다이그래프를 이용한 KOSHA-yFTA 개발

Theories and Applications of Chem. Eng., 2002, Vol. 8, No. 1

김지용, 이근원*, 문 일↕

연세대학교 화학공학과, 한국산업안전공단 산업안전보건연구원*

Development of KOSHA-yFTA using Digraph

Jiyong Kim, Keunwon Lee*, and Il Moon↕

화학공학의 이론과 응용 제8권 제1호 2002년

Department of Chemical Engineering, Yonsei University

Korea Occupational Safety & Health Research Institute

INTRODUCTION

FTA is based on constructing a hypothetical tree of base events branching into numerous other sub-events, propagating the fault and eventually leading to the top event. The goal of FTA is to evaluate the probability of the occurrence of the top event and show the events that cause the top event to occur and merits of FTA are; 1) The results of FTA is objective due to its statistical analysis, 2) FTA can achieve both quantitative and qualitative safety analysis result of target processes. But manual FTA depends on experts and requires a lot of manpower, cost and time. In addition to this, the result of manual FTA is often unreliable. To resolve these problems, the FTA needs to be automated. The automated FTA can be used as many times as users want and it can analyze a process effectively and conveniently. Lots of researchers therefore, are interested in the automatic FTA. Examples are Fussell's transfer function (1973), Salem's Decision table (1977), Lapp and Powers's Digraph (1977), Camarda's Reliability graph (1978), Kelly and Lee's Mini fault tree (1986) and Abbasi's PROPAT II(2000). But most of the studies about the FTA automation are concentrated on not the whole procedure of FTA including automatic construction of FT, but only a part of analyzing FT. The aim of this paper is to develop an automatic FTA system including the digraph-FT conversion algorithm. The new FTA system of this study is able to transform a Digraph to a FT and analyzes FT automatically.

DIGRAPH METHODOLOGY

In order to synthesize a fault tree automatically, the development of an accurate representation for the system is required at first. This representation must be general so that any type of chemical processes can be analyzed and suited for their computation. A digraph is therefore, used to meet both of the above needs in this study. The digraph is a set of nodes connected by directed edges. The nodes of digraphs used in fault tree synthesis represent process variables (temperatures, pressures, flow rates, etc.) and certain types of failures (equipment failures, human errors, etc.). If a deviation in one variable causes a deviation in a second variable, then a directed edge is drawn from the node representing the first variable to the node representing the second. A number is assigned to the edge as the direction (positive and negative) and the magnitude (1 and 10). Loop identification and classification in the system digraph are very important to build digraph-based fault tree. Loops are classified four types: feedforward loops (FFL-two or more paths from one node to another in a digraph), feedback loops (FBL-a path through the nodes in a digraph that starts and terminates at the same node), positive loops and negative loops.

Further, faults and failures are classified into three types based on the digraph representations and the patterns of their propagation in the system as follows: Type A(f) (It is noted that, if both x1 and x2 are on the same PFBL(Positive Feedforward Loop), the values of x2 can be affected not only by f but also by x1 and, in case of NFBL(Negative Feedforward Loop), then x2 is always affected by f alone.), Type B(f) (The edge between x1 and x2 can be considered as nonexistent.) and Type C(f) (The occurrence of a failure of this type change the direction of the effects of an additional fault propagating from x1 to x2.). Type A(f) means that the failure has an effect by not only a normal process variables but the facts composing the process. Type B(f) means vanishing of the failure in the facts composing the process. Type C(f) means finally that the failure of the facts causing the converse relationship between processes. It increases the efficiency of the automatic FT construction algorithm to make a failure classification simply.

The FT generation rule to transform the information of a digraph to a FT consists of four structures depending on the situation of nodes formation as following: (StructureⅠ); when the node is in PFFL,PFBL, or when the node is in NFFL and is not a terminal node, or when the node is not in loop. (Structure Ⅱ); when node is a terminal node of NFFL. (Structure Ⅲ) when the node is in NFBL. Finally (Structure Ⅳ) ; when the node is a terminal node of NFFL and it is in NFBL.

