Causal path

From hindsight analyses of accidents by Heinrich (Heinrich, 1959), Turner (Turner, 1978), Leplat (Leplat, 1987), Reason (Reason, 1997), etc., it is known that failures or deviations in normal operations are present prior to, and are directly related with, an accident. From hindsight analysis as reported in FACTS, the failures or deviations as well as the accident trajectory or causal path, of 70 accidents are known. To derive the risk coverage area these deviations, are placed in the risk matrix. The only deviations taken into account are those which occur in the operational process and are part of the accident trajectory or causal path prior to the critical events as described in FACTS. So the latent conditions lying behind these operational deviations as described by Reason (Reason, 1997) are not yet taken into account but will be discussed in the following Chapter. 

Using these definitions of deviations, hard and soft deviations were found in the causal path prior to the critical events of the 70 accidents. In total 158 deviations were derived from the operational process. These deviations consist of 48% hard and 52% soft deviations. 

Similar remarks can be made about accident reports, it was observed that the focus of the majority is on the direct safety related deviations in the accident causation path, and almost no attention is given to the indirect safety related deviations. Indirect safety related deviations were mentioned but no attention was given to the fact that these deviations were in the causal path, re-occurring, and often present for a long time prior to the accident. Korvers (Korvers et al., 2002) gave some good examples by showing ten cases in which identical indirect safety related deviations present prior to accidents repeatedly caused similar accidents. 

From this analysis a hypothesis posed as follows can be derived Frequently reoccurring deviations, present in the operational process of an organization, can be identified in the causal path of an accident. Subsequently, a prediction can be made, that the hypothesis will be valid in many cases. The final test of this hypothesis, confirming or disputing it, will be done in Chapter 6, where several accidents will be analysed on re-occurring deviations present in the accident trajectory. 

The similarity is assumed to be caused by the latent genetic factor shown in the circle (G). The causal paths are labeled with path coefficients. Again the rules of path analysis tell us that the correlation is made up of the sum of the multiplication of the terms of each path that connect the trait. Thus the equation ... 

Instructions Review each classification statement to determine if it is TRUE or FALSE for the incident investigation finding in question. Any statement that is answered with FALSE presents a causal path and an associated management system improvement opportunity. 

Undoubtedly, there is growing evidence for an association between disturbed sleep and impaired adolescent functioning however, more attention needs to be directed toward identifying possible causal paths and possible strategies for intervention. Furthermore, clinicians need to become more aware of the potential role of sleep disorders when evaluating children with neurobehavioral deficits. 

Also, it is a unique feature of human beliefs that they may be self-fulfilling by a causal path that involves the emotions they generate. Below, I discuss each of these categories of beliefs and the emotions they may generate. 

The lack of a clear image in quantum molecular dynamics has been a handicap for most researchers. This is in comparison to classical molecular dynamics which is strongly linked to the notion of a trajectory, a causal path leading from reactants to products. Imaging the flow of a trajectory constitutes one of the main sources of insight on classical molecular dynamics. 

The backward chaining may also stop because the causal path disappears due to lack of information. Rasmussen suggests that a practical explanation for why actions by operators actively involved in the dynamic flow of events are so often identified as the cause of an accident is the difficulty in continuing the backtracking through a human [166]. 

First, it is assumed that all storage elements are in integral causality for all system modes. That is, no residual sinks are switched on at discrete events to keep some storage elements in integral causality that otherwise would be become dependent and would get derivative causality accordingly. Causal paths between resistive ports are allowed. As the switch model contains a resistor in conductance causality, there may also be causal paths between a resistor and a switch or between switches. If a switch in one of these causal paths is in OFF mode, the switch and the causal path can be disregarded. Causal paths between resistors mean that their outputs are determined by a set of algebraic relations. Let a denote the vector of the outputs of resistors and of switches, then the DAE of a switched LTI system is of the form... 

In [42], van Dijk has shown that the determinant of det(E ) = det(I — A22), is non-zero for bond graphs with causal paths between resistive ports. That means that the inverse of E exists and that differentiation of the algebraic equation (2.18) is sufficient to transform the DAE system (2.17) into a set ODEs. Accordingly, (2.17) is a DAE system of index 1. 

