Service dependability of Italian high speed railway system: modeling and preliminary evaluations R. Calabria, L. Delia Ragione, G. Pulcini & M. Rap one Istituto Motori CNR, Via Marconi 8, 80125 Napoli, Italy Abstract In this paper a dependability model is proposed in order to predict the effect of failures on the service quality of a transit system. The model has been developed for analysing the Italian High Speed railway system and applied to the Turin-Milan line. Numerical evaluations of the service quality have been carried out to assess the effect of failures of the train power supply system and sensitivity analyses have been performed to indicate how service quality can be improved. 1 Introduction Since the conception phase of the life cycle of transit systems, reliability and quality analyses play an important role to define the structural and operative characteristics of the system and to set reliability and maintainability specifications which could assure that service quality goals will be met. Thus, mathematical methods have been developed in order to provide quantitative tools to designers and managers of transit systems for a) evaluating service quality measures of transit systems, b) detecting the critical (from a service quality viewpoint) subsystems, and c) suggesting changes both in reliability or maintainability specifications of subsystems and in structural characteristics of the whole system. To describe service quality of transit systems, the dependability has been recognized in the transportation reliability literature as an effective measure which represents the user's viewpoint (see Prascker [1], Heimann [2, 3]). Dependability models link up system dependability with reliability and maintainability characteristics of all subsystems which constitute transit system, incorporating operating characteristics and recovery policy
464 Railway Operations from failure of each particular transit system. In this paper, a dependability model is proposed, which has been developed in order to analyze the Italian High Speed railway system, which is actually in the development phase. This model has been developed taking into account that it has to be used in the pre-design phase when the definition level of reliability and maintainability characteristics does not allow detailed analyses of failure mode and recovery policy from failure to be performed. The proposed model assumes as a measure of system service dependability (SSD) the probability that any total delay a passenger experiences on his trip will be no greater than an acceptable quantity 8: SSD = Pr{delay < 6} This measure reflects the fact that a passenger is willing to accept a delay only if it is of short duration and happens with low frequency over the long-term use of the transit system. An analytical approach is used to evaluate SSD, assuming that a) the passenger cannot experience more than one elementary delay in his trip, and b) all elementary delays are independent random variables. The dependability model has been applied to the Turin-Milan line (120 km length) and the effect of the failures of some technological subsystems on SSD has been evaluated. In particular, all the subsystems which constitute the train power supply system in the selected line have been considered: a) the overhead contact line, b) three electric traction substations which feed the overhead contact line, and c) three high-voltage transmission networks (one for each electric power substation). Numerical evaluations of SSD are based on the preliminary analyses and evaluations (given in Capasso et al. [6]) of the reliability and maintainability characteristics of the above subsystems. Sensitivity analyses have been also carried out to evaluate the influence both of reliability characteristics of some subsystems and of design alternatives on SSD. 2 Dependability modeling Many approaches exist in the development of a dependability model which evaluate SSD starting from a) the identification of all possible failure modes of subsystems which constitute the transit system, b) the probability that each failure mode occurs, and c) the distribution function of elementary delay caused by each failure. Such approaches can be classified into analytical and numerical ones. Analytical approaches are based on the following hypotheses: a) the passenger cannot experience more than one elementary delay in his trip, and b) all elementary delays are independent variables. Models which use
Railway Operations 465 such an approach are very attractive because, as a result of their semplicity, they require short run time and can run on most personal computers. However, thay can be used with a good approximation only if the probability of occurrence of more than one failure in a single trip is negligible. The numerical approach, on the contrary, does not assume any restrictive hypothesis on the number of delays and/or on the stochastic independence among the elementary delays (see Rapone et al [4] and Calabria et al. [5]). Such an approach requires longer run times and produces more accurate results, with respect to the analytical one, only if input data are very accurate. In developing the dependability model which analyses a line of the Italian High Speed system, the analytical approach has been chosen due to both the large reliability values of the analysed subsystems and the very short travel distance and time. This choice is strengthened by the fact that in the conception phase of a transit system the specification level of reliability and maintainability characteristics does not allow failure modes and recovery policy from failure to be defined in details. Notice that if the hypothesis on the number of elementary delays is not satisfied, then the analytical approach tends to overestimate the SSD. In the analitical models, the SSD is expressed as: N SSD = Pr{delay < 6} = [] Pr{d, < 6} 2=1 (I) where di is the elementary delay caused by the i-th failure mode, and N is the total number of failure modes which can delay the train. By using the Bayes theorem on the conditional probabilities, the probability that each elementary delay is no greater than the acceptable quantity 8 is given by: PrR <«} =!