number of parts of the whole system; Effectiveness index (O): ratio between effectiveness time and the mission total time.
the
unit
To apply the new method to more complex systems, characterized by components with different technology, we have introduced a Technology index (S) (being S=0,5 for traditional components and S=1 for innovative components). To discriminate electronic systems against mechanical ones, characterized by the same complexity, we have introduced a further Electronic Functionality index (E) (E =1: completely electronic system; E=0,1: completely mechanical system). Finally, we have considered an increase (M) of the Effectiveness index (O), caused by a greater operative severity.
3. Reliability allocation improvement: advanced integrated factors method (AIFM) In order to improve the reliability value of more critical components, two approaches are possible:
• •
Old Component Redundancy: benefits coming out from parallel units [18] [19]; New Component Development: redesign of a more reliable component [20].
Therefore, the IFM method was perfected by the introduction of a decisional support procedure based on technical-economical indexes, to evaluate the convenience of a possible choice of improvement. In the first phase, the procedure allows recognizing the most critical components, subsequently it suggests the better actions to improve the allocation.
The developed methodology, called “Advanced Integrated Factors Method” (AIFM), considers the following two phases:
Crp: costs needed for redesigning the component and modifying the system configuration; Trp: estimated period of time to complete the project;
3.1 Reliability level identification Calling Ral the allocated value and Rav the available one, we have to choose a specific level of alert ΔR = Ral – Rav, called ΔR*. By valuing the difference ΔR for each component, it is possible to compare this value with the fixed level of alert ΔR*, pointing out critical components. Then, for those critical components, we can value a particular index able to suggest improving actions, called R-R index, (Component Redesign-Redundancy Index). That index measures the “sacrifice” needed to obtain the required reliability improvement, as described below. The proposed index takes into consideration both technical and economical aspects. It is possible to guide designers towards the modification of the system because of the introduction of redundant components, rather than the redesign of critical components, to improve their performances. To make the right choice, the main items of interest are: • Expected reliability growth due to the component/system redesign; • Costs estimated to achieve the growth; • Time required for developing the project; • Failure Risk.
ΔRrd: increase of reliability, achieved through the redundancy of the component and the introduction of a parallel model; FLrp: risk of failure in introducing a redundancy in the existing system. This parameter can assume only discrete values: 0 and 1, respectively, in the case of impossibility or possibility of redundancy; Crd: costs to introduce the redundancy of the component, due to the purchase of similar components and to the adjustment of the system; Trd: estimated time to complete the redesign of the system redundancy. Times introduced in the previous indexes can be easily estimated, based on similar systems. In case of redundancy, costs must be calculated taking into account costs for an additional component and needed changes on the whole system. Instead it is necessary to perform a market investigation in case o redesigning a new component.
3.2 Calculation of R-R index (Component RedesignRedundancy Index) The mathematical formulation of the index is: R-R = Red-Red = Redesign / Redundancy
(3.2.1)
Where Redesign = (ΔRrp * FLrp) / (Crp * Trp)
(3.2.2)
And Redundancy = (ΔRrd * FLrd) / (Crd * Trd)
(3.2.3)
The meaning of each term is the following: ΔRrp: increase of reliability, achieved through the choice, development, design of a new component, able to guarantee the required performances; FLrp: risk of failure in redesigning the component. Range between 0 (in the case of a high possibility of failure, close to 100%) and 1 (in the case of a low possibility of failure).
Figure 2. AIFM application procedure If it is better to redesign the component, the R-R index assumes values greater than 1, instead, if the redundancy is the better choice, we have values less then 1. If the index is about equal to 1, the choice is almost equivalent and more detailed evaluations are needed, such as designer competence, supplier qualification etc.
If we can’t duplicate the component and the only way is its redesign, the R-R index becomes equal to zero. By applying the whole method suggested (IFM – AIFM), it is possible, after the allocation of reliability values, to make appropriate actions on critical components, based on objective factors. In the figure n. 2, the flowchart for the application of the AIFM method, is shown.
