Analysis of experience in assessing the extent of full-scale testing of anti-aircraft missile products during development and modernization

Introduction

Today, many design schools in the missile building industry are having a new lease of life. This is linked with the fact that in the recent years hu­man resources of the design organisations have undergone a remarkable renewal, new technol­ogies of developing and testing the missile en­gineering products are being mastered, and all kinds of computer-aided and semi-realistic mod­elling techniques are actively applied. The pro­duction facilities of the enterprises engaged in development of the missile engineering products and of those engaged in development of the on­board equipment and units are also going through substantial renovation.

Quite often the renewed teams of develop­ers have to face problems that had been success­fully solved by their predecessors earlier. In this context, in order to determine optimal ways for further development of the design schools, it is necessary to analyse the experience accumulated by the previous generations of developers and ap­ply it in solving current tasks of R&D planning, designing and testing new-generation products.

The paper’s objective is to analyse the ap­proach to determining the scope of full-scale tests with account of reliability of anti-aircraft missiles based on the experience accumulated in Joint Stock Company “P. D. Grushin Machine-Building Design Bureau “Fakel” (JSC MKB “Fakel”) in the beginning of its activity and taking into account the developments of the 21st century. The issue of assessing reliability of the products being devel­oped remains important, since for determination of the scope of new products testing and for estima­tion of the required funds and development terms it is necessary to know the attainable level of func­tional efficiency of products of the corresponding technology level at different testing stages. It has been proved in practice more than once that errors in estimation of the required quantity of products at the development test stage lead to considera­ble risks of failure to perform work within the set time frames.

Terminology

In the 1960s, the term “reliability” had no es­tablished definition. Thus, in OKB-2 (at present, JSC MKB “Fakel”, making part of JSC “Al­maz - Antey” Air and Space Defence Corpora­tion) the term “reliability”, as applied to an anti­aircraft missile, would characterize a probability of missile fault-free operation in flight [1], i. e., a probability that a test prototype of the missile will execute the test launch task under specified conditions. Therewith, a key factor was the effi­ciency of launch task execution by the missile. A missile launch would be considered successful and the missile fit if the main launch tasks were fulfilled.

However, this definition does not comply with the contemporary notion of reliability. In the well-known multi-volume reference book under the editorship of V. S. Avduevsky [2], as well as in GOST 27.002-2015 [3], reliability is understood as an object’s property allowing to maintain over time and within specified limits the values of all the parameters characterising the capability to perform the required functions in the prescribed modes and specific conditions of application, maintenance, repair, storage, and transportation.

The key notion of the contemporary defi­nition of “reliability” is the capability to pre­serve certain properties and characteristics. May it be pointed out that to solve the task of preserv­ing the aggregate of efficiency parameters and characteristics, it is necessary to first solve the task of achieving them and confirming stability of the results. It is exactly this task that is solved at the development flight test stage. During this period, search for and refinement of such technical solu­tions that are supposed to ensure compliance with the specified requirements is performed. For this reason, the term “product launching reliability” is not quite suitable for the refinement (testing) stage. Moreover, at this stage the necessary num­ber of test launches cannot be estimated referring to the product reliability requirement given in the technical requirement specifications.

A seeming contradiction in the approaches to the assessment of missiles reliability at the flight test stage can be overcome, without any corrections required, taking into account the fol­lowing facts. In the 1960s, the number of the test-stage product prototype launches at the JSC MKB “Fakel” amounted to several hundred and more (Fig. 1). The test engineers had to their avail an impressive statistics of launches, and, on the whole, there were grounds for obtaining statisti­cal estimates of reliability at the test stages. Under those conditions, proceeding from the reliability assessment, it was indeed possible to determine a test launch task fulfilment probability.

At the modern stage of new engineering products development, the situation is different. Thus, the amount of full-scale test activities has reduced due to high costs of the prototype specimens of missile engineering products and R&D budget limitations. Considering that the material and software refinements implemented during the tests more often than not lead to pro­found changes in the anti-aircraft missile proper­ties form launch to launch, drawing any statistics from a small series of launches is out of the ques­tion. Statistical assessments of the results at the test stages are possible, with certain allowances, on the mathematical simulation models. However, the modelling result will only have the desired integrity after verification of the models, which, in its turn, is on the whole over after completion of the entire scope of flight tests. Besides, the use of mathematical models as a powerful tool of making up for the lacking test scope has not been duly approved by the ordering customers thus far.

