Lecture No. 3

Topic # 1. EMC reliability indicators

Indicators of reliability characterize those of the most powerful systems, such as lack of awareness, tenacity, efficiency, repairability, saving, goodwillі. Assessment of indicators of the reliability of folding technical systems on the other stages of the life cycle vikorize for the vibration of the structure of the system from a set alternative options, the recognition of the guarantee terms of operation, the choice of the strategy and tactics of technical service, the analysis of the inheritance of the system elements.

Analytical methods for assessing the indicators of the reliability of folding technical control systems and the improved solution are based on the provisions of the theory of immobility. I will look at the imovirnin nature of the assessment of the indicators of the fields in the victorian methods of mathematical statistics. At the same time, a statistical analysis is carried out, as a rule, in the minds of a lack of significance, according to the laws of the system, as well as for the vibrations of the interconnected communication, and also to take into account the data on the moments of the display of the system and of the device.

Ymovirnist bezwidmovy robots(VBR) - the value of the fact that for the singing minds of exploitation at a given interval of time, it will not become very useful. Ymovirnist P(t) - function, spade div. fig. 1 moreover,

VBR for statistical data about vidmov and evaluate viraz

(1)

de - statistical assessment of the VBR; - the number of virobes on the cob of viprobivan, for a great number of virobes, a statistical estimate is practically practicable to get out of it P(t) ; –Number of virobes, which were generated per hour t.

Figure 1. Curves of immobility of w / o robots and immobility of drives

Ymovіrnіstіvіdmovi Q ( t ) - the value of that, for the singing minds of exploitation at a given interval of hour, one would like to see it. Vidmova and bezvidmovna robot

(2)

Vidmov frequency a ( t ) - є Vidnoshennya virobiv, wіdmovili, in one hour before the cob number of virobіv, wіll try out.

(3)

de - the number of virobs, which was seen, in the interval hour D t.

The frequency of the messages, or the density of the messages

The sign (-) characterizes the speed of the decrease in reliability for the hour.

Average napratsyuvannya to vidmovi - Average value of the triviality of the robot of an unrepaired annex to the first update:

de - the triviality of robots (forcing) to widmovi i I will add it; - The number of outbuildings.

butt. Keeping an eye on the operation of 10 electric motors viyavili, which first proputized in 800 years, the other - 1200 and as long as possible; 900, 1400, 700, 950, 750, 1300, 850 and 1500. Visitors to the direction of speeding up the engine before the rapid change,

Decision... For (5) maєmo

Intensity of images l ( t ) - cleverness of the number of virobes, when the number of virobos was read, in one hour before the middle number of virob, is good enough to start with the results of an hour.

, (6)

de - The number of outbuildings that were introduced in the period of the hour; - The number of an average number of outbuildings, which is correct to start in the period of caution; - Period of caution.

The power of a wormless robot P (t) through hanging

. (8)

stock 1. It takes about 10 hours of exploitation of 100 transformers with a length of 10 rockets in a new transformer. The visibility of the intensity of the transformer output at the period of caution.

Decision. For (6) maєmo vidk. / Рік.

Butt2... Change in the number of BJI views via viral activity third-party organizations for months of rock are represented by the following rank:

Visually, there is a mid-thousandth vidma intensity.

Decision. ; відк. / міс.

Ochikuvana rozrakhunkova intensity l = 7.0.

Average napratsyuvannya on vidmova - the mean value of the attachment, which is being repaired, between the widgets, is the mean value of the arithmetic:

, (9)

de - napratsyuvannya to the first, the other, n th vidmovi; n- number of views from the ear of operation until the end of the warning. Directed to vidmova, for the middle hour of no-vidmovy robots, є mathematical clarification:

. (10)

butt. The transformer was brought into being, and it was close to fate. Writing about the reasons for seeing them, they prophesied more than three rock and know the winners for joy. Viznachiti middle napratsyuvannya transformer on vidmovu.

Decision... For (1.7) it is computable rock.

The parameter for the vidmov stream is The average number of views to the outbuilding, to be repaired at one hour, is taken for the analyzed time of the hour:

(11)

de - number of messages i I will camp at the analyzed moment of the hour - and t for certain; N- The number of outbuildings; - Looking at the period of the robot, moreover.

Renewal of the average number of views of the object, which must be renewed, for a rather small amount of improvement to the value of

butt... The electrotechnical attachment is stored from three elements. Stretching out the first rock of exploitation, the first element saw two views, the other - one, the third did not. Bring the parameter to the stream of views.

Decision

Stars (1.8)

Average resource value support for the operation data or viprobuvan with victories in the same home viraz for pricing:

.

Average hour of update - Average hour caused by abnormally regulated downtime, viciously caused by the same messages:

de - serial number of vidmovi; - The middle hour of the appearance of that usunennya of the vidmovi.

Coefficient of readiness - the fact that it will be possessed by the most vibrational moment for an hour at the time of the planned technical service. Under the exponential law, the hour of no-wipe robots is increased, and the hour of renewal of readiness performance

.

Coefficient due to downtime - the price of an hour due to downtime until the sum of an hour of the right robot and in the event of downtime.

