**3. Materials and methods**

#### **3.1 Functional resonance analysis method (FRAM)**

FRAM methodology aims to analyze how the variability of one or more functions can be combined between them and how to prevent their resonance, which could lead to unwanted results [25]. For this purpose, FRAM method studies the system first under normal conditions, after FRAM analyzes the variability that cause to the event unwanted. The aim is obviously to be able to issue recommendations that prevent the repetition of the event. FRAM consists of four steps: 1) Identify system functions; 2) Characterize the potential variability of the functions; 4) Determine the dependencies among functions and 4) Monitor the variability. Some more details about each step are provided below [26].

**Step#1 "Identification of the essential functions".** The present step aims to identify the functions or the specific action that are needed to carry out a specific task [27]. Each function is described using the six aspects (as shown in **Figure 4**): INPUT (I); OUTPUT (O); TIME (T); CONTROL (C); PRECONDITIONS (P) and RESOURCES (R). Functions can have links to each other. They can typically have multiple links and dependencies. From a practical point of view, to represent the variability it is possible to use the *FRAM Model Visualiser* (FMV). FMV allow to build a graphical representation of a FRAM model.

**Step#2 "Identification of variability".** The present step identifies the variability of functions in order to understand how functions can become coupled and how this can lead to unexpected outcomes [28]. The FRAM assume that there are characteristic differences in the variability of technological functions (T), of human functions (M), and of organizational functions (O).

**Step#3 "Aggregation of variability and define functional resonance".** This step aims to analyze the variability of functions and how they interacted with each other [29]. The variability of a function depends on couplings among functions. It is not enough to evaluate the variability for the single function. It is necessary to

**5**

**Table 1.**

**Figure 4.**

*FRAM hexagon: The six aspects used to characterize functions.*

*Example of aggregation of functions (output – input).*

Time Too early False start (V+)

Accuracy Inaccurate Waste of time (V+)

*The Analytic Functional Resonance Analysis to Improve Safety Management*

A sensitivity analysis is performed to evaluate different solutions.

understand how variability can be combined. This is achieved using the upstreamdownstream functional coupling. The variability of the function can be the result of couplings of upstream functions that influence downstream functions. Each upstream variable can be connected to its downstream variable using the 5 available inputs (showed in **Figure 4**). Depending on the type of connection, different vari-

**Step#4 "Monitor and manage the variability".** The step aims to propose ways to manage the possible occurrences of uncontrolled performance variability – or possible conditions of functional resonance – that have been found by the preceding steps [30]. The purpose is to find critical combinations and reinforce the barriers. The problems of complex systems cannot be eliminated, eliminating the variability of the performances, because this is essential to ensure the reliability of the systems.

The main feature of Analytic Hierarchy Process (AHP) is to break down a decision-making problem in a hierarchy [31]. AHP uses a mathematical approach

**Output variability of upstream function Possible effects on downstream function**

Acceptable No change (V=) Accurate Possible damping (V-)

In time Possible damping (V-) Too late Delayed activities (V+) Omission Start imprecision (V+)

Possible damping (V-)

*DOI: http://dx.doi.org/10.5772/intechopen.93998*

ability occurs (see **Table 1** as example).

**3.2 Analytic hierarchy model**

*The Analytic Functional Resonance Analysis to Improve Safety Management DOI: http://dx.doi.org/10.5772/intechopen.93998*

understand how variability can be combined. This is achieved using the upstreamdownstream functional coupling. The variability of the function can be the result of couplings of upstream functions that influence downstream functions. Each upstream variable can be connected to its downstream variable using the 5 available inputs (showed in **Figure 4**). Depending on the type of connection, different variability occurs (see **Table 1** as example).

**Step#4 "Monitor and manage the variability".** The step aims to propose ways to manage the possible occurrences of uncontrolled performance variability – or possible conditions of functional resonance – that have been found by the preceding steps [30]. The purpose is to find critical combinations and reinforce the barriers. The problems of complex systems cannot be eliminated, eliminating the variability of the performances, because this is essential to ensure the reliability of the systems. A sensitivity analysis is performed to evaluate different solutions.