Proceeding from the above argumentation, the author believes that the process of new engi­neering products testing, as regards result achieve­ment, would be more appropriately referred to by the term “product functional efficiency” under given conditions, as this term determines the de­gree of launch tasks fulfilment by the aggregate of missile’s functional blocks and units. Quan­titatively, functional efficiency must correspond to the probability of missile fulfilling the task of a test launch.

The term “reliability” can be best applied when assessing repeatability of the result in serial production, when the design documentation (DD) is assigned letter “O1” and the state commission has acknowledged that the product manufactured according to the approved DD has verified cor­rectness of the design and technical solutions implemented, and consistently complies with its functional purpose. From that moment on, a statis­tical record of failures can be started, with simul­taneous improvement of the production processes for subsequent reliability assessment of serially produced items.

Attention should as well be paid to some ques­tionable interpretations of the notion of “failure” as used in the past. In the 1960s, a failure was understood in OKB-2 as missile performance loss in flight, which rendered a given launch unsuc­cessful [1].

Considering the foregoing, it should be pointed out that non-fulfilment of launch tasks during new products testing may occur for a num­ber of reasons.

Firstly, it can be a failure proper of some or other missile equipment block or unit, asso­ciated with malfunction of respective equipment caused by a breakdown or faulty condition of the elements of that block (unit).

Secondly, in a number of tests non-fulfil­ment of the launch tasks can be conditioned by incorrect operation of some or other block or unit caused by incorrect performance of their functions in specific conditions. In that case the block or unit proper can be functioning in accordance with its integrated logic.

Correctness of algorithm (function) exe­cution is ensured by both absence of errors in the algorithm, i. e., of outright inconsistencies between the runtime code and the initial algo­rithm, and the adequacy of reality representa­tion on the basis of which the algorithm (unit) is designed. If the developer lacks a clear notion of all the phenomena, internal and external pro­cesses, environment properties, and other cru­cial issues, it may become a cause of incorrect algorithm (block, unit) building for some of the mentioned conditions. In this case, characteris­tics of the process of new engineering products testing, one should talk not about failure, but rather about inadequate functional efficiency of the equipment, units or missile as a whole in specific application conditions.

Such interpretation of an occurring prob­lem is important so as to be able to formulate the problem more correctly and plan subsequent work for solving it. It is obvious that, given the above speculations, looking for a fault that may as well not be there and determining the cause of unsuccessful performance are in fact two dif­ferent tasks.

The considered differences in the inter­pretations of the notions of missile “reliability” and “failure” can be explained by different lev­els of technical perfection of the missiles of the 1960s and their modern counterparts. Thus, the first-generation missiles were, for the most part, complex analogue automatic control systems. For this reason, in all application conditions there was practically no variety of situations implying selection of task solving algorithms. Many disruptions in the automatic control systems could indeed be interpreted as faults (failures).

For modern missiles carrying digital sys­tems on board [4], the causes of task non-fulfil­ment and negative results of the launches can be algorithm improprieties, situations occurring in flight that were not accounted for, other uncer­tainty types, as well as breakdowns (failures) of the assemblies of equipment and units.

Offered in the next section is the analysis of the testing experience gathered in OKB-2 at the initial stage of enterprise activity, the results of which give a notion of the scopes of testing of new-generation engineering products in that period.

To enable citation of the initial texts in the materials mentioned, the old terminology is used as concerns determination of reliability and failures.

MKB “Fakel” work experience in determining reliability of the mainstream products in 1953-1968

The subject discussed within the framework of an open publication can be based on the mate­rials of the past years, of the period of OKB-2 evolvement, which in the present time are freely accessible in the public domain.

Despite the fact that over half a century has elapsed since then, with several genera­tions of the missile engineering products suc­ceeding one another, the experience of the Soviet defence industry is very important at the current stage of national engineering practice development.