Coefficient technical victorian - the price of delivery of possession in one hour for a certain period of exploitation until the sum of time of all downtime, due to technical service that repairs for the same period of operation:

.

Besides [GOST 27.002-83] visnacha indicators of good fortune, in terms of such slides, they mean the form diy pislya setting of the boundary mill of the object (for example, the average resource up to overhaul; gamma-ray resource until the average repair is too small). As far as the border camp is zoomed in, the residual knowledge of the operation, the indicators of the service life are called: a new average resource (term of service), an additional gamma-ray resource (term of a service), an additional value of a resource (term of a service).

Average resource- Mathematical ochіkuvannya resource.

Gamma-ray resource- napratsyuvannya, stretching out what kind of object is not up to the border camp іf the given ymovіrnіstyu g, whirled around the sides.

Resource values- the sumarne napratsyuvannya ob'єkta, with the achievement of what kind of stasis for the signs, maє buti is pinned.

Middle term of service- Mathematical clarification of the term of service.

Gamma-specific term of service- The calendar triviality is due to the ear of the operation of the object, stretching which is not up to the boundary line due to the given dimension g, which is rotated at the sides.

The meanings of the terms of service- the calendar triviality of the exploitation of the object, when it is reached, it is assigned for the signs.

Indicators of repairability and safety will begin with an offensive rank.

Ymovіrnіstnіnіstіnіvіvnі czatelnogo country- The reason is that the hour of renewal of the original camp will not change the given.

Average hour of renewal of the country of origin yaniya - tse mathematical clarification of the hour of renewal of the original camp.

Middle term zberigannya- Tse mathematical clarification of the term of preservation.

Gamma-high definition term zberigannya- Tse terms of saving, how to reach the object from the given ymovirnistyu, twisted around the sides.

1.1 Ability of a silent robot

Imovirnistu of a bezvidmovy robot is called the imovirnist of that, which for the singing minds of exploitation, at the boundaries of a given direction will not become a vidmovy.
The immobility of a silent robot is known as a yak P(l) , Yaka start with formula (1.1):

de N 0 - The number of elements per ear of viprobuvannya;r(l) - The number of views of elements until the moment of delivery.Slid means, which is a larger valueN 0 Tim with greater accuracy you can use itP(l).
On the cob of exploitation of the reference locomotive P(0) = 1, so when trying l= 0 If the element cannot be processed, the maximum value is 1. l ymovіrnіst P(l) will change. The process of approaching the term of exploitation to an indefinitely great value has the value of the error-free robot and is less than zero P(l→∞) = 0. Thus, in the process of directing, the value of the energyless robots varies between 1 and 0. 1.1.

Figure 2.1. The graph of the change of the iMovirnosti of the Wi-Fi robot P (l) fallow from napratsyuvannya

The main passages of the victorious indicator at rozrahunka are two officials: in a persistent way, all officials are eager to see the power of the uninvolved robots; more valueP(l), tim vischa nad_ain_st; on the other hand, the power of no-wipe robots can be found in vikoristan in terms of the reliability of folding systems, which can be stored from more than one element.

1.2 Image efficiency

Imovіrnіstyu vіdmov and name the imovіrnіst of that, which for the singing minds of exploitation, in the boundaries of a given direction, one would like to see one.
Immovability of vision and recognition of yak Q(l), which starts with formula (1.2):

On the cob of exploitation of the reference locomotiveQ(0) = 0, so when tryingl= 0 If you want to edit one element, the minimum value is 0.liMovieQ(l) will be zbіlshuvatisya. In the process of approaching the term of exploitation to an indefinitely great valueQ(l→∞ ) = 1. Thus, in the process of directing, the value of the change in readiness and change between 0 and 1. 1.2. The immobility of the uninvolved robots and the immobility of the imagination and the way they are opposed and insane.

Figure 2.2. Graph of change of information Q (l) fallow from napratsyuvannya

1.3 Vidma frequency

The frequency of messages is the price of the number of elements in one hour, or the breakdown of the number of elements reported to the cob. That is, the frequency of images is an indicator, which characterizes the speed of change in the speed of vision and the speed of error-free robots in the growth of triviality of robots.
The frequency of sorts is meant as and by means of the formula (1.3):

de - a number of elements, which were considered for the progress of the run.
The Danish indicator allows you to judge by its value about the number of elements, which can be used for any hour or even run, and the number of necessary spare parts can also be used for the value.
The nature of the change in the frequency of messages in the function of probig is shown in Fig. 1.3.

Small. 1.3. Graph of changes in frequency

1.4 Intensity of images

Intensity of views є I will clear up the recognition of a vision and an object, which is meant for the moment to the hour, or directed for the mind, but until the moment the view is not won. Intensity of views - the price of the number of items, which were seen, in one hour, or I will go to the reference items in Denmark at one hour.
The intensity of the messages is recognized as and is based on the formula (1.4):

de

As a rule, the intensity of images is a constant function of the hour. The intensity of the minds is inviting to get stuck on the basis of the assessment of the mental health before the minds at the beginning of the robotics.
In fig. 1.4. representations the theoretical nature of the change in the intensity of the messages in the function of the test.

