X-tree analysis

See Event Tree Analysis (ETA), Safety Barrier Diagram, and X-Tree Analysis for additional related information. 

Rgure 2.68 shows a bow-tie analysis model (also referred to as X-tree analysis) of barriers. This analysis technique is a combination of FTA and ETA. The analysis begins with identification of the IE of concern in the center. An FTA is performed to identify the causal factors and probability of this event. Then an ETA is performed on all the barriers associated with the IE, and the possibilities of each barrier function failing. The various different failure combinations provide the various outcomes possible, along with the probability of each outcome. 

To determine maximum individual risk, generic frequency data are required for explosion events for Process Units 1 and 2. For Process Unit 1, incident data were available from the unit licenser identifying three explosions in approximately 15,000 operating years, for an explosion frequency of 2.0 x 10-4 per year. For Process Unit 2, a fault tree analysis of the nitrogen vessel brittle fracture event had been conducted as part of an unrelated project. That study concluded that the frequency of brittle fracture failure of the nitrogen vapor storage vessel was 5x10"4 per year. 

Prior to installing a new shutdown system, however, a fault tree analysis was performed on the proposed modifications. From this study, it was concluded that the overall frequency of brittle fracture was lowered from 5x10"4 to 5 x 10-5 (occurrences/year). Using this new frequency in the calculation for aggregate risk would result in revised outcome frequencies and F-N data points, as shown below. 

Irinotecan (1) is a derivative of the pentacyclic quinoline alkaloid camptothecin (2) the latter was first isolated from the heartwood of the tree species Camptotheca acuminata (Nyssacea) by Wall et al. in 1966.1 Two years later A. T. McPhail and G. A. Sim determined the structure of 2 by X-ray analysis.2... 

Dugan, X, Sullivan, K., Coppit, D. (2000). Developing a low-cost high-quality software tool for dynamic fault-tree analysis. IEEE Trans, on Rel. 49-59( ), 49ff. 

In possibilistic (fuzzy) fault tree analysis, the basic event probabilities (chances) or failure rates, are considered to be fuzzy numbers with membership functions (possibility distributions) 7r,(X,). A possibihty distribution 7r, (X, ) can be interpreted in terms of prob-abdity by considering its a-cuts i.e., the intervals for which 7r,(X,) > a. The key relation is (Baudritetal. 1996)... 

Huang, H. Z., Tong, X. Zuo M. (2004) Posbist fault tree analysis of coherent systems. Reliability Engineering and System Safety 84 153-16. 

FTA, fault tree analysis LOPA, layer of protection analysis NR, not recommended PFDavgt probability of failure on demand SIL, safety integrity level X, acceptable. ... 

As a simple example of selecting an appropriate SIL, assume that the maximum tolerable frequency for an involuntary risk scenario (e.g., customer killed by explosion) is 10 pa (A) (see Table 2.1). Assume that 10 (B) of the hazardous events in question lead to fatality. Thus the maximum tolerable failure rate for the hazardous event will be C = A/B = 10 pa. Assume that a fault tree analysis predicts that the unprotected process is only likely to achieve a failure rate of 2 x 10 pa (D) (i.e., 1/5 years). The FAILURE ON DEMAND of the safety system would need to be E = C/D =10 column of Table 1.1, SIL 2 is applicable. 

Alfonsi, A., Rabiti, C., Mandelli, D., Cogliati, X, Kinoshita, R., Naviglio, A. 2013. Dynamic event tree analysis through Raven, In Proceedings of ANS PSA 2013 International Topical Meeting on Probabilistic Safety Assessment and Analysis. 

Huang. H. RebabUity Evaluation of a Hydraulic Truck Crane Using Field Data with Fuzziness. Microelectronics and Reliability 36, no. 10 (1996) 1531-1536. Huang, H., X. Yuan, and X Yao. Fuzzy Fault Tree Analysis of Railway Traffic Safety. Proceedings of the Conference on Tnyfic and Transportation Studies, 2000,107-112. Hudoklin, A., and V. Rozman. Human Errors Versus Stress. Reliability Engineering System Safety 37 (1992) 231-236. 

From a human reliability perspective, a number of interesting points arise from this example. A simple calculation shows that the frequency of a major release (3.2 x lO"" per year) is dominated by human errors. The major contribution to this frequency is the frequency of a spill during truck unloading (3 X10" per year). An examination of the fault tree for this event shows that this frequency is dominated by event B15 Insufficient volume in tank to imload truck, and B16 Failure of, or ignoring LIA-1. Of these events, B15 could be due to a prior human error, and B16 would be a combination of instrument failure and human error. (Note however, that we are not necessarily assigning the causes of the errors solely to the operator. The role of management influences on error will be discussed later.) Apart from the dominant sequence discussed above, human-caused failures are likely to occur throughout the fault tree. It is usually the case that human error dominates a risk assessment, if it is properly considered in the analysis. This is illustrated in Bellamy et al. (1986) with an example from the analysis of an offshore lifeboat system. 

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