The domestic school of anti-aircraft mis­sile building actively developed under the lead­ership of academician P. D. Grushin. In those years the priority task was that of delivering the required result within the shortest time possible. The country was in dire need of efficient protec­tion of its air borders. Given large volumes of the production output, a key role in the Soviet period was played by the correct assessment of those volumes and the test deadlines, which explicitly determined the state’s expenditures on new technology development. Not all was a success on the first attempt, launch problems and failures would happen, but in the long run the tasks would be solved, which ensured global leadership for our developments. Domestic air defence (AD) technologies virtually at all times have been applied in local military conflicts, undergoing refinement along the way based on the results of combat application. It is worthy of mention that the air attack weapons applied in those conflicts were state-of-the-art develop­ments of the American and European (Israeli) origin. For that reason for many years Russia managed and continues to prove in practice its leadership in the development and production of anti-aircraft missile weapons.

In the 21st century, the determining fac­tors in the new technology development are the budget allocated by customer for the purpose and the strictly set deadlines for development completion, legally fixed by the system of pe­nal sanctions against enterprises and CEOs for non-fulfilment of orders in due time. This dif­ference has laid a mark on the output of work undertaken and has impacted the deadlines for reaching development objectives, efficiency of financial investments, and the general state of developer enterprises. For this reason it is ever so important to be able to correctly estimate the scope of tests required for solving of the task within the specified time and at minimum risks.

A profound analysis of the rich scientific and practical legacy of the predecessors - the first generation of national rocket builders, goes to show that the requirements to the test scopes and outputs were thoroughly studied in the past, with the basic approaches to the organisation and management of tests and their unbiased eva­luation formulated on the base of overall assess­ments.

Based on the experience of development tests and application of the first-generation anti­aircraft missiles of type V-750, used in the S-75 SAMC, and their modifications, a conclusion was drawn that a reliability index close to the target value was achieved no earlier than after 3 to 4 years of serial production and with the total of 600-800 missiles fired. In that peri­od, refinement of the missile equipment was underway, technical solutions were perfected, and serial production technology was mastered. A schedule of launches required for achieving the specified reliability of the missiles is giv­en above (see Fig. 1). Statistical data of the achieved reliability level for the anti-aircraft missile family developed by JSC MKB “Fakel” are given in Fig. 2. The following designations are used:

P₀₀ - stabilised missile reliability level upon completion of factory cycle of serial pro­duction launching (after 3-4 years of serial output);

RMSD P₀₀ - root-mean-square deviation of the stabilised reliability level value over the entire sample collection;

P_n - reliability level achieved by the time of completion of certain product-oriented tests planned prior to serial production commence­ment;

RMSD P_n - root-mean-square deviation of reliability level value Pn.

For some products of V-601P, V-611, 9M33 types, the values of stabilised reliability level are not given in Fig. 2 as the said data were obtained later and did not make it into the materials cited.

By way of Fig. 2 it is possible to analyse specific features of testing different missile types. Besides, these data can be used to establish links to specific design features of the said missiles. The reader may avail of this possibility at their discretion.

The works of MKB “Fakel” of the 1960s show that over the period of setting up of industrial production of missiles and during as­similation of new equipment in the forces, the reliability of such equipment turns out to be lower than the target value. At the same time, missiles from different manufacturers, as a rule, have different reliability level due to differences in production preparation level, technologi­cal infrastructure, personnel qualification, and workplace culture at large.

During joint (state) tests of missile V-750V, conducted from May through August 1958, missile “reliability” stood at 0.7 after 30 missile launches. In missile launches conducted subsequently at the Kapustin Yar test range from August 1958 till the end of 1959 under conditions similar to those of the joint flight tests (JFT), reliability of the missiles was characterised by the value 0.859 (by the results of 368 launches), and in 1960 - 0.928 (by the results of 223 launches).

Similar data exist for missile V-600P as well, however, due to less intensive testing in case of these missiles, the process of their re­liability improvement up to the desired level took longer.

On the whole, the experience of deve­lopment tests performed on serial anti-aircraft missiles demonstrated that, with the number of launches equalling 150, the average reliability (functional efficiency) level achieved by the end of JFT was about 0.7. By the example of missiles of V-750V type it was established that to achieve a reliability level close to the maxi­mum attainable one, it took about 600 launches of serial missiles, which makes the total of 750 together with missile launches performed under the factory and joint tests.

The practice of anti-aircraft missile de­velopment tests proves that in the course of factory and joint tests all insufficiently reliable elements cannot be revealed completely, and it is only the apparent defects, which manifest themselves often enough, that are eliminated. At the same time, due to extremely complex organisational procedure of anti-aircraft mis­sile tests and insufficiency of information on operation of the entire on-board equipment, it often takes a large series of tests before a correct way to eliminate some or other defect can be found.