Small. 1.4. Graph of changes in intensity

On the graph of the change in the intensity of images, shown in Fig. 1.4. You can see three main steps, which show the process of the ex-operation of an element or an object as a whole.
The first step, which is also called the increment step, is characterized by an increase in the intensity of images in the cob period of exploitation. The reason for the increase in the intensity of changes in the general stage is the adherence to the defect of the viral character.
Another stage, during the period of normal robots, is characterized by a decrease in the intensity of vidms to a permanent value. Throughout the period, you can see the difference between the various elements.
The third stage, so the ranks of the period of the forced old. Characterized by errors of information. Submission of the operation of the element without replacing it with an economically rational one.

1.5 Mid-level adjustment to visualization

Average run - the middle run of the w / o robot element vscnt.
The middle way is to be called a yak L 1 and start with formula (1.5):

de l i- napratsyuvannya to vidmovi element; r i- Number of views.
Medium napratsyuvannya can be found in the city for prior designation of terms of repair or replacement of an element.

1.6 Average value of the parameter to the stream of images

The average value of the parameter to the stream of views characterizes the average value of the image flow, which is indicated for the moment of the hour, when you look at it.
The mean value of the parameter to the stream of images is referred to as W Wed and start with the formula (1.6):

1.7 Butt rocking indicators of lack of performance

Pochatkovі danі.
Stretching the run from 0 to 600 yew. km., at the locomotive depot there is a collection of information and information about TED. In a whole number of reference TEDs, the ear of the period of exploitation became N0 = 180 approx. The total number of TEDs, which was considered for the analysis of the period, was ∑r (600000) = 60. The interval for the sample was equal to 100 yew. km. At the same number of TEDs, which were taken, according to the skin diagrams: 2, 12, 16, 10, 14, 6.

Required.
It is necessary to develop indicators of the lack of damage and to persuade them to fall asleep in the hour.

A collection of it is necessary to memorize the table of the reports of the collection shown in table. 1.1.

Table 1.1.

Vykhіdni danі to rozrakhunku

, yew. km	0 - 100	100 - 200	200 - 300	300 - 400	400 - 500	500 - 600
	2	12	16	10	14	6
	2	14	30	40	54	60

With a handful of equivalents (1.1), it is important for the skin to test the value of the immobility of the uninterrupted robot. So, for dilyanka from 0 to 100 and from 100 to 200 yew. km. I will test the stability of the w / o robots in the warehouse:

Zrobimo razrahunok frequency of views for rivnyannyam (1.3).

Today the intensity of the sizes of the boxes is 0-100 thousand km. dor_vnyuvatime:

Similarly, the value of the intensity is significant for an interval of 100-200 yew. km.

Behind the level (1.5 and 1.6), the mean value of the parameter to the message flow is significant.

Systematization of the results and the presentation of the results is given in the view of the tables (Table 1.2.).

Table 1.2.

The results of the growth of indicators of lack of performance

, yew. km.	0 - 100	100 - 200	200 - 300	300 - 400	400 - 500	500 - 600
	2	12	16	10	14	6
	2	14	30	40	54	60
P (l)	0,989	0,922	0,833	0,778	0,7	0,667
Q (l)	0,011	0,078	0,167	0,222	0,3	0,333
10 -7, 1 / km	1,111	6,667	8,889	5,556	7,778	3,333
10 -7, 1 / km	1,117	6,977	10,127	6,897	10,526	4,878

Evidently, the nature of the change in the immobility of the TED robot is fallow in the run (Fig. 1.5). Slide means, with the first dot on the graph, tobto. when running, the road is 0, the value of the iMoviness of the w / o robot is the maximum value - 1.

Small. 1.5. Graph of the change in the size of the error-free robots in the fallow area from the point of view

Evidently, the nature of the change in immobility and PEP is fallow in the sample (Fig. 1.6). Slide means, with the first dot on the graph, tobto. when running, which is 0, the value of iimovarnosti vidmo and if the minimum value is 0.

Small. 1.6. Graph of changes in growth rates and changes in fallowness in terms of growth

Probably, the nature of the change in the frequency of the TED is fallen in the sample (Fig. 1.7).

Small. 1.7. Graph of changes in frequency

In fig. 1.8. the abundance of changes in the intensity of views is presented.

Small. 1.8. Graph of changes in intensity

2.1 The exponential law of the distribution of values

The exponential law is to achieve exactly the value of the higher educational institutions in case of rapt vidmovs, which may seem to be of a vague nature. Try to fix it for some of the types and types of ideas, especially for actions, due to wear and tear and change of physical and chemical powers, elements showed their lack of acceptability.

Pochatkovі danі.
As a result of viprobvannya ten pumping pumps in a high vise, the correctness is reduced to the following: 400, 440, 500, 600, 670, 700, 800, 1200, 1600, 1800. It is allowed to start ordering before the pumping pumps are installed.

Required.
Evaluate the value of the intensity of the messages, and build the power of the wireless robot for the first 500 years. and you can see it at the end of an hour from 800 to 900 years. diesel robots.