AUTOMATIC FTA SYSTEM (KOSHA-yFTA)

The digraph-FT conversion algorithm is developed with the recursive method using the FT generation rules. On digraph, the algorithm investigates the top event that is chosen at the beginning. According to that process, algorithm can also apply each FT generation rule to compose an FT. We use repeating techniques to compose a FT, which depends on the situation of the node. After these are done, the algorithm recognizes the digraphs next node related to the top event as a new target node on the algorithm, and it applies the FT generation rule following the situation of nodes. If the node considered is a basic event, the composition of an FT is over.

The next step of the FT automation requires the quantitative analysis. This study uses Fussell algorithm that searches minimal cut sets. For the qualitative analysis this study computes the probability of occurrence of the top event with the unavailability for each basic event. The probability data is q(Unavailability), which is presented as the combination of □(The Failure Rate) and □(The mean time to repair).

With the generated FT, users can search the minimal cut sets, the ranking of basic event frequency and the gate list. Especially minimal cut sets in FT analysis is the most accurate way to find a basic event that has the most powerful effect on failure of the top event.

This automatic FT conversion algorithm includes the following procedures; 1) user input node data representing process variables and failure data to build the system digraph according to P&ID, 2) names of these node data and failure data are defined by a user, 3) top event is selected, 4) loops in the system digraph are identified and classified, 5) fault and failure types are classified, 6) probability data are calculated, 7) the system digraph is conversed to a fault tree automatically, and 8) the minimal cut sets or the ranking of basic event frequency is represented as users demand.

CASE STUDY

A reactor shown in Figure 1 is monitored by two temperature elements (TE) and two pressure transmitters (PT). High system pressure or temperature indicates a possible exothermic reaction in progress. The processor provides a shutdown signal if it receives a high signal from either the TEs or PTs. The reaction pressure and temperature are continuously monitored. The processor is tested once every shift (8hrs). If the processor (combination of output card and CPU) is found failed, the reactor is shut down while the processor is repaired.

Figure 1. System diagram for the example process

Figure 2 is the digraph for the example process. To construct the FT for this digraph, the required data are node data (variable on the process diagram), failure data (equipment failure, Human error etc.), probability data (□, □) and description data.

Figure 2. The digraph corresponding to the example process

A huge explosion is possible if the shut down signal is not sent to the reactor because of high pressure and temperature. If the top event is selected as the shut down signal, an FT for this case is shown in Figure 3.

Figure 3. The FT for the example process

CONCLUSION

This study developed Automatic FTA System (KOSHA-yFTA) using the FT automatic construction algorithm and the automatic FT analysis algorithm. KOSHA-yFTA improves the defeat of manual FTA and can get minimal cut sets and the probability of the occurrence of the top event with less time and cost. This system could overcome the technical problems even with a little information like PFD or P&ID and accomplish FTA simply. This system could also get over objectivity problems of FTA results possibly happened due to users logical problem or subjective experience because it composes and analyzes FT with regular rules. Various case studies (Loss of capability to shut down, Flash tank, Loss of cooling water etc.) proved that the weakness of the manual FTA (much time, manpower and cost consuming) is overcomed. Many chemical processes can be more safe by KOSHA-yFTA.

REFERENCES

1. Lapp, S. A and Powers, G. J., "Computer-aided Synthesis of Fault Tree", IEEE Trans. Rel., 1977

2. Powrer Gary J., Tompkins. JR. F. C., "Fault Tree Synthesis for Chemical Processes", AIChE, Vol. 22, No. 2, pp376-387, 1974

3. Fussell J. B., Powers Gary. J., "Fault Trees- A State of the Art Discussion", IEEE Trans. Rel., Vol. 23, No. 1, 1972

4. Chang C. T., Hwang H. C., Hwang, D.S., Hsu., Comp. & Chem. Eng., Vol. 21, 1994

5. Khan Faisal I., Abbasi S. A., "Analytical simulation and PROPAT Ⅱ: a new methodology and a computer automated tool for fault tree analysis in chemical process industries. journal of hazardous Materials. A75 1-27, 2000