A NEW NETWORKING METHOD FOR CONSTRUCTION EDUCATION

INTRODUCTION

Several procedures for applying network analysis to construction projects have been introduced in the past three decades. Kelley and Walker developed the Critical Path Method (CPM) in 1956 [7]. Fondahl introduced a precedence technique which simplifies CPM [1], and has since become a standard tool for modeling construction projects. The technique is used in education and in practice to assess project schedules deterministically. A non-deterministic approach for studying construction schedules is the Program Evaluation Review Technique (PERT) initiated by Clark et al. [10].

This paper describes a Modified Fault Tree Networking (MFTN) technique which has been developed and used as a training tool for modeling both deterministic and non-deterministic network activities. Fault tree qualitative and quantitative analyses were initially developed by Watson for the missile launch control system of the Minuteman [8]. Haasl extended the concept for use in safety analyses of nuclear power plants [2,3]. Hadipriono modified this concept in a detailed study of the qualitative fault tree procedures for use in structural systems [4] and in network analysis [5]. Tirtotjondro used regressed data for quantitative network analysis [11].

To facilitate the learning of these new methods by senior level construction students in Civil Engineering, a computer program has been written for and used in our course called "Construction Network Analysis." The program, which is written in BASIC for use on an IBM PC or XT, has the capability of performing both qualitative and quantitative analyses, and displays results graphically. The program is briefly discussed in this paper following sections which review the development of the MFTN technique.

MFTN DEVELOPMENT

A MFTN diagram is a logical and sequential graphical representation of construction activities, indicating the causality and interrelationship among the basic events that contribute to a predefined top event. An example of a top event is the delay of a project according to its late finish schedule (note that some construction activities have both early and late finish dates.). The diagram also shows why and how an activity is delayed. An MFTN encompasses the development of both non-critical and critical activities. A non-critical activity usually has a flexible deadline date called "slack time" (the difference between early start/finish and late start/finish dates). A critical activity, on the other hand, does not have a slack time; therefore, its start and finish dates can not be extended.

Unlike the conventional methods of network modeling, the development of MFTN involves a deductive procedure. The procedure begins with the delay of the last activity and proceeds deductively to the preceding activities. Suppose a construction project consists of eight activities, A through F, as listed in Table 1 which shows activity durations and preceding activities. Assume that the delay of the last activity F is chosen as the top event (this delay is called event F') as shown in Figure 1. Table 1 indicates that F' occurs if activity E or D is delayed (or if El OR D' occurs). Note that an OR gate is used in Figure 1 in order to relate F' to El and D'. Deductively, El is caused by C' OR B', while DI is caused by B'. Further deductive analysis of each event will eventually reach the occurrence of event A', or the delay of activity A.

Based on the diagram in Figure 1 and the information given in the first three columns In Table 1, we can compute the early start (ES), early finish (EF), late start (LS), and late finish (LF) dates. These dates are computed using the generally accepted procedures used in the precedence diagram calculations [6,9]. However, here we use the terms "bottom-up" and "top-down" computations Instead of the "forward" and "backward" passes to determine these dates. The approach used for the precedence diagram calculations can also be employed here to find the total-float (TF), free-float (FF), and Interference-float (IF). A TF is the time difference between LS and ES or between LF and EF of an activity. A TF is usually composed of a FF and an IF. A FF is the slack time of an activity whose completion will not cause the delay of any following activity. This float is obtained from the difference between the EF of an activity and the minimum ES of the following activities. An IF will result In the delay of any succeeding activity. Thus, an IF is the difference between TF and FF, and an activity begins to interfere with its follower when its FF is exhausted. Therefore, activities whose TF is zero (activities A, C, E, and F) are critical and those remaining (activities B and D) are non-critical. In Figure 1, the critical path is represented by double lines. Note that since the delay of a non-critical activity is conditioned upon the exhaustion of its FF, an INHIBIT gate (hexagon) with the conditional event FF is required.

EXPANDED MFTN

The limit to which one develops a tree usually depends on the needs of the project and the judgment of a student when modeling the activities. For example, If the need for detailed information concerning either resource constraints (e.g., problems with material, labor, and equipment) or environmental constraints (e.g., bad weather) can justifiably cause a project delay, one may investigate these basic events and further. expand and include them in the tree.

Consider the delay of activity F, or event F', in Figure 2 which can be caused by the following: (1) disturbance of the activity's ES causing the delay of its EF without the extention of the duration, (2) the delay of the activity's EF despite its successful ES due to the extention of its duration, and (3) the combination of both (1) and (2). Event F' can then be expanded through an OR gate to Fs' and Ff', representing the first and second types of delays (note that the OR gate takes care of the combination of Fs' and Ff'). The occurrence of event Fs' is caused by the occurrence of the activity's basic events, and by events E' and D'. The basic events Fs' and Fs' represent the uncertainties in the resources and environments, respectively. Similarly, by definition, the occurrence of event Ff' is caused only by the activity's own basic events.