In a word, the value of the average performance of the fire pumps is more significant than the average:

Let's take away the value of the intensity of the vidm:

Size of imovirnosti novidmovnoy robotic pumping pumps at a 500 year warehouse:

Immovability of vision and progress between 800 and 900 years. robotic pumps in stock:

2.2 Weibull-Gnidenko rose law

The law of Weibull-Gnedenko rozpodilu, having expanded a wide range of systems, which can be stacked in a number of elements, which have been stored after the last time with the help of securing the system's lack of control. For example, systems for servicing a diesel generator installation: milling, cooling, living with a fire, just too much.

Pochatkovі danі.
An hour of downtime for diesel locomotives for unscheduled repairs due to pre-house ownership is subject to the Weibull-Gnєdenka law of growth with parameters b = 2 and a = 46.

Required.
It is necessary to determine the availability of diesel locomotives for unscheduled repairs after 24 years. downtime for that hour downtime, with a stretch of quality, it will be renewed with a value of 0.95.

It is known that the locomotive can be renewed due to the idle time in the depot by reaching for equal amounts:

For the hour of renewal of the locomotive's pre-serviceability from the given value of the pre-set value of the locomotive as well as the victorious viraz:

2.3 Rozpodil Rayleigh's Law

Rayleigh's law is based on the basic analysis of robotic elements, so that it can easily rotate the old effect (elements of electric control, of a kind of deflation, washers, gaskets, synthetic rubber materials)

Pochatkovі danі.
At the same time, when the contactors are directed according to the parameters of the old isolation of the coils, it is possible to describe the Rayleigh function with the parameter S = 260 thousand km.

Required.
For the size of the napratsyuvannya 120 yew. km. it is necessary to determine the efficiency of the wireless robot, the intensity of the messages and the average direction to the first drive and the coil of the electromagnet contactor.

3.1 Basically data collection

The system, which is stored from decal independent elements, tied functionally by such a rank, which is seen by any of them wiklikov to the system, appears to be a rosary structural scheme of robots and without video messages sent by robotic

Pochatkovі danі.
Unreserved storage system for 5 items. Intensity of each type according to the route 0.00007; 0.00005; 0.00004; 0.00006; 0.00004 year-1

Required.
It is necessary to take into account the indicators of the system's reliability: the intensity of the messages, the average hour of the increase, the efficiency of the uninterrupted robots, the frequency of the messages. Indicators of reliability P (l) and a (l) are trimmed in the interval from 0 to 1000 years with a crock of 100 years.

Numerous is the intensity of the population and the average level to the level of the following:

The value of the idleness of the non-video robot and the frequency of the vidmov can be recognized, the vikoristovuyu ryvnyannya, pointed to the view:

Result P (l)і a (l) on the interval from 0 to 1000 years, the robots can be represented in the table. 3.1.

Table 3.1.

The result is the development of the system's drive-by-frequency capability at intervals from 0 to 1000 years.

l, year	P (l)	a (l), year -1
0	1	0,00026
100	0,974355	0,000253
200	0,949329	0,000247
300	0,924964	0,00024
400	0,901225	0,000234
500	0,878095	0,000228
600	0,855559	0,000222
700	0,833601	0,000217
800	0,812207	0,000211
900	0,791362	0,000206
1000	0,771052	0,0002

Graphic illustration P (l)і a (l) on dilyantsi until the middle napratsyuvannya is shown in Fig. 3.1, 3.2.

Small. 3.1. Possibility of an uninterrupted robotic system.

Small. 3.2. System display frequency.

3.2 Reserve items

Pochatkovі danі.
In fig. 3.3 and 3.4 shows two structural diagrams of the storage of elements: zagalny (Fig. 3.3) and single-element reservation (Fig. 3.4). Immobility of no-motion robots of elements according to different directions P1 (l) = P '1 (l) = 0.95; P2 (l) = P'2 (l) = 0.9; P3 (l) = P '3 (l) = 0.85.

Small. 3.3. Scheme of the system from the home reserves.

Small. 3.4. Scheme of the system from elementary reservations.

Impossibility of a wireless robot to a block of three elements without a redundancy rozraєmo behind a viraz:

The immobility of the system without the worm-free robotics in the case of back-up reserving (fig. 3.3):

Immobility of the skinless robotics from three blocks with unit-by-element reservation (Fig. 3.4).

The immobility of a wireless robotic system with a unit-by-unit backup becomes:

In such a rank, one elementary reserve is given to a greater sutta of hopelessness (the immobility of the uninvolved robot grew from 0925 to 0965, that is, by 4%).

Pochatkovі danі.
In fig. 3.5 presents a system of combining elements. In a wide range of immobile robotic elements, there are the following values: P1 = 0.8; P2 = 0.9; P3 = 0.95; P4 = 0.97.

Required.
It is necessary to determine the reliability of the system. It is also necessary to determine the importance of the system for the mind, so that the reserve elements are available.

Figure 3.5. Scheme of the system for combined functions of elements.

For the development of the outgoing systems, it is necessary to see the main blocks. The representations of the system have three (Fig. 3.6). We give rise to the need for the skin block okremo, and then we know the strength of the system.

Small. 3.6. The circuit is blocked.

Requirements of the system without reserve storage:

Thus, a system without a reserve is 28% lower than a system above a reserve.

Intensity of images- The cleverness of the wisdom of the mind and of the new object has been cleared for the moment of the hour, to look, for the mind, but to the moment the mind has not been won.

