Failure occurrence probability

Ammunition fulfils its function only at a shot. The lasting of a shot is very short in order of several milhseconds. That is why we use a failure occurrence probability as an indicator for safety risks. The ammimition belongs to the gronp of one-shot weapon systems (Vintr Vahs 2007). 

The quantification of measures of failure occurrence probability Qi(t) - Qiv(t) includes only those failures that belong to the given failure category. 

With the assumption that failure occurrence probability and time to repair probability have exponential distribution and maintenance costs probabihty has normal distribution (Sirok Neugebauer, 2005), then equation (17) transforms to form ... 

The failure propagation in Eq. (1) is computed based on the knowledge of the probabilities of input error causing a failure / (El.) in component Cj. System reliability in Eq. (2) is also computed based on the knowledge of the failure occurrence probabilities of system components. Our model assumes the availability of these parameters. However, several data change probability models [1,14,29] and component reliability models [8,6,13] can be adopted to estimate these parameters for the individual components. 

The calculation of the RAPP characteristics is as follows The risk probability of the critical product fleet P can be estimated using the failure occurrence probability Ppi (Integral of f(x)pj (1) regarding to the critical area, step C) and the product fleet kilometrage probability Ppp (Integral of f(x)pp(2) regarding to the critical area, step C). 

The function f(x)p describes the failure occurrence probability of the product fleet in dependence on a life span variable (e.g. kilometrage). With this specific characteristic the failure occurrence probability can be determined (4) at any point of observation time with respect to an appropriate life span variable. Furthermore, the probabihty to find one unit at the point of observation can be easily calculated by finding the maximum of the failure occurrence function (5). 

Step 4 Assign failure occurrence probability/rate to each part/ component failure mode... 

We can demonstrate the notions of risk and risk assessment using Figure 1.18. For a given probability of failure occurrence and severity of consequence, it is possible to map the general relationship of risk and what this means in terms of the action required to eliminate the risk. 

If severity increases to, say, complete failure with probable severe injury and/or loss of life S = 9), the designer should reduce occurrence below the level afforded by two independent characteristics protecting against the fault. If each is designed to, then this implies a failure rate of ... 

Tlie oval symbol represents a probability or failure rate. A diamond is an event that is not developed because the preparer did not know what to do or thought it insignificant. A house-top is an expected occurrence (probability of one). Rectangles identify and explain gates. 

FMEA is a quantitative risk analysis for complex systems (Fig. 6). As this approach involves assessment of occurrence probabilities, detection of failures, and judgment as to the severity of a failure, it should only be chosen if some practical experience with the technical system is available. Each of the three values will be assigned a number from 1 to 5. Multiplying these values results in the risk priority number. This number indicates the priority of the assessed failure. The pure version of the FMEA is seldom practiced in the pharmaceutical industry. 

An equipment may have different failure modes involving different parts of the equipment. It can fail because of deterioration of mechanic parts (possible consequence is complete failure that requires equipment replacement) or electronic parts malfunction (partial failure that can be repaired). Different failure modes need different repair costs and repair times and induce different economic losses. The sampling of different failure modes of equipment is done as follows i) assign a probability of occurrence for each type of failure mode using information on how common a failure mode is, ii) at the simulated failure time of the equipment, the type of failure mode that actually occurred is sampled in accordance with the failure modes probability of occurrence. 

Failure Mode and Costs Analysis. Failure Mode and Cost Analysis (Figure 2) applied to the omission of an activity in the Integrated Management System enables the systematic consideration of the failure modes that may result from the described omission and the evaluation of the probability and cost effective of this failure form. The P Index (on a scale of 1 to 10), called rate of occurrence, is assigned to the probability occurrence of the failure form. The C Index (on a scale of 1 to 10), called cost index is assigned to the effective failure cost. The product of both indices is called cost priority number (CPN). Value of CPN identifies the significant failure forms. The cost of a failure form will be the product of the failure mode probability and the effective failure cost. 

