Quantitative safety analysis

Quantitative safety analysis utilises what is known and assumed about the failure characteristics of each individual component to build a mathematical model that is associated with some or all of the following information  

Similar to the qualitative analysis, the occurrence probability of each system failure event and the magnitude of possible consequences are to be obtained. However, these parameters are to be quantified. 

Within the overall aim it is the task of quantitative safety analysis to ascertain the frequency or occurrence probability of undesired events leading to incidents. Safety analysis will, in the case of problematic results of qualitative analysis, necessarily inspire the question of whether it should be continued in quantitative form. The question arises in particular when new technical equipment and processes are used. Quantitative safety analysis starts with knowledge of the logic structure of the system to be examined, as has already been ascertained in the course of qualitative analysis. A condition for execution is the presence of sufficient data—information about the behavior of the individual system components and parts. The information must be arranged in such a way that reliability characteristics (failure probabilities, failure rates) and maintenance characteristics (rates of repairs) can be derived. It is only when it is certain that sufficient data are available that quantitative analysis is possible. 

Procurement and Evaluation of the Data Base. Determination of reliability characteristics of components and structural parts requires extensive data acquisition and evaluation. Data acquisition can be done in the course of operation or through the systematic investigation of components and structural parts in the laboratory with simulation of operational stress. In the latter case, however, it is necessary to observe conditions necessary for the applicability of test results to actual in-plant behavior. In this connection, test frequencies should be mentioned by way of an example, since in the laboratory test they often have to be higher than actual frequencies during operation. It depends on the individual case whether such circumstances are significant or not. To estimate the failure rate of a component or structural part, it is necessary to examine a large number no of identical test pieces which are still operational at time / = 0. After time t, N t) test pieces should have failed and n t) test pieces should be intact. Accordingly, 

In the event that there are, in the time interval Af, AM failures, the failure rate A(r), according to Section 4.2.1, results by approximation from 

The failure probability F t) dependent on operating time results directly from the data as 

It is frequently impossible to determine time dependence because of inadequate data and limited available observation periods. In (he case of some components, e.g., electronic parts, failure rate time dependence does not exist for practical purposes. Hierefore, in such cases, constant failure rates A(t) = A = const are often used. 

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There are several important questions in drug safety evaluation How to detect unexpected adverse drug reactions while handling the multiplicity issue properly How to s)mthesize data from different trials, or even different sources How to deal with rare events How to evaluate multidimensional, complex safety information as a whole Can we monitor a potential safety issue in a continuous manner during a trial so that patients can be better protected These questions lead to some unique statistical challenges in quantitative safety analysis including low power due to rare events, multiplicity. 

Due to uncertain data, it is frequently not justified to view data obtained from quantitative analysis on the expected frequency or (he occurrence probability of undesired effects in systems as certain absolute quantities. In this case as well, relative comparison of different event progressions or technical constructions frequently provides valuable information. This also holds true when quantitative safety analysis is not applied to entire systems but only to specific safety equipment for the purpose of comparing various implementation alternatives,... 

In a representation of the logic structure in a compressed decision table, this corresponds to a consideration of individual columns. This also shows when which columns determine the critical state concerning the event sequence dependent on time. This is shown by way of an example in Figure 4.18. Subsequently quantitative safety analysis is applied to the leaching solution settling tack system. 

M. Rousand, Preliminary Hazard Analysis, NTNU/Willey, October 2005. AuthorAnonymous, J.F. Shortle, Applying Qualitative Hazard Analysis to Support Quantitative Safety Analysis for Proposed Reduced Wake Separation ConOps, George Mason University, Fairfax, VA M. Allocco, FAA, Washington, DC. 

Figure 9. Quantitative safety analysis of the filling process for filler store sizes in the range 0-10.

A second topic of inductive and deductive safety analysis, we also differentiate between qualitative and quantitative safety analysis. The quantitative safety analysis should also consider the frequency of failures, but for both the fault modes and effecting errors need to be analyzed. Generally, the norm says of course that the quantitative safety analysis is used to fulfill the quantitative metrics from part 5, Chaps. 8 and 9. 

A quantitative safety analysis is highly recommended (which, in fact, can be interpreted as mandatory ) form ASIL C, but recommended also for ASIL B. This means, it depends on the special case, and perhaps the safety regulations of the car OEM, whether or not probabilistic analysis is required. When probabilistic failures cannot be neglected (high failure rates in some parts, e.g. FPGAs or memory devices), as a compromise, at least a dedicated argument should be provided, e.g. that some Error Detecting Code (EDC) is applied and sufficient to cover the major parts of n-bit errors to be expected. 

FMEA is applicable to any system or equipment, at any desired level of design detail— subsystem, assembly, unit, or component. FMEA is generally performed at the assembly or unit level, because failure rates are more readily available for the individual embedded components. The FMEA can provide a quantitative reliability prediction for the assembly or unit that can be used in a quantitative safety analysis (e.g., FT). FMEA tends to be more hardware and process oriented but can be used for software analysis when evaluating the failure of software functions. 

Depending on the requirement of the safety analysts and the safety data available, either a qualitative or a quantitative safety analysis can be carried out to study the risks of a system in terms of the occurrence probability of each hazard and possible consequences. As described in Chapter 3, qualitative safety analysis is used to locate possible hazards and to identify proper precautions (design changes, administrative policies, maintenance strategies, operational procedures, etc.) that will reduce the frequencies or/and consequences of such hazards. 

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