Thus, statistically, the intensity of the messages is proportional to the number of images that were seen in one hour, which was not reported until the moment.

A typical change in the intensity of vidms in an hour is shown in Fig. 5.

Dosvid of the operation of folding systems showing the change in the intensity of the video λ ( t) large numbers of objects are described U- Figuratively crooked.

An hour can be cleverly added to three characteristic files: 1. Period of operation. 2. Period of normal exploitation. 3. The period of the old object.

Small. 5. Typical change of intensity of video

The period of the operation of the object will increase the intensity of the images, the visibility of the incremental video, zooming defects of the video production, the installation and the improvement. From the end of the period to knit guarantee of service Ob'єkta, if the usunennya of the vidms is a virobnik. During the period of normal exploitation, the intensity of the messages is practically unnecessary, at the same time, they are of a vague nature and appear to be rapid, in front of them, through the vines of the minds of the attention, the lack of attention to the minds, call factors etc. The same period is considered the main hour of the operation of the object.

The increase in the intensity of the images is carried out until the period of the old object and the increase in the number of losses due to wear, the old and the other reasons, linked to the trivial exploitation. Tobto imovіrіnіst vіdmov and element, uh, having lived for the moment t at the beginning of the hour, the value of λ ( u) only a few progress, and also the intensity of images is a local indicator of the reliability of an element for every hour.

Topic 1.3. The need for new systems

Modern automation systems can be applied to folding systems, which can be introduced. Such systems, in the process of a robot, are repaired and returned to the robot when certain elements are removed. The power of the systems is controlled in the process of robots "being pledged" when they are designed and taken care of before the hour of preparation, and the repair and maintenance operations are transferred from the normative and technical documentation.

Carrying out repair and replacement visits є, on the day, in one more way, we will direct it to the adjustment of the system's reliability.

1.3.1. Indicators of reliability of blowing systems

On the other hand, such systems, surrounded by earlier indicators of hopes, are characterized by the same complex indicators of hopes.

A complex indicator of hopefulness є an indicator of hopefulness, which characterizes the number of powers that be to establish the hopefulness of an object.

Complex indicators of the reliability, which are the most widely stagnant in the characteristics of the reliability of the systems, є:

Coefficient of readiness;

Coefficient of operational readiness;

Coefiction of technical victoriannya.

Coefficient of readiness- It’s the fact that it’s about the object to return to the stationary camp at a certain moment of the hour, except for the planned interruptions, by stretching out such an object for the signs not to be transferred.

In such a rank, the efficiency of readiness characterizes at once the two developmental power of the object - the lack of security and the repairability.

Readiness rate є important parameter However, it is not universal.

Coefficient of operational readiness- It’s a matter of fact that it’s about being able to return to the stationary camp at a certain moment, except for the planned interruptions, by stretching out such an object’s being held over

The performance characterizes the reliability of the objects, the need for the storage of such winnies at a certain moment in the hour, for which the need for a non-operating robot is needed. Until the moment, the equipment can be in the charging mode, the locking mode in the other working functions.

Coefficient technical victorian- The period of mathematic examination of the intervals at the hour of transferring the items to the former station for the singing period of the operation to the sum of the mathematical studies of the intervals during the hour of transferring the items at the former technical station, repairs

The frequency of views is called the number of views of the apparatus, which they saw, one hour before the calls, the number of people who were raised on the screen for the mind, but they did not see the viewers, and do not ask for help.

Some of the images that were seen, in the interval of an hour, can be stuck out from the center of the hour, then the purity of the images is the function of the hour. This characteristic is necessary to be recognized.

Interval hour;

The number of times the apparatury was received

Viraz (10) є statistical values ​​of the frequency of vidms. The most common characteristics of the hope are easy to date. It is calculated in viraz (10), that is, the number of samples that were seen in the interval.

Obviously:

de N () - number of images, which is correct at the time of the hour;

The number of zrazk_v, which is correct to start at the moment of the hour;

For achieving a great number of educators, fair wages:

Pidstavlyayuchi (11) (10) and vrahoyuchi (12), (13), we can say:

Directly up to zero and converting to the border, we can make:

For urahuvannyam (4):

It’s obvious that the frequency of vidmov є gustin rose from one hour to another. Numerically, you won’t get taken from a vocal sign of an obscene sign of immobility without a robot. Viraz (16) є vidma frequency values.

By such a rank, by the frequency of views, by the same number of messages, by the number of unambiguous robots, and by the number of views for any law, the hour of recognition of ideas is clear. The number of deposits on display (16) and (4) may look like:

The average frequency of views is called the display of the number of calls, when they were seen, one hour before the calls, when they tried to try, for thinking, for all the times when they went out of tune, to be replaced by the help (new or) updates.

Intensity of images

Intensity of views is called the number of calls to apartments that were seen at one hour before the middle number of calls.

de - a number of images, which were seen, in the interval of an hour from before;

Interval hour;

The average number of images, which is just right, in the interval;

The number of reference images per ear interval;

The number of reasonably efficient signals for the interval.

Viraz (19) on the statistical values ​​of the intensity of the images. For an imaging presentation of the general characteristics, the presence of both the intensiveness of the images, the imaging of the uninterrupted robots and the frequency of the images is recoverable.