In the course of subsequent serial pro­duction and application of anti-aircraft missiles their reliability keeps on steadily rising up to the limit level, since the technology of missile production and application is further perfected, the production and maintenance staff quali­fication is improving, and, most importantly, individual defects revealed during anti-aircraft missiles firing and type testing of the equipment are continuously eliminated.

The intensity of tests, as well as the scope of missile manufacturers’ product output deter­mines the duration of tests.

Shown in Fig. 3 are the values of full- scale testing duration for several product types developed by JSC MKB “Fakel” in the 1960s.

It should be pointed our that in those years, the term “joint flight tests” was used in­stead of the contemporary term “state tests”.

Also worthy of note is the duration of flight tests of missile V-611 (see Fig. 3), de­veloped specially for the surface-to-air missile complex (SAMC) “Shtorm” of the Navy and having no land-based analogues. The design and development (D&D) work on this mis­sile required the longest time of development tests. This is associated with specific features of the material for the Navy and additional com­plications faced during the tests, even though special test facilities were available in those years: testing ships, optoelectronic shore-based measurement positions, a wide spectrum of spe­cially engineered targets. For testing V-611 mis­siles, a specially furnished sea test range in the town of Feodosiya was used. It can be surmised that without the above test support facilities the period of implementing this D&D project might be considerably longer.

Testing of anti-aircraft missiles in a ship­board SAMC at sea is much more complicated and bears great risks of yielding negative test results. During sea tests, a longer testing time is required, since, with remnants of the targets sinking, it is not possible to retrieve a hit object for detailed analysis.

Fig. 4 provides important data on the initial reliability level of anti-aircraft missiles newly developed by JSC MKB “Fakel” in the 1960s, obtained by the method of statistical processing of the results of full-scale testing of sufficient scope. The initial reliability was understood as reliability of the missile engineering products at the initial stage of fullscale works, i. e., autonomous flight tests and preliminary tests performed upon completion of the on-ground checks. At this stage, the risk of equipment blocks and units failure is high due to their novelty, manufacturability issues, and insufficient quality of check inspections. Notice the result of “sea” missile V-611, whose initial reliability level was no higher than 0.12. It goes to show that the initial stage of the sea tests of those missiles proceeded with difficulty, with many launches being unsuccessful. In the opinion of the author of this paper, supported by the sea work experience at the stage of modern missile engineering products design, those results were conditioned by the objective laws of maritime systems development. 

Solving of the tasks of determining the required test scopes, quality of the tests, per­formance dynamics, and a number of other tasks in OKB-2 was put in charge of Evgeny Samuilovich Iofinov, an experienced designer, Candidate of Engineering Sciences at the time. He worked at “Fakel” from 1954 till the last days of his life, rising from Senior Engineer to the Head of Project Planning Department - Deputy Chief Designer for Research Work and Advanced Developments. He was awarded the Order of the Red Banner of Labour, became a laureate of the Lenin Prize and State Prize for his contribution to the development of anti­aircraft missiles V-750 and their modifications, and for a number of other works.

Having analysed the results of launches of the anti-aircraft missiles of classes V-750, V-1000, V-860P, V-600, V-601, 9М33, and others, E. S. Iofinov had obtained unique statistical data on the reliability levels of newly developed surface-to-air missiles (SAM) at different stag­es of their life cycle. He determined the initial reliability levels of various SAM types before their designer flight tests and made important generalisations on the regular patterns of de­signer tests conduct.

E. S. Iofinov’s doctoral thesis (hereinaf­ter - thesis) until recently has had a restricted- access status, for which reason the scientific community were deprived of a possibility to get familiar with the fundamental results of the works performed. The results of this work have not lost relevance after all these years and can be used for alternative assessments of a required number of test launches when developing engi­neering products of new generation.

Given below are the most important con­clusions of E. S. Iofinov’s doctoral thesis [1].

“…

1. The paper contains a detailed analy­sis of the development tests of 13 anti-aircraft missile types, 7 of which are newly developed missiles and 6 represent modifications made during 1953-1968.