Similar procedures can be applied to expand E' and D'. In case of D', which is a non-critical activity, INHIBIT gates are needed to satisfy the condition explained earlier. The conditional events associated with the first and second types of D' are Ds* and Df*, respectively. Figure 2 depicts the MFTN which is expanded to the basic events of each activity. Clearly, the expanded MFTN is more complex than the previous one in Figure 1. However, it shows the interrelationships among the basic events of the activities, and it has the capability of determining the importance of the basic events as well as accomodating the non-deterministic nature of the construction activities.

IMPORTANCE OF ACTIVITIES

The importance of activities that configure a project can be determined through the minimal cut sets (MCS) of the basic events. A MCS is a set of basic events in a fault tree that guarantees the occurrence of the top event. These MCS are used by the students to determine possible sets of events that may contribute to the occurrence of the top event. Furthermore, the MCS list will serve to warn the student of potential problems that can result in the delay of a project. Although each MCS contributes to the delay of a construction project, its rank of importance may be different. The ranking of these potential problems is of Importance when students plan measures to prevent the delay of a project. Three methods incorporated in this MFTN concept are used to determine this rank: (1) qualitative method associated with the criticality and sequence of the activities, (2) quantitative method associated with the uncertainties involved in the basic events, and (3) the combination of both (1) and (2).

The qualitative method is derived based on Boolean algebra discussed In earlier papers [4,5]. The MFTN is first translated into the algebra of events represented by Boolean expressions. The OR and AND (INHIBIT) gates in the MFTN are translated into "+" and ¹¹.¹¹ symbols. Through the use of this algebra, the MFTN leads to a more simplified tree by eliminating the redundancies when replication of basic events are encountered, and hence, producing the MCS [4,5]. A list of the MCS for the example discussed earlier is presented in Table 2. Note that all critical activities are ranked higher than the non-critical. This is reasonable, since a critical activity does not have the flexibility to extend its duration. Next, ranking Is based on the sequential order of the activities. For example, delay of activity F is considered more important than delay of A, since the former event constitute the project delay, while the latter can still be recovered if need be. For the same reason, the second type of delay (e.g., Ff') is considered as more important than the first type of delay (e.g., Fs'). It can be seen, however, that the MCS that belong to a certain group of MCS are equally ranked. For example, Ff' and Ff' are equally important. In order to refine this rank, a quantitative method is needed.

The quantitative method requires the acquisition of construction data. In practice, the required probability distributions may not be readily available, but information about each event can be obtained from the construction field and regression analysis can be performed to obtain the probabilities of occurrence of the events. Details of the procedure can be found in [11]. The quantitative ranking for the MCS based on the probability figures is shown in Table 3. Note that the MCS for the critical activities contains a single basic event, while that for non-critical contains a pair of basic events. Hence, the probability of the former MCS is equal to the probability of the individual basic event, while that of the latter is equal to the product of the probabilities of the basic events.

Since the criticality and sequential order of the activities play dominant roles in project completion, the qualitative ranking is more important than the quantitative method. However, the latter can be used to refine the former, particularly to determine the importance of MCS that have equal rank. For example, since the probability of Ff' is higher than that of Ff', the former is ranked higher than the latter. Table 4 shows the final rank of importance of the MCS based on both the qualitative and quantitative methods.

THE COMPUTER PROGRAM

The MFTN program, written in BASIC language for the IBM PC or XT (64K RAM, 2 disk drives), consists of 12 subprograms. The user-friendly software can be used by a student who has little knowledge of either computers or the fault tree concept. It offers many options through an interactive mode.

The MFTN program has the capability of displaying the list of activities and computing the activity dates and floats (see Table 1). It is also capable of displaying the deterministic fault trees (Figure 1) and expanded fault trees (Figure 2). Furthermore, it will compute and list the MCS based on a qualitative analysis (Table 2), a quantitative analysis (Table 3), and both (Table 4). The information input by a student in order to obtain the fault tree diagrams and the qualitative analysis includes the duration and predecessor(s) of each activity. For quantitative analysis, a student also needs to input the probability of occurrence of each event.

Due to display limitations, a maximum number of five activities may be used for each tree level (a total number of five predecessors is allowed for each activity). However, the program can accomodate over a 100 activities. The benefits of the program far outweigh this limitation, particularly from an educational point of view.

SUMMARY AND CONCLUSIONS

In this paper, the MFTN technique has been described. Also, a new computer program for teaching this technique to senior level civil engineering students has been discussed. The program permits students to perform both deterministic and non-deterministic studies of construction schedules (well established methods). In addition, it permits one to use both qualitative and quantitative fault tree studies (new methods).

The computer program has the capability to expand and simplify the models depending on one's needs. It has the flexibility to allow students to determine the limits of expansion of the tree in accordance with the details of the project analysis. Hence, depending on the needs, this method provides options for students to construct either a simple or an expanded tree. Also, one can conveniently perform a detailed observation of a delay of any activity by isolating related activities through a subtree construction.

ACKNOWLEDGMENT

Grateful appreciation is given to the Office of Learning and Resources at The Ohio State University which provided funding for this research. The writers wish to thank Nancy Grace, who edited this paper.

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