Apparently, for viraz (19), change the value of z (11) and (12). Todi otrimaєmo:

Vrahoyuchi, we know:

Pragnemo to zero і transitions to the borderline, іmаkеmo:

Integrating, recognizing:

Average hour of a wired robot

The average hour of a wormless robot is called mathematically an hour of wormless robotics. The average hour of no-wipe robots starts to fallow:

For a mid-hour, no-wandering robots from static tributes should be reprimanded with the formula:

every hour without a wake-up robot of the i-th eye;

N0 - the number of tests, over the yachts the test is to be carried out.

At the same time, at the viraz (25), I will replace the lost from a silent robot with a symbolic symbol and a vicious integration with parts. Otrimaєmo:

Oscillations can be negative, change to 0, because i todi:

KILKISNI CHARACTERISTICS OF SUPERIORITY

Criteria and some characteristics of hopefulness

The criterion of hope is to be called a sign, which can only be assessed on the basis of the need for new attachments.

Prior to the most widely stated criteria for the hope of adherence:
- Possibility of w / o robots by stretching the singing hour P (t);
- middle napratsyuvannya to the first vidmovi T av;
- napratsyuvannya on vidmova t cf .;


- Parameter to the stream of w (t);
- readiness function K g (t);
- Coefficient of readiness K p.

The characteristics of the hopefulness of a particular attachment are not meaningful.

The vibration of the most likely indicators of hopes to lie in the type of object.

Criteria for the reliability of non-faulty objects

I will attach a model of the robot.

Don't let the robot (on viprobuvanny) have N 0 elements that let the robot get involved in the end, as all the stinks were brought up. Moreover, the replacement of elements, which were removed, were not installed. These are the criteria for the hopes of the virobes є:
- Possibility of w / o robots P (t);
- Vidmov frequency f (t) or a (t);
- Intensity of images l (t);
- mid-range up to first view and T time.

Imovirnistu bezvidmnoy robots to call it the name of the one that is for the singing minds of exploitation at a given interval of hour, otherwise in the boundaries of a given direction it is not possible to see it.

According to the date
P (t) = P (T> t), (4.2.1)
de T - the hour of the robot element from the start up to the first time; t-hour, with a stretch of what form, the power of an uninvolved robot begins.

The power of a wormless robot for statistical data about vidmov and evaluate viraz
(t) = / N 0, (4.2.2)
de N 0 - The number of elements per ear of robot (viprobuvan); n (t) is the number of elements that were updated in an hour t; (t) - statistical assessment of the imocy of the novidmnoy robot. With a large number of elements (virobes) N 0, a statistical estimate (t) is practical to get from the iMovirnist of a wireless robot P (t). As a matter of fact, there is a handy characteristic є the ability to display Q (t).

Ymovirnistu vidmovi to be called the ymovirnist of that, which for the singing minds of exploitation at a given interval of time, one would like to see one. Vidmova and bezvidmovna robots є do not mind and protolezhny, that
Q (t) = P (T £ t), (t) = n (t) / N 0 Q (t) = 1-P (t). (4.2.3)

Frequency of views on statistics To call the given number of elements, which were seen, in one hour before the cob number of working (viprobuvanih), think, that all virobi, which went wrong, do not change.

According to the value

(t) = n (D t) / N 0 D t, (4.2.4)
de n (D t) - the number of elements that were seen in the interval of an hour from (t ‑ D t) / 2 to (t + D t) / 2.

Vidmov frequencyє The power of immobility (or the law of growth), an hour of the robot is virob until the first time it is seen. Tom

P (t) = 1 - Q (t), P (t) = 1 -. (4.2.5)

Intensity of images on statistics It is called the report of the number of virobes, which were seen, at one hour before the middle number of virobes, which is just right for the Danes at about an hour.

According to the value

(t) = n (D t) / (N cf D t), (4.2.6)
de N cf = (N i + N i +1) / 2 - the average number of elements, which is just right, in the interval D t; N i - The number of virobs, which can be correctly applied to the cob at the interval D t; N i + 1 - the number of elements that can be processed correctly in the interval D t.

Imovirna assessment of the characteristic l (t) go from viraz
l (t) = f (t) / P (t). (4.2.7)

Intensity of wits and immobility of wormless robots tied around with fallowness

P (t) = еxp .(4.2.8)

Average napratsyuvannyam to first view to be called a mathematical ochіkuvannya hour of the robot element vschent.

Yak is mathematically calculated, T avg is calculated through the frequency of messages (the power of the hour without a robot):

M [t] = T cр =. (4.2.9)

So as t is positive i P (0) = 1, and P (¥) = 0, then
T cр = .4.2.10)

per statistics about changing the average number of up to the first time you see it and calculating the formula

.(4.2.11)

de t i - Hour of w / o robots of the i-th element; N 0 - The number of pre-recorded elements.

Yak can be seen from the formula (4.2.11), for the value of the middle direction to the first time, it is necessary for the nobility of the moment to go out with the harmony of all the elements. It is not handy for calculating the average napratsyuvannya on vidmovu. Mayuchi dans about a number of elements i-th interval hour, mid-day to the first time, and more beautifully, start from the

.(4.2.12)

In virazi (4.2.12), t ct and m are found behind the following formulas:
t avi = (t i-1 + t i) / 2, m = t k / D t,
de t i-1 - hour ear of the i-th interval; t i - Hour of the end of the i-th interval; t k - hour, stretching out all the elements; D t = t i - 1 - t i - hour interval.