In total, over 8200 missile launches were analysed, of which ca. 5000 were used for analysis of the reliability growth process. In so doing, the basic regularities of the existing practice of development testing of anti-aircraft missiles were revealed.

2. It is demonstrated that the stabilised reliability level of the anti-aircraft missiles reaches the value P₀₀ = 0.92...0.95 for remotely controlled missiles and P₀₀ = 0.90...0.92 for self-guided missiles. This reliability level is achieved in serial production after several years of operations in the field and 600-800 missile launches.

For serial missile modifications, the sta­bilised level of P₀₀ is higher than that given above.

3. It was determined that the anti-aircraft missiles’ initial reliability level P₀, with which they are delivered to flight tests, is, as a rule, 0.2...0.4. For serial missile modifications, the initial reliability level is higher than that of the prototype but lower than the reliability level achieved in the series.
4. The reliability level of newly developed anti-aircraft missiles at the end of flight tests stage equals to 0.70...0.75 and rarely exceeds 0.8. To achieve such reliability level, 160-200 launches of anti-aircraft missiles are made on average, with the test period lasting 2-4 years. In so doing, the average reliability of the anti-aircraft missiles at the stage of flight tests is 0.5...0.7.

For serial missile modifications, the reliability level at the end of flight tests is 0.75.0.90, depending on modernisation depth. Missile consumption in the flight tests of such missiles is 50-100 pieces, with the test period amounting to 1-2 years.

5. Over the period of flight tests of a single missile type, an average of 20-30 types of de­fects resulting in failed launches are eliminated.

On average, 2.4 unsuccessful launches are re­quired for elimination of a single failure type. In some cases, elimination of a single defect takes 10-12 unsuccessful launches. Each de­fect is eliminated by a single successfully per­formed rework.

6. The core information for improving re­liability of the anti-aircraft missiles is gathered based on unsuccessful launches. Successful launches have virtually no influence on the growth of anti-aircraft missiles reliability, al­though the available information allows to re­veal faults in the operation of on-board equip­ment and units, which eventually lead to failed missile launches.”

In spite of the differences between con­temporary assessments of the key parameters of the tests and the data given above, the ten­dencies highlighted in the original source re­main relevant in the 21st century as well. Con­clusion 6 given above is undoubtedly essential at all times. It is important to remember that for successful completion of the tests one has to travel the entire hard path of errors and set­backs in practice.

As shown in the paper [4], the probability of test launch task fulfilment by a new-generation product depends on the level of final ad­justment of equipment and software (SW), and can be assessed by analytical methods. Despite this, the obtained assessments in the cited thesis conclusions can be useful as guidelines when carrying out calculations with the use of novel techniques.

To obtain assessments of the required number of launches at the test stages, with con­sideration of the achieved reliability (functional efficiency) level, it could be appropriate to use the known formula of accumulation of positive outcome probability in a series of tests [4].

All this said, the data obtained based on extensive statistics of the past years have prac­tical applicability in the 21st century as well.

Practical aspects of application of functional efficiency assessments at the test stages

As pointed out above, to obtain reliable esti­mates of the costs of a new D&D project, and hence, of successfulness of missile technology development on the whole, it is necessary to have a correct forecast of the required number of launches (full-scale tests). The said number of tests is constituted by the following factors.

Firstly, for verifying the efficiency of products application within the scope of techni­cal requirement specifications, a certain number of episodes with specified condition parameters is planned. In the test engineers’ language, each episode is a so-called test launch point (here­inafter - point). Normally, the following con­dition parameters are used: target type, radar cross-section characteristics of the targets, co­ordinates of objects and their derivatives in the hit point, interference situation, modes of mis­sile interaction with the complex, and others.

Secondly, when performing each launch into a particular point, situations leading to launch tasks non-fulfilment may occur. The causes of such situations are considered in the paper [4]. On the whole, the specified phenomenon characterises the achieved product efficiency at the respective stage of the tests. As can be seen from Fig. 4, at the initial stage of the tests the value of functional ef­ficiency of newly developed products amounted to 0.32 on average. Therewith, for the most complex products (e. g., V-860P of the surface-to-air missile complex S-200) the functional efficiency value was 0.2. Such low efficiency index at the initial stage of the tests can be explained by application of a high-sensitive semi-active radar homing head in the missile of new design, which was for the first time in the practices of JSC MKB “Fakel”.