- Pr{f,} PrR > #} (2) where f; denote the i-th failure mode event. If the i-th failure mode produces different delay distributions (as a function, for example, of the position of the failed subsystem with respect to the train, or of different recovery policies) different failure dynamics are defined. Thus (2) is rewritten: (3) where mi denote the number of failure dynamics of i-th failure mode and dij is the elementary delay caused by the j-th failure dynamic. (Notice that the m^ events f*j must be mutually exclusive.) The above situation occurs frequently when the distribution of delay times changes if: a) the
466 Railway Operations Table 1. Input data for dependability evaluations HTN's ETS's CL MTBF#I = 1.945 h MTBF -- = 3457^3 h MTBF = 182150 h MTBF#2 = 1.786.# h RT = 5 min di 0.80 MTBF#3 = 1.923.# h T#l = 0.154 h 0.04 RT=t> min 0.167 h #3 0.16 T #1 = 0.154 h 0.115 h MT7^R = 3 h T#2 = 0.167 T#3 = 0.115 h h ~R = 0. 930933 T = 0. 436 h failure of a subsystem occurs when the train is using that subsystem, or b) the failure occurs before the train uses that subsystem. In subsections 2.1-2.3, for each subsystem the explicit expression of Pr{di < 8} is given. Note that, in evaluating the failure probability Pr{f^}, times between two successive failures are assumed to be independent and identically distributed, according to an exponential distribution. Under this hypothesis, the mean time between failures (MTBF) is equal to the inverse of the (constant) failure rate. 2.1 High- Volt age Transmission Network On the basis of the engineering analyses given in Capasso et al [6] and under the assumption that the success probability of the restoring and rearrangement (R&R) action is equal to 1, the probability (2) that the delay caused by the failure of each high-voltage transmission network (HTN) is no greater than the acceptable quantity 6 is given by: where R(T) is the reliability of each HTN at the 'use' time T. In case of failure, the HTN is restored through R&R action which is in the average 5 minutes long (see Table 1). Thus, the availability A of each HTN is evaluated by using such an R&R time, say RT, as mean time to repair: (4) A= MTBF -h RT (5) ^ ' Since the failure of HTN produces a delay approximately equal to.rt, then Pr{d,HTN > f/rzw} is set equal to 1 for any 6 < 5 minutes. 2.2 Electric Traction Substation When an electric traction substation (ETS) fails, an R&R action is tried. If this action fails, then the section of overhead contact line fed by the failed ETS is fed, through appropriate switching operations, by the contiguous ETS. The success probability of such a switching is practically
Railway Operations 467 equal to the probability that the ETS contiguous to that failed is functioning. Such a probability is given by: where M DT is the mean down time of the ETS. Such M DT is given by: (6) (1 - ^R) (7) where RT is the R&R time, R is the success probability of the R&R action of the ETS (see Capasso et al. [6]), and MTTR is the mean time to repair. In the conservative hypothesis of series structure, MTTR is evaluated as the weighted average of the mean times to repair of the components of ETS, where the weights are the failure rates of each component. By using data in Capasso et al. [6](see also Table 1), we have: M7T# = 168h MD7=16.3h (8) from which the success probability of feeding through the contiguous ETS is equal to 0.9995. Such a value seems to be sufficiently high to disregard the case where a failed ETS finds the contiguous ETS unavailable. Since, from preliminary analyses, the success probability of the R&R action of ETS cannot be set equal to 1, two different failure dynamics have been recognized for each ETS: 1. ETS fails and the R&R action successes, 2. ETS fails and the R&R action fails. A different delay distribution is associated to each failure dynamic. Thus, (3) can be written: 6} = 1 - [(1 -,4 a(t)) ' ^ ' Pr{d^,i > ^1 Ws,i} 4- (9) where T denotes the 'use' time of ETS (equal to the 'use' time of the segment of overhead contact line fed by that ETS), and A denotes the probability that the segment of overhead contact line is fed when the train is going to use it. For evaluating A, the mean time of no feed (MTN F) is used as down time. MTN F is given by: M7WF = #7 7? + TF (1 - ^R) (10) where TF = 10 min is the time needed to feed the overhead contact line through the ETS contiguous to that failed. Thus, by using data in Table 1, MT7VF=5.35 min. The conditional distributions of delay times, given the occurrence of the above failure dynamics, can be derived by noting that, if the R&R action successes (failure dymanic #1), the delay is equal to RT = 5 minutes, whereas, if that action fails (failure dynamic # 2), the delay is greater than 10 minutes.