It can be seen from the view of the assessment of some of the characteristics of the reliability, as well as the characteristics, in addition to the average performance of the first view, by the functions of the hour. Specific visibility for a practical assessment of some of the characteristics of the attachments' reliability are seen at the "Laws of views" section.

The recognized criteria for hopefulness make it possible to achieve a general assessment of the reliability of viruses, but not to be updated. The stench also allows judgment the need for new virobes to be seen before... The availability of certain criteria does not mean that it is necessary to assess the reliability of the elements for all the criteria.

Mostly the need for viruses to be characterized frequency of views f (t) or a (t). It’s worth explaining to them that the frequency of the messages is very sensitive, and that doesn’t contain all the information about the video phenomenon - the hour of the video-free robot.

Medium napratsyuvannya to first vidmoviє to finish off by chance with the characteristic of hope. However, the criterion for assessing the reliability of the folding system and encirclement in quiet cases, if:

The hour of the robot system is less than the average hour of the wired robot;
- the law for an hour without a motionless robot is not one-parameter;
- The system is backed up;
- The intensity of the messages is not permanent;
- An hour of robots surrounding the parts of the folding system.

Intensity of images- The most reliable characteristic of the reliability of the simplest elements, so as it is possible to more simply enumerate some of the characteristics of the reliability of the folding system.

The most advanced criteria for the superiority of the folding systemє iMotionless robots... The most advanced features of iMovinnosti novidmovnoy robots:
- you should enter as a multiplier in іnshі, more general characteristics of the system, for example, efficiency and partiality;
- characterizing the change of hope in the hour;
- can be otrimanovanno simply rozrakhunkovy path in the process of designing the system and assessed in the process of viprobuvannya.

The taku robot model is visible.

Do not let the robot have N elements and do not know the elements that you saw, inaccurately ask for help (new or renovated). If it’s not in the hour required for updating the system, then because of the characteristics of the reliability, there can be a parameter for the stream of messages w (t) that is directed to the drive t time.

The parameter to the stream of vidm To be called the given number of virobes, which they saw, one hour before they were quiet, who tried to try to wash, but all the virobes who went out of harm's way, be silent with a help (new or if they were repaired).

Statistical values ​​є viraz
(t) = n (D t) / N D t, (4.2.13)
de n (D t) - the number of images, which were seen, in an interval of an hour from t ‑ D t / 2 to t + D t / 2; N is the number of elements to be tested; D t - hour interval.

The parameter to the stream of views and the frequency of views for ordinary streams with interconnected interconnected Voltaire's integral equivalents of another genus
w (t) = f (t) + .(4.2.14)

Behind the view of f (t), you can know all the few characteristics of the virob's hopes, but not new ones. To that (2.14), the basic principles, which tie together the characteristics of the superiority of the elements, do not and should not be updated, but should be updated with a new update.

Equivalent (4.2.14) can be written in operator form:
, .(4.2.15)
Relationship (4.2.15) allows you to know one characteristic through the insha, which is Laplace's re-implementation of the functions f (s) and w (s) and the revolting re-implementation of virazs (4.2.15).

The parameter to the stream of messages is so important for the authorities:
1) whether at any moment of the hour it is right to the law of the hour without a drive, the parameter to the stream of messages is higher, the frequency of messages is lower, tobto. w (t)> f (t);
2) independent of the form of the functions f (t), the parameter to the flow of w (t) at t® pragne up to 1 / T The power of the parameter to the stream of images is important, which means that during trivial exploitation the virob must be repaired, because of this kind of view, according to the law, the hour of the uninterrupted robot becomes stationary. However, the price does not mean that the intensity of the messages is a permanent value;
3) if l (t) is an increasing function for the hour, then l (t)> w (t)> f (t), if l (t) is a decay function, then w (t)> l (t)> f ( t);
4) for l (t) ¹ const, the parameter is to the flow of the video system and not the amount of parameters in the flow of the video and elements, tobto.
w s (t). (4.2.16)

The power of the parameter to the flow of images is allowed to be true, but when some of the factors are calculated in the reliability of the folding system, it is not possible to show the intensity of the images of the elements given by the statistical parameters.

5) for l (t) = l = const, the parameter to the traffic flow to the road w (t) = l (t) = l.

By looking at the power of the intensity of this parameter, the flow of images shows that the indicators are different.

In this hour, statistical data about the ideas won in the minds of the exploitation of possession are widely disseminated. With a lot of stench, it is often crumbled in such a rank that the characteristics of reliability are induced, є not by the intensity of images, but by the parameter of the flow of images w (t). To keep the pardons at the time of the rosary. A number of vipadkiv can be significant.