Thirdly, for contemporary technological products carrying a large amount of digital com­puting devices on board, a crucial factor for im­plementing high functional efficiency is the SW advancement level. Attention should be paid to the specific features of contemporary missiles’ SW fine-tuning, as described in [4]; such features are characterised by dependence on the volumes of the runtime used, work deadlines, SW developers’ qualifications, and many other factors.

Fourthly, considerable effect on the func­tional efficiency of the anti-aircraft missiles being tested is produced by the optimisation level of SAMC facilities and the quality of interaction with the missile on-board equipment under various application conditions. As shown by the experi­ence of JSC MKB “Fakel”, up to 20...30 % of test launches with unsatisfactory result occurred through the errors or incorrect operation of the missile complex facilities rather than through those of the missile. It means that even if the missile is completely ready for flight task exe­cution, a positive result could only be achieved in 70.80 % of cases, depending on the missile complex operational optimisation. It is clear that when a missile is introduced in the existing and optimised complex, the said probability will be higher.

Fifthly, when determining the test scope, it is necessary to consider availability or absence, as well as completeness, of specialised test range outfit, sufficiency level of the available modern test-range measuring equipment, including multi­position optical facilities for combat gear opera­tion documenting. Lack of full scope of the ex­ternal measurement data increases the number of unsuccessful launches needed for finding and eliminating algorithm errors of inconsistencies.

Sixthly, when running check tests at the D&D work completion stage, it is necessary to prepare in advance the target types, launch con­ditions, and methods for analysing the results that most comply with the requirements of the tactical and technical requirement specifications. It should be reasonable to envisage the consequences of setbacks, which are inevitable at the check firing stage. It is necessary to set the conditions and methods for considering the check firing results a partial pass. Otherwise, firing “to the bitter end” may turn into a battle for survival in conditions of intensive depletion of developer enterprise’s re­sources and replenishment of product quantities at own cost and expense.

Considering the importance of correct esti­mation of the D&D costs, and, hence, correct deter­mination of the required number of test launches, it is reasonable to include in the technical require­ment specifications for developing missile engi­neering products, in addition to the target types, respective target silhouettes and target hitting conditions, referring to which the pass-fail ver­ification will be done at the state tests stage. A number of instances can be cited when the tar­gets that the test engineers had to their avail were considerably different in terms of vulnerability from the real targets given in the technical require­ment specifications, which was associated with the absence of a major part of equipment units and blocks as compared with the real targets. Obvi­ously, to obtain a desired result in said conditions a large missile consumption is required.

The described instantiation of the require­ments will ensure a reliable estimate of the re­quired number of launches at the test stages and, consequently, enable to mitigate the overall risks of violating the set work deadlines.

In this way, taking into account all the above factors, it can be possible to figure out a required quantity of products manufactured within the D&D framework for conducting the whole scope of tests and achieving an expected result. Proceeding from the prototype cost estimate, it is not difficult to come up with tentative D&D costs.

As an example, let us estimate the quantity of products required for the entire scope of work within a new D&D project, with the initial data being those of one of the products developed by MKB “Fakel” in the 1960s.

Suppose that at the stage of autonomous flight tests, when missile tests are conducted with­out the use of SAMC radar facilities, it is neces­sary to check product operation in three points differing by the flight range. For the sake of argu­ment, the efficiency of test range supporting faci­lities is taken equal to 0.9, i. e., the probability of obtaining the entire data volume is close to high but not maximum. Selection of the value can be explained by the fact that testing of new engineer­ing products always demands an improvement of the test range’s equipment, while look-ahead support of the tests is not always implemented to the full extent yet.

We shall take the initial-stage functional efficiency value equal to 0.2 (as that of missile V-860P in Fig. 4). Then the probability of task ful­filment in an experimental launch, assuming that all the necessary experimental data are obtained, will make 0.18. To end up with the desired result for a single point with 0.95 probability, at least 15 launches will be required, considering failures and other unforeseen situations. For conducting the full scope of autonomous flight tests under conditions of the assumed initial data, the quantity of products will be N_AFT: 15 · 3 = 45.

Under correct organisation of tests at the initial stage of the work it is not necessary to check all points of the kill zone. Otherwise, there will be considerable overconsumption of the pro­ducts. It should be appropriate to determine such episodes (points), in which operation of the en­tire missile equipment in flight can be checked. However, for checking all the features of complex equipment operation, a sizeable scope of flight tests will still be required.