Random fadures occur as a result of physical causes typically traceable to the usage of the system. The metrics used to estimate the random failure occurrence and to decide their acceptability is usually based on service experience (e.g., failure rates), predictive probabilities calculations (e.g., piece part FMEA, MTBF evaluation, etc.) and accelerated life testing run by manufacturers ahead of service experience. 

NOTE Following the standard it is assumed that for electronic items the calculation based on an exponential probability model of failure occurrence might be used. 

Failures of category II must also be extremely improbable, but the probability of failure occurrence is in one order lower than in the category III. That is why Qn must be lower than 10 during the whole period of ammunition use or in the period of its retirement (disposal). 

Failures of category I having the most serious consequences for persons, assets and environment must be extremely improbable. The probability of failure occurrence Qi must be lower than 1.10 in all climatic (weather), mechanical and electrical environments, in all defined regimes of use (storing, transport, manipulation and shooting) as well as in the defined way of disposal (liquidation). This definition of the requirement for safety risk tolerates ammunition failure resulting in user s death not more than once in 100 milliard of shots. 

Failures of category IV are without an impact on the safety, and so they can be probable on the level that is acceptable for the user. From the point of view of safety, ie probability of failure occurrence Qjv can be higher than 10 during the whole period of ammunition use retirement (disposal). See Fig. 4. 

The mission model is created in three steps. The vehicle operation model is designed in the first step. The input variables are the probability of failure occurrence and the probability of failure repair with utilization of maintenance resources. The maintenance model is... 

Failure occurrences for different demands are statistically independent, i.e. the failure probability of one demand does not affect the failure probabilities of other demands. 

Pyj = the occurrence probability of those failures that will result in accidents unless possible corrective actions are taken in a timely manner. 

S = severity of failure an assessment of the seriousness of the effect O = the likelihood of the occurrence of a failure D = probability of detection of any failure... 

FMEA consists of imagining possible failures that could occur in a process and identifying various reasons for these failures. By attaching a probability to these reasons, one could arrive at the probability of the occurrence of the failure. A failure mode is defined as a manner in which a component or process could potentially fail to meet the design intent. A failure mode in one system could be the cause for a failure in another system. Once the possible cause for the failure has been listed, it may be addressed. A risk priority number (RPN) is estimated for each of the failures the RPN is a product of the severity of the failure, the probability of its occurrence, and the probability of its detection. This RPN is used to prioritize the risks, and suitable action is taken, beginning with the most serious risk. 

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. 

The probability of the system failure occurrence by time t will then be... 

The result of numerical evaluation is shown in Figure 4.19. Particular weak points appear in columns 1-3. They especially include failure of cut-off armatures, in which case escape of the operation medium into the open air is possible. For columns 5 and 6, occurrence probabilities of the undesired event are lower by several orders of magnitude. This relation is not shifted in the event that the input data are not very accurate. The influence of failure rate uncertainty on components in column 1 is shown in Figure 4.20, while the failure rate of components 18, 22, and 25 has been multiplied once by 0.1 and once by 10. Quantitative evaluation in this case clearly confirms the result of qualitative analysis. 

II 3 For each failure mode identify the root cause and consequences in the system, customer, product production process, software (as applicable), personnel safety, environment, regulation, and services. Effect is determined in terms of severity (S) and occurrence probability (O) for each cause Here, effect is determined by severity rating in terms of (say) 1—10. For occurrence probability a 1—10 scale may be used... 

II 4 There will some existing process controls to prevent/reduce some of the failures. To see how it affects the occurrence probability and how it detects the cause of or the failure mode. The detection rate (D) is determined Here also a scale of 1—10 is used... 

The probability of component-failure occurrence is largely determined by means of deterministic stress analyses which supply detailed information of the damage mechanisms of a specific component and their significance for the component s overall failure behavior. Thus the findings obtained in stress analysis and the results of fault-tree analysis allow knowledge-based determination of the optimum method to safeguard the function of a component. 

In woody environment, the more than six consecutive GNSS position errors greater than 50 m with occurrence probability of 7.59E is the critical event which leads to the global service failure. 

In tunnel environment, the occurrence probability of this factor is reduced and is non significant while the missing GNSS data for more than 60 s with its occurrence probability of 1.53E is the main cause of the service failure. 

---