To reject the intensity of the types of elements from the statistical data about the systems to be repaired, it is necessary to speed up the formula (4.2.6), for which it is necessary to know the history of the skin element of the technological scheme. The whole sutta can speed up the method of collecting statistical data about information. That is why l (t) start after the parameter to the stream of w (t). The technique of rozrahunku is made up to the following calculus operations:
- for the statistical data about the type of elements of the repaired virobes and the formula (4.2.13), the parameter to the stream of views will be calculated and the histogram w i (t) will be calculated;
- the histogram will be replaced by a crooked one, as it is approximated to the equal;
- Reincarnation of Laplace w i (s) function w i (t);
- for the view w i (s) on the submission (4.2.15), the Laplace re-creation f i (s) of the frequency of views is recorded;
- behind the view fi (s) there is a change in the frequency of the views fi (t);
- there is an analytical viraz for the intensity of the messages for the formula
;(4.2.17)
- There will be a graph l i (t).

If dilyanka, de l i (t) = l i = const, then gradually the value of the intensity of the images will be used for the assessment of the immobility of the uninterrupted robot. At the same time, to be involved in a fair and exponential law of hope.

The technique is imposed, but it cannot be stuck, because it is impossible not to get into the knowledge of f (s). And here it is necessary to establish the approximation of the method for the development of the integral іvnyannya (4.2.14).

Napratsyuvannyam on vidmova to be called the middle value of the hour between the suspicious vidmovs.
Qia characteristic for statistics about the formula ,(4.2.18)
de t i - hour of reference of the element mіzh (i-1) -m and i-th video; n is the number of views per day t.

From the formula (4.2.18) it can be seen that in the given vipaduvannya on vidmovu vidma start for the viprobauvannya of one vyrazka virobu. If you are on viprobuvanny, there are N times in an hour t, then you can count on the formula
,(4.2.19)
de t ij - reference hour of the j-th pupil virobu mіzh (i-1) -m ta i-th vidmoyu; n j - number of views per hour t j-th time.

Directed on vidmovu є to add a new characteristic of hope, that there has been a wide expansion in practice.

The parameter of the stream of messages and direction to the message characterizes the reliability of the video, which is updated, and does not cover the hour required for the update. That stench does not characterize the readiness of the annex to the visit of its functions at the required hour. At the same time, such criteria are introduced, such as the efficiency of readiness and the efficiency of downtime.

Coefficient of readiness call the business hour of the reference robot until the sum of the hour of the reference hour of the robot I will simply add, recognized for the same calendar term. Qia characteristic by statistics start
= t p / (t p + t p), (4.2.20)
de t p - sumarny hour of the spraying robot virobu; t p - sumarny hour of downtime.

Hours t p і t p are calculated according to the formulas
; ,(4.2.21)
de t pi - hour of the robot virobu mіzh (i-1) -m and i-th video; t pi - hour of idle time of the i-th view; n - number of messages (repairs) of the virob.

For the transition to the imovirnіsny interpretation of the value of t p і t p, be replaced by mathematical calculations for an hour between suspected ideas and an hour for updating. Todi
K g = t cf / (t cf + t c), (4.2.22)
de t cf - napratsyuvannya to vidmova; t - average hour of renewal.

Coefficient due to downtime It is called the business hour of downtime until the sum of the hours of the right robot and of the downtime of the virob, taking the same calendar term.

According to the date
= t p / (t p + t p) (4.2.23)
abo, going to average values,
K p = t in / (t cf + t in). (4.2.24)
Coefficient of readiness and performance due to idle time of tying between itself
K p = 1 - K p. (4.2.25)
When analyzing the expectations of systems, which are being introduced, adjust the efficiency of the readiness to be calculated according to the formula.
K g = T av / (T av + t in). (4.2.26)
Formula (4.2.26) is true only in the same way, since the type of the form is the simplest, and only t avg = T avg.

Often the coefficient of readiness, calculating for the formula (4.2.26), denotes the fact that at any moment the system is correct. On the other hand, the characteristics of irregularities and can be attributed to singular spills.

Really, the validity of the confirmation of the installed and repaired systems is very small. In the early hours of growth. This means that it is possible to find the system in the reference station for the first time of exploitation until the end of the day. Tim for an hour, on the basis of the formula (4.2.26) the coefficient of readiness not to lie down for an hour of robotics.

For the definition of the physical meaning of the readiness coefficient K g, we write down the formula for the definition of the system in the reference station. At the same time, it is the simplest problem, if the intensity of the changes is l and the intensity of renewal is the magnitude of the change.

Admittedly, when t = 0, the system is located at the reference station (P (0) = 1), the number of times the system is found at the reference station is located at the reference station.
;
(4.2.27)
,
de l = 1 / T cf .; m = 1 / t; K g = T av / (T av + t in).

Tsei viraz will establish a fallowness between the efficiency of the system and the presence of the right state at any moment at the hour of t.

3 (4.2.27) it is seen that P g (t) K g as t ®, that is. practical function of readiness is easy to find out at the reference station when the process of exploitation is established.

In some kind of vipadkah Criteria for the reliability of failing systems can be criteria for non-failing systems, for example: imocy of no-vidmovy robots, vidma frequency, average to first vidmovy, intensity of vidmov... Taka need for wine:
- if there is a sense of assessing the reliability of the system, it will be updated before it is first updated;
- once, if there is a reservation for the renewal of backup attachments, it was introduced in the process of a robotic system, and it is not allowed to update all backup systems.