At the stage of JFT with SAMC, the follow­ing number of products may be needed. Let us take functional efficiency at the considered stage equal to 0.7, in accordance with conclusion 4 of E. S. Iofinov’s thesis. It is also assumed that the anti-aircraft missile system (complex), in which the new product is used, is a newly designed one too. The value of functional efficiency of this sys­tem at the JFT stage is taken equal to 0.8. Then the probability of task fulfilment in an experi­mental launch of the JFT stage, assuming that all the necessary experimental data volume (test range measurements efficiency) is obtained, will be 0.7 · 0.8 · 0.9 = 0.5. To end up with the desired result for a single point with 0.95 probability, at least 4.3 launches are required. For conducting the full scope of JFT under conditions of the as­sumed initial data, taking into account the checks by 15 points, the quantity of products will be N_JFT = 4.3 · 15 = 65. It should be pointed out that the number of points checked at the stage of designer tests is determined by joint decision of customer and developer with regard to the test programme and may differ from the above value. May it be reminded too that a point is understood not just as spatial position of the missile hit point, but also as the parameters of a target (its radar cross-section, vulnerability of its blocks and units, etc.). Con­cerning vulnerability, as was mentioned above, it is very important to ensure compliance with the characteristics of simulated targets. Under­estimation of this requirement leads to overcon­sumption of missiles during the tests. Number 15 is taken solely by way of example.

Let us assume that at the stage of state tests 10 points are checked with consideration of not only the hit points, but also various target types. At the stage of state tests, product functional ef­ficiency value may reach 0.8. Suppose functional efficiency of the complex has reached 0.9 and efficiency of the test range measurements is 0.9 as well. Then it can be reckoned that under con­ditions of the assumptions made, for the state tests stage ca. 30 experimental missiles will be required.

Under conditions of the assumptions made, the full scope of flight tests, taking into account functional efficiency changes along the way, will amount to ca. 140 launches.

Without consideration of functional effi­ciency of the products and the missile complex po­tentially implemented at the test stages, the scope of planned full-scale works will be estimated substantially lower relative to the objectively re­quired amount of those works. In the considered example, proceeding from the planned test points, this amount will make 3 + 15 + 10 = 28, i. e., 20 % of the total amount required. This seeming cost saving in estimation of D&D financing amounts considerably increases a risk that the planned test scope will be insufficient even for the autonomous flight testing. With high probability the deadlines of the tests will be violated for the need of finding additional funds, manufacturing additional quan­tity of missiles and proceeding with the tests.

In this way, the use of objective statistical data accumulated in JSC MKB “Fakel” in different periods of its activity makes it possible to ob­tain expert estimates of the number of launches of the prototypes of missile engineering prod­ucts required for completion of the entire test scope planned. At the same time, remaining out­side of the framework of the presented material is the methodological machinery for selecting the scopes of full-scale work, i. e., the number of hit zone points of the complex to be checked at the test stages and the acceptable share of the simulation modelling methods used for op­timisation of the amount of full-scale tests. It is planned to dedicate a special research to this issue.

Conclusions

1. In spite of the years passed since the time of generalisation of the first results of testing do­mestic anti-aircraft missile engineering products, as well as the emergence of new technologies of developing and testing of such products, the methodological relevance of the past years’ re­search efforts has not lost its significance.
2. For correct estimation of the required scope of full-scale tests of the missile engineering products, it is necessary to consider objective data on the ultimately attainable functional efficiency characteristics of products at different test stages.
3. The development and tests of new- generation anti-aircraft missiles is a pretty expen­sive process. The largest part of the total expendi­ture on the development of new engineering pro­ducts are the costs of manufacturing missiles for conducting the entire scope of full-scale works. The experience of JSC MKB “Fakel” goes to show that unreasonable cost-saving as regards the scopes and intensity of tests will with high probability lead to violation of the development deadlines and increase of the material expenditure.

In this context, when drawing up contract performance sheet on development of new missile weapon prototypes, it should be appropriate for the customer to make, jointly with the developer, overall assessment of test risks for the purpose of planning an optimal scope of the tests and esti­mating D&D costs on the whole.