Loading...
Please wait, while we are loading the content...
Similar Documents
Reliability of complex system with one shot items
| Content Provider | Semantic Scholar |
|---|---|
| Author | David, Valis |
| Copyright Year | 2007 |
| Abstract | This article deals with modelling and analysis of the reliability of complex systems that use one-shot items during their operation. It includes an analysis of the impact of the reliability of used one-shot items on the resulting reliability of the system as a whole. Practical application of theoretical knowledge is demonstrated on an example of a model of reliability of an aircraft gun that was used for optimization of the gun’s design during its development and design. The analysed gun uses two types of one-shot items – rounds intended for conducting of fire and special pyrotechnic cartridges designed for re-charging a gun after a possible failure of the round. Vališ David Reliability of complex systems with one shot items 348 Mission: It is an ability to complete a regarded mission by an object in specified time, under given conditions and in a required quality. In our contribution it is a case of cannon ability to put into effect a fire in a required amount – in a number of shot ammunition at a target in required time, and under given operating and environmental conditions. As it follows from the definition of a mission it is a case of a set of various conditions which have to be fulfilled all at once in a way to satisfy us completely. Our object is supposed to be able to shoot a required amount of ammunition which has to hit the target with required accuracy (probability). We will not take into consideration circumstances relating to evaluation of shooting results, weapon aiming, internal and external ballistics, weather conditions and others. We will focus only on an ability of an object to shoot. [4] As we have stated above we will deal with isolated function blocks only. We are presuming that these blocks act according to required and determined boundary conditions. In order to understand functional links fully we introduce our way of dividing an object. We are talking about the following block: manipulation with ammunition, its charging, initiation, failure detection and indication during initiation, initiation of a backup system in order to recharge a failed cartridge, all mechanical parts, all electric and electronic parts, interface elements with a carrying device Block A; ammunition – Block B; pyrotechnic cartridges – Block C. 3. Description of a process The process as a whole can be described this way: From a mathematical and technical point of view it is a fulfilling of requirements ́ quee which gradually comes into the service place of a chamber. The requirements ́ quee is a countable rounds ́ chain where the rounds wait for their turn and are transported from the line where they wait in to a service place (fulfilment of a requirement) of a chamber and there they are initiated. After the initiation the requirement is fulfilled. An empty shell (one of the essential parts of a round) leaves a chamber taking a different way than a complete round. When the requirement is fulfilled, another system which is an integral part of a set detects process of fulfilling the requirement. The process is detected and indicated on the basis of interconnected reaction processes. In this case fulfilling the requirement is understood as a movement of a barrel breech going backwards. Both fulfilling the requirement and its detection are functionally connected with transport of another round waiting in a line to go into a chamber. Let’s presume that rounds are placed in an ammunition feed belt of an exactly defined length. A maximum number of rounds which could be placed in a belt is limited by the length then. The length is given either by construction limitations or by tactical and technical requirements for a weapon set. Let’s presume that despite different lengths of an ammunition belt, this will be always filled with rounds from the beginning to the end. Let’s also assume that the rounds are not nonstandard and are designed for the set. The process of fulfilling the requirement is monitored all the time by another system which is able to differentiate if it is fulfilled or not. The fulfilment itself means that a round is transported into a chamber, it is initiated, shot, and finally an empty shell leaves a chamber according to a required principle. If the process is completed in a required sequence, the system detects it as a right one. Because of unreliability of rounds the whole system is designed in the way to be able to detect situations in which the requirement is not fulfilled in a demanded sequence and that is why it is detected as faulty. Although a round is transported into a chamber and is initiated, it is not fired. A function which is essential for a round to leave a chamber is not provided either, and therefore another round waiting in line cannot be transported into a chamber. That is the reason why fulfilling of the requirement is not detected. The system is designed and constructed in such a way that it is able to detect an event like this and takes