The bond graph in Fig. 2.18 contains three causal paths between resistors and switches. 

The two switches commutate conversely. There are two system modes, in which one switch is on while the other one is off. A third feasible mode, in which both switches are off is not considered. If one of the switches is on, conductance causality of its ON resistance can be changed. The result is a causal path between the two non-ideal switches. In Fig. 2.21, it has been assumed that Sw m2 is on. 

However, as one of two switches is off, i. e. the current through that switch vanishes, the causal path can be disregarded. That is, in system modes Wi = 1 a m2 = 0 and mi = 0 A m2 = 1, there are no causal paths between resistive ports and no dependent storage elements giving rise to an algebraic constraint between state variables. Hence, the dynamic behaviour in these modes is described by a set of two ODEs. In the context of DAEs, the special case of ODEs without any additional algebraic constraints is termed a DAE system of index 0. 

If there are storage elements with derivative causality in all system modes then causal paths may exist to other storage elements of the same type in integral causality. 

As an example, consider the bond graph of a clutch in Fig. 2.15. There are no causal paths between resistors and no dependent storage elements. Clearly, as long as the clutch is disengaged, the DAE system is of index 0. In the case when the clutch is engaged, the unknown constraint force M between the two plates keeps their inertia elements in integral causality and at the same time ensures that the algebraic constraint... 

Let the inductor current ii = fe be the first state variable xi and the current across the capacitor uc = e the second state variable X2- As there is a direct causal path from the capacitor C C to the inductor I L... 

Furthermore, there is a direct causal path from the C-element to the detector De y but no direct causal path from the I-element to the sensed output variable y = uc-... 

If integral causality is applied to the energy storage elements as the preferred causality then every storage element in integral causality must have at least one causal path to either an effort sensor De or to a flow sensor (Df). This reachability requirement is a necessary condition. 

Its application to the example circuit in Fig. 2.17 confirms that the circuit with the one voltage sensor is completely observable for all system modes. In the bond graph with preferred integral causality (BGI) (Fig. 2.18), there is a direct causal path from the C-element to the detector and a causal path from the I-element through the C-element to the detector so that condition 1 is satisfied. 

In bond graphs of hybrid system models, some storage elements in integral causality may be connected to a detector only via a causal path through a switch model Sw m or even through several switch models. Clearly, the necessary reachability condition is only satisfied when the switch involved in the causal path is closed. That is, a model is not fully state-observable in those system modes in which a switch being part of the only causal path from a storage element to a detector is off, i.e. m = 0 for the switched MTF of that switch model. 

For illustration, the example of the buck converter is considered once again. As can be seen from the bond in preferred integral causality in Fig. 2.20, there is a causal path from the effort source to the C-element. However, the I-element is in derivative causality. It can be brought into integral causality by inverting the causality at one of the two switches. If the causality at switch Sw m2 is inverted (cf. Fig. 3.2) then there is a direct causal path from the effort source to the I-element that passes through both switches. 

The C-element, however, is not reachable by a direct causal path starting from the effort source. Hence,... 

The necessary reachability condition requires that for every storage element in integral causality, there must be at least one causal path from a controlled source. 

Inspection of the bond graph in Fig. 2.18 shows that there is a direct causal path from the effort source to the I-element and a causal path from the effort source through the I-element to the capacitor. That is, both storage elements are reachable from the effort source independently of the switch states. The sufficient condition is also satisfied. Both storage elements take derivative causality in the bond graph with preferred derivative causality in Fig. 3.1. Hence, the model of the circuit in Fig. 2.17 with two independent switches is structurally completely state controllable with the one effort source for all four system modes. 

Derivation of ARRs from a diagnostic bond graph then starts by summing power variables at all those junctions that have a BG sensor element in inverted causality attached to it. At first, these balances of power variables will contain unknown variables. They may be eliminated by following causal paths and by using constitutive equations of bond graph elements. The result may be a set of ARRs in closed symbolic form [cf. (4.2)] if nonlinear constitutive element equations permit necessary... 

Furthermore, there is a causal path between resistor R R2 and the ON resistor of the switch Ron, which means that there is an algebraic loop for the current /sw As both resistors are linear, this algebraic loop can be solved symbolically. 

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