IFM FACTOR
In order to validate the AIFM procedure, we applied it to a real system whose reliability data were known in detail. The industrial system chosen for the application and validation of the method, is a metallic waste press. To allocate the reliability to the components, it was necessary to analyze the system in order to break it down and find an initial configuration through a Reliability Block Diagram. The starting configuration of the system is showed in Figure 3.
Cooling System
c1
1
2
3
4
c2
2
4
5
5
1
0.50
0.50
0.60
0.80
1.00
C = (c1/c2)
1
f1
2
4
5
5
1
F
17
17
17
17
17
F= (f1/f)
4. AIFM application to an industrial system
RELIABILITY ALLOCATION Metallic Electr. Feed Structure Pistons System Pump
0.12
0.24
0.29
0.29
0.06
O
0.4
0.8
0.8
1
0.67
K
0.2
0.6
0.5
1
0.7
GIi
0.02
0.23
0.20
0.37
0.03
2.25%
27.02%
23.45%
43.98%
3.30%
GI%i Us target Ui
4.50E-02 4.50E-02 4.50E-02 4.50E-02 4.50E-02 0.10%
1.22%
1.06%
1.98%
0.15%
Ri Alloc.
99.90%
98.78%
98.94%
98.02%
99.85%
Ri Avail.
99.72%
98.90%
99.13%
88.30%
99.23%
Table 1. Reliability allocation through IFM method In particular we can notice the bigger value of ΔR, higher than a fixed Alert Value ΔR* of 1%. The lowest value of reliability of the pump compromises the whole system reliability target. Subsequently, the AIFM procedure has been applied to the critical component.
Figure 3. Press starting configuration The decomposition of the system is purely theoretical and demonstrative. In fact, in the real configuration, there are two fluid power pumps. We want to understand if the methodology is able to suggest the redundancy of the component "pump", corresponding to the real configuration of the system, as the best choice. At this point, we calculated, through a Fault Tree Analysis, the reliability value of the system, in the assumed serial configuration. For the simulated configuration of the system, the reliability is RavailableS = 85.66% (lower than the real configuration, characterized by two pumps). In a second step, analyzing the identified subsystems, we have allocated the reliability value to each unit thanks to IFM Method [15]. In particular, we have assigned to the system a reliability target (RtargetS = 95.5%), coincident with the real reliability value that in exactly equal to 95,57%. A FMEA Analysis was performed to collect the necessary information. The obtained results are summarized in Tab. 1. By comparing allocated values with available ones (serial configuration), a critical component has been identified: the feed pump, as showed in Tab 1.
Figure 4. Reliability Allocation In order to improve the system performance, we collected the necessary data about the items of interest for the R-R index evaluation. Subsequently, the AIFM procedure has been applied to the critical component. In Particular, evaluating the R-R Index of the pump, we obtained a value less than 1 (Table n. 2). Time (weeks )
Cost (€)
ΔR
Fl
Index
Redundac y
4.000
6
0,103
0,8
3,44E-06
Redesign
7.500
4
0,060
0,9
1,80E-06
Table 2. R-R Index
Therefore, according to AIFM Method, we had to introduce a redundancy in order to increase the availability of the system. Through the redundancy of the pump, it was possible to get a new value of reliability equal to about 98.6%, for the parallel of two identical components. The changed configuration of the system is shown in the figure n. 5.
[2] J.A.Boyd, Allocation of Reliability Requirements: a new approach, Proc. Annual Reliability and Maintainability Symposium, Las Vegas, USA, 1992. [3] F. De Felice, A. Petrillo, Methodological approach to reduce train accidents through a probabilistic assessment, International Journal of Engineering and Technology (IJET). Vol. 4 No 6 Dec 2012-Jan 2013, 500-509 [4] D.Falcone, A.Silvestri, G.Di Bona, Integrated Factors Method (IFM): a new reliability allocation technique, SEA 2002, IASTED, Cambridge USA.