appropriate countermeasures. A redundant system which has been partly described above is initiated. After a round is initiated and the other steps don’t carry out (non-fire, non-movement of a barrel breech backwards, non-detection of fulfilling the requirement, non-leaving of a chamber by an empty shell, and nontransport of another round into a chamber) a system of pyrotechnic cartridges is initiated. It is functionally connected with all the system providing mission completion. A pyrotechnic cartridge is initiated and owing to this a failed round is supposed to leave a chamber. A failed functional link is established and another round waiting in line is transported into a chamber. In order to restore the main function we use a certain number of backup pyrotechnic cartridges. Our task is to find out a minimum number which is essential for completing the mission successfully. 4. Mathematical model To meet the needs of our requirements we are going to use a mathematical way which helps us to express successful completing the mission. We know that the number of rounds n in an ammunition belt is final. We also know that an event-failure of a round B SSARS 2007 Summer Safety and Reliability Seminars, July 22-29, 2007, Gdańsk-Sopot, Poland 349 (ammunition block – B) can occur with a probability pn. All the requirements and specifications mentioned above will be used in further steps. Because it is about a stream of rounds of a number n which wait in line to meet the requirement, and each of them has a potential quality pn, a number of failed rounds has a binomial distribution (Bi) of a an event occurrence. The distribution is specified by the parameters n and pn: Bi(n,pn). A number of occurrences Xn of an event B follows the distribution in Bernoulli’s row n of independent experiments, and probability of event occurrence P( B ) = pn. A number pn is the same in every experiment. [5]; [6] Because there is an occurrence of a number of events in an observed file we are talking about a counting distribution of an observed random variable. A random variable is in this case a number of failed rounds. A probability function of a binomial distribution can be put that way: x n n x n n p p x n x X P 1 ) ( ; x{0,1,2,...,n}. (1) Qualities of binomial distribution like a mean value E(Xn) and dispersion D(Xn) are obtained by calculating the formula: E(Xn) = n . pn , (2) D(Xn) = n . pn . (1pn). (3) A number of failed rounds follows a binomial distribution with parameters n – a number of rounds and pn – failure occurrence probability of a round. In order to specify a mean number of possible failures in an ammunition belt of a given length (there is a certain amount of rounds) we quantify the formula (2) and replace n by a real number of rounds in an ammunition belt. On the basis of construction, technical and technical requirements we can have ammunition belts of different length at a given moment, and consequently we have a different number of rounds. Only a maximum number of rounds in an ammunition belt is considered in another calculation. The ammunition belt is supposed to be of a maximum length which is able to fit a loading device In case a round fails initiation of a backup system for function restoration occurs according to a mechanism described above. It is a case of successive initiation of pyrotechnic cartridges (in a system of pyrotechnic cartridges) which are supposed to guarantee restoring of a required broken chain of function. A number of pyrotechnic cartridges in a backup system is m. Pyrotechnic cartridges have also a probability pm of a failure occurrence which unable their initiation. Pyrotechnic cartridges too are placed in line waiting for meeting the requirement which results from their function. In case of a failure of the first pyrotechnic cartridge the next one is initiated up to the moment when either a function is restored or all pyrotechnic cartridges are used up. On the basis of the facts mentioned above it is obvious that the process of fulfilling the requirements follows geometrical distribution (Ge). It means that the process of fulfilling the requirements repeats so often until it meets them in terms of reversion of all the process to an operational state. It is a case of an observed discreet random variable. Pyrotechnic cartridges also have failure rate pm (failure probability) and there is a limited number of them. It means that a failure can occur up to m-times. A geometrical distribution Ge(pm) generally follows this outline. We are going to assess the succession of independent attempts, and probability of an observed event occurrence equals the same number pm in each attempt. The quantity Xm is a serial number of the first success which means that a required event occurs. The event here means a function of a block C, and a probability pm means an event occurrence C . Characteristics of the process are as follow. A probability function: P(Xm=x) = pm x-1 (1-pm); x{1,2,3,...,m}. (4) It is a special case of a g |
| File Format | PDF HTM / HTML |
| Volume Number | 2 |
| Alternate Webpage(s) | http://ssars.am.gdynia.pl/upload/SSARS2007PDF/VOL2/VALIS.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