468 Railway Operations Table 2. Conditional distribution of delays, given CL failure 5 CROSIS-O\ 'ER POINTS CL.,1 CLl,2 CL2,2 CL3,2 tj} 1.000 0.606 1.000 1.000 Pr{dij>2 f, tf) 1.000 0.600 0.925 0.921 Pr{dij > 5 f, y} 0.454 0.369 0.925 0.921 ij} 0.039 Pr{^>15 f(;} 0.013 0.209 0.185 0.925 0.925 0.921 0.921 4 C-O CL.,1 1,.000 1,.000 0,.605 0.166 0.026 POINTS CL1,2 0.606 0.600 0.435 0.245 0.208 2.3 Overhead Contact Line Three different failure modes of the overhead contact line (CL) have been defined: 1. failure independent from train passing (CL1), 2. failure caused by short-circuit on board (CL2), 3. failure caused by breakage of locomotive pantograph (CL3). For each failure mode, two dynamics have been detected: 1. the failure occurs before the train uses CL, 2. the failure occurs when the train is using CL. Thus, for example, in case of failure mode CL1, the probability (3) is: < 6} = 1 - [(1-4 The mean time between failures relative to each failure mode is to be computed in order to evaluate the reliability and availability of CL. For example: MTBFi = MTBF/gi, where MTBF is the total mean time between failures relative to all failure modes of CL, and g± is the occurence frequency of failure mode # 1. Hence, by using data in Table 1: MTBFi = 15319h MTBF^ = 306375 h MT Fs = 76594 h (12) The availability A has been evaluated by setting the mean time to repair equal to 3 h. The delay distributions relative to all the failure modes and dynamics have been derived, via Monte Carlo simulation, in Capasso et al. [6] and are summarized in Table 2. Notice that the failure dynamic #1 produces the same delay distribution, independently from the failure mode. 3 Dependability Evaluation The proposed dependability model has been applied to the Turin- Milan line and the effect of the failures of the train power supply system has
Railway Operations 469 Table 3. SSD evaluation for different 8 values Acceptable delay 6 (minutes) 0 0,,999710 2 0.999711 5 0.999870 10 0.999977 15 0.999985 been evaluated. In particular, seven subsystems have been considered: 1) CL, 2) ETS #1, 3) HTN #1, 4) ETS #2, 5) HTN #2, 6) ETS #3, 7) HTN #3, for a total of 7V=9 failure modes. The choice of considering different failure modes for CL, only, is motivated both by engineering considerations on the failure mechanism of the above subsystems, and by the fact that the failure probability of CL is quite greater than that of the other subsystems. By using data provided by Capasso et al [6] and summarized in Tables 1 and 2, SSD has been evaluated for different values of the acceptable delay 8 (see Table 3). These SSD values, which take into account the effect of failures of the train power supply system only, seem to show that the design choices on that system allow high dependability values to be achieved. Of course, the larger potentiality of such dependability models is in performing sensitivity analyses. In fact, such analyses allow to indicate how the SSD can be improved and how much this improvement is. Hence, alternative options can be compared in a trade off analysis, and the consequent operational and/or design modifications can be done. In Figure 1, results of sensitivity analyses versus mean time between failures of ETS's and of CL are shown. It appears that reliability improvements of ETS's do not produce sensible increments in SSD, and that the failures of CL produce large effect on SSD. This fact strengthens the choice of defining three different failure modes of CL. CD < Q Q 111 O g 0.9999-0.9998 - OVERHEAD CONTACT LINE ELECTRIC TRACTION SUBSTATIONS 8=2min ELECTRIC TRACTION SUBSTATIONS 2 4 6 8 ACTUAL / NOMINAL MTBF Figure 1. Sensitivity analyses of SSD versus reliability changes
470 Railway Operations Table 4. Sensitivity analyses of SSD versus design options 6 (min) 0 2 5 10 15 5 CROSS-OVER POINTS 0.999710 0.999711 0.999870 0.999977 0.999985 4 CROSS-OVER POINTS 0.999710 0.999711 0. 999832 0,,999944 0. 999981 In Table 4, results of sensitivity analyses versus different design options are given. In particular, the reduction of the number of cross-over points (by eliminating the point at 50 km) is analysed. Such a reduction causes variations in some conditional distribution of delay times (see Table 2). The above results show that SSD is not sensibly degraded by the elimination of that cross-over point, thus suggesting the opportuneness of such an option. Acknowledgment This research is funded by Finalized Project on Transportation Research of National Research Council (CNR) of Italy. References 1. Prashker, J.N. Direct analysis of the perceived importance of attributes of reliability of travel modes in urban travel, Transportation, 1979, 8, 329-346. 2. Heimann, D.I. Availability: concepts and definitions, pp. 486-490, Proc. of Annual Reliability & Maintainability Symposium, Las Vegas, USA, 1976. 3. Heimann, D.I. The determination of transit system dependability, pp. 314-322, Proc. of Annual Reliability & Maintainability Symposium, Washington, USA, 1979. 4. Rapone, M., Calabria, R. & Pulcini, G. A multi-failure additive dependability model for transit system effectiveness analysis, Quality and Reliability Engineering International, 1989, 5, 47-52. 5. Calabria, R., Delia Ragione, L., Pulcini, G. & Rapone, M. Service dependability of transit systems: a case study, pp. 366-371, Proc. of Annual Reliability & Maintainability Symposium, Atlanta, USA, 1993. 6. Capasso, A., Ciaccio, N., Lamedica, R. & Prudenzi, A. Service dependability of Italian high speed railway system: influence of fixed installation design. Submitted to COMPRAIL 94-