Figure 5. Press changed configuration According to the methodology, at this point, it was necessary a Fault Tree Analysis of the new configuration of the system, verifying the reliability target achievement. By placing the fault tree analysis, we obtained a new reliability value of the press equal to R availableS = 95.68%. The result has been easily obtained, calculating the reliability (Rp) of two identical components positioned in parallel is: Rp = 2R – R2.
(4.1)
Was subsequently calculated the new system reliability, such as the product of the reliability of the components, which is known. The value is almost coincident with the predetermined target, so the AIFM application can end.
4. Conclusion The case study shows the validity of the procedure. R-R Index, together with the allocation method used, was able to identify the need for a redundant component, guiding the designer towards the real system configuration. Therefore it’s possible, starting from a series system, reaching a final configuration, whose complexity is driven by the required standards of reliability. Ultimately it is reasonable to assert that the proposed methodology has been able to achieve the objectives for which it was developed.
References [1] H. S. Balaban, H. R. Jeffers, The allocation of System Reliability - Vol. I: Development of Procedures for Reliability Allocation and Testing, Technical Documentary Report, Armed Services Technical Information Agency Alington Hall Station, Virginia USA.
[5] D.Kececioglu, Reliability Allocation Apportionment, Lecture Notes of Aerospace Engineering, University of Arizona, USA, 1987. [6] D. Falcone, G. Di Bona, V. Duraccio, A. Silvestri, A. Forcina Application and development of R.A.M.S analysis for maintenance plans in metallic scrap iron reworking Industry, Maintenance and Facility Management Journal December 2007, 50 -56. [7] D. Falcone, G. Di Bona, V. Duraccio, A. Forcina, A. Silvestri, Allocation of reliability requirements to a liquid nitrogen cooling system through a new technique: Critical Flow Method (C.F.M.), WCEAM 2009, Athens 2009. [8] F. De Felice, A. Petrillo. Methodological Approach for Performing Human Reliability and Error Analysis in Railway Transportation System., International Journal of Engineering and Technology Vol.3 (5), 2011, 341-353 [9] George P. Sutton, Oscar Biblarz Rocket Propulsion Element, (John Wiley & Sons Inc, 2010), www.eu.wiley.com. [10] Military Standard: Procedures for performing a failure mode, effect and critical analysis, Department of defence USA. [11] MIL-STD-721C, Reliability, Department of Defence USA. [12] NASA Report, Designing for Dormant Reliability, Johnson Space Center (JSC) Guideline n° GD-ED-2207. www.nasa.gov/news/reports [13] NASA Report, Improving Reliability and Writing Specifications, Lewis Research Center (LRC). www.nasa.gov/news/reports [14] Tian Z, Levitin G, Zuo MJ., A joint reliability redundancy optimization approach for multi-state series-
parallel systems, Reliability Engineering and System Safety 2009; 94:1568-1576 [15] Misra K.B., Reliability Analysis and Prediction, A Methodology Oriented Treatment, Elesevier 1992, ISBN 0-444-89606-6. [16] Thiokol Report, Solid Rocket Motor Briefing, Solid Propulsion Industry Action Group (S.P.I.A.G.), 1999. www.atk.com. [17] D. Falcone, F. De Felice, G. Di Bona, A. Silvestri, R.A.M.S. Analysis in a sintering plant by the employment of a new Reliability Allocation Method” Modelling and Simulation 2004 Marina del Rey, CA, USA 2004. [18] D.Falcone, A.Silvestri, G.Di Bona, V.Duraccio: Integrated Hazards Method: a new safety allocation technique. Modelling and Simulation, Montreal Canada, 2007. [19] D. Falcone, F. De Felice, G. Di Bona, V. Duraccio, A. Silvestri Risk assessment in a cogeneration system: Validation of a new safety allocation technique Applied Simulation an Modelling, Palma de Mallorca, Spain, 2007.
[20] F. De Felice, D. Falcone, A. Silvestri, G. Di Bona “Proposal of a new reliability allocation methodology: the Integrated Factors Method” International Journal of Operations and Quantitative Management, Volume 16, Number 1, March 2010 pp.67-85
