The components are then ranked in a descending order, the component with the largest value of IB is considered as the most important. Note that the original Birnbaum importance measure is
defined by partial differentiation of the systems reliability with respect to component reliability. Equivalent formulation given in (2) was obtained by applying pivotal decomposition (Høyland and Rausand, 2009).
3.1.2. Risk achievement worth (RAW) and risk reduction worth
(RRW)
The RAW and RRW importance measures can be observed as measures derivate from Birnbaum importance measure. Let h(p(t)) represent the real system reliability. Then, using previously intro- duced notation, RAW and RRW can be defined as follows (Aven and Nokland, 2010):
Unloaded at the place of treatment, it is weighed and then steril- ized, so it loses its pathogenic features. Based on description of infectious waste management and analysis of the entire system, the fault tree has been created (Figs. 1e5). The undesired event e infection spreading has been defined within the system, and it will be further looked into, regarding the causes through intermediate and basic events. Fifteen intermediate and eleven basic events are the result of decomposition of the top event where some of them frequently repeat.
At the first level of decomposition, infectious medical waste management process was divided into four sub-processes: diag- nostic and treatment, transport (both internal and external) and waste treatment (Fig. 1). This decomposition is based on physical apartness of the facilities in which they are conducted, employees who participate in their execution and the activities they contain. Infection spreading can be caused by infection at any of these four stages of infectious medical waste management. Each sub-process was further decomposed into unwanted causal events in a sepa-
IRAW ðijtÞ ¼
hð 0i ; p ðt ÞÞ
1 hðpðtÞÞ
(3)
rate sub-tree. The diagnostic and therapy infection can occur if an employee (nurse or physician) is without protective equipment and injured during health services to an infected patient (Fig. 2). While
the injury at work and insufficient training can be characterised as
IRRW ðijtÞ ¼
1 hð p ðt ÞÞ
1 hð1i ; pðtÞÞ
(4)
skill-based error, intentional failure to respect the procedure and inattention at work are a so called violation (Wiegmann and Shappell, 2003; Shappell et al., 2013). The internal transportation is transport from the diagnostic and treatment places to the in-
3.1.3. FusselleVesely importance measure
FusselleVesely importance relies on minimal cut sets, and as- sumes that components have an influence on system failure only
when some of the minimal cut sets, to which their failure event
^j
belongs, occur. Let Q i ðtÞ denote the probability that j-th minimal
cut set which contains the component i occurs at a time t and Q(t)
denotes the real probability of the system failure. FusselleVesely importance measure is:
ternal medical waste warehouse (Fig. 3). The employees involved in this sub-process are nurses who pack infectious medical waste (Prcic-Kljajic, 2011). The infection at this stage can be caused by inadequate transport conditions and injury at work which causes contact with infectious waste disposal packaging. Basic events in this sub-tree can be skill-based errors (injury at work and inap- propriate training), violations (not using protective equipment) or use of inadequate containers for the waste disposal. The external transport is transport from the warehouse to the place of treatment
mi
1 Y
^j !
1 Q i ðtÞ
m ^j
in the Clinical centre (Fig. 4). Employees from the warehouse load
waste packaging into the vehicles for medical waste transportation.
IFV ðijtÞz
j¼ 1
Q ðtÞ
j¼1 Q ðtÞ
Q ðtÞ
(5)
The infection can appear if the waste spills or leaks during the loading and the employees without protective equipment get in
contact with the infectious medical waste. The same situation can
Note that the components can be rank only based on numerator
in (5) since Q(t) is constant.
4. Implementation of FTA and measures of importance in evaluation of infectious risk hazards in the Clinical Centre of Serbia
The Clinical Centre of Serbia, with its headquarters in Belgrade, the Republic of Serbia, presents a unique health institution. It was formed by merging clinics and institutes of the Medical Faculty, University of Belgrade. The Clinical Centre of Serbia consists out of
41 organizational units, 23 clinics, nine centres, polyclinics, and nine services (The Clinical Centre of Serbia, 2015). Large amount of infectious waste are produced on a daily basis in the Clinical Centre of Serbia, and must undergo a special treatment due to its patho- genic features. This study deals with defining the causes and assessing the risk o