METHOD FOR PREDICTING THE DURABILITY OF ELECTRONIC EQUIPMENT

Context. Constant growth of spacecraft operating life requirements leads to creating equipment which fits these requirements. From this point of view, specifically durability prediction allows to evaluate the potential of creating equipment with a long operating life. On early stages of equipment’s development analytical methods of durability prediction are used. Obviously, the more precise the estimation is, the more likely that the practical test will confirm the durability predictions. Therefore, improving the engineering techniques of the durability prediction is a relevant problem. Objective. The objective of this research is to improve the quality of design work by enhancing the engineering techniques of the durability prediction, which raise the authenticity of the evaluations. Method. Life of the equipment are calculated using the statistical modelling method (Monte-Carlo method). This method takes into consideration probabilistic characteristics of constituent elements’ life. Results. As a result, the problem of predicting operating life of electronic equipment using the reference data on early stages of development is solved. An analysis of standardized method of durability prediction was performed which revealed existing limitations for using this method when predicting operating life of electronic equipment. An alternate, statistical method of predicting operating life of electronic equipment was suggested and a software implementation was created. Developed software was tested and verified. Analytical experiments were performed to show the authenticity of the suggested method and to compare it to the standardized one. Conclusions. Thus, results of the performed research show that the standardized method is applicable only for calculating the minimum operating time. Also, it was concluded that the truncation parameter of element’s life distribution, variation coefficient of life and some specific qualities of dependability prediction scheme have to be taken into consideration when predicting durability of electronic equipment.

INTRODUCTION Level of quality of renewable and modifiable electronic equipment largely depends on quality and effectiveness of engineering such equipment. This is a big factor in competitiveness on global and local markets. Moreover, this applies to modern on-board equipment of spacecraft which has complex operating algorithms, heightened dependability, noise immunity and persistence against external influences.
Besides, in addition to growing complexity of equipment and more strict requirements, time allotted for designing machinery is shortened. First stages of engineering are usually hindered by countless revisions and modification targeted not to raise the quality of equipment, but to eliminate flaws, defects and failures. This happens due to a number of shortcomings of traditional engineering process, mostly from insufficient integration of math modeling into modern information technology.
Main difficulties of using math modeling methods in engineering process come from two reasons. Firstly, methods of selecting and analyzing engineering decisions are not developed enough. In addition, malfunctions modeling and dependability-oriented engineering are often neglected. Secondly, there aren't many software packages to choose from, and their capabilities are limited.
Modern reliability calculation software packages (ASRN, "ARBITR", "Nadejnost" module of KOK complex, "Reliabilty" modules of CAD-systems, RAM Commander, WQS, BlockSim and others) focus mostly on reliability prediction, leaving durability out. However, these factors do matter a lot for spacecraft with its long lifespan, and for competitiveness on the market too.
It is known that durability is established with design, implemented with manufacturing and kept with maintenance. Better accuracy of durability characteristics evaluation on early stages of designing means more chances to construct durable equipment. This makes improving methods of durability characteristics calculation for equipment with heightened operating life a relevant problem.
This research examines standard procedure of equipment's life prediction and also methods, models and algorithms used for equipment durability analysis.
The objective of this research is to heighten equipment engineering quality by improving durability calculation method with durability probability characteristics of equipment's composite elements usage.

PROBLEM STATEMENT
Durability characteristics of equipment's components is the initial data for equipment operating life prediction. These characteristics are «minimum operating time» and «gamma-percentile life». Result of the calculations is the gamma-percentile life of electronic equipment which indicates the time during which equipment won't reach it's limiting state with gamma-probability. Limiting state criterion of electronic equipment is decided by a predetermined percentage of equipment's components reaching their life expectancy (in the worst-case scenario -of any component . 100 2 REVIEW OF THE LITERATURE Many publications are devoted to the problems of equipment's operating life evaluation. They review three main methods of operating life prediction -experimental, analytical and experimental-analytical. Experimental methods rely on operational life testing (usually, accelerated testing) [1]. experimental-analytical methods assume that dependability tests are performed for a part of equipment's composing elements (usually in place developed elements), and the technical equipment's operating life itself is calculated. Since there is no equipment to test on early stages of engineering and the equipment consists of elements with known durability characteristics, these methods won't be reviewed. The most widespread durability assessment methods are the methods of calculating mechanical equipment's operating life under cyclic stressing, mechanical wear and other fatiguing stresses. These methods are used in calculating operating life of separate elements of equipment's carcass [2], which is a separate problem and it will not be reviewed here. There are also operating life prediction methods based on using probability-physical failure patterns [3,4]. But using these methods also requires experimental tests of the component base, so they haven't found much use in engineering routine.
Perhaps, the only document which regulates durability prediction on the stages of development is the standard [5], which is used ether directly (for example, [6]) or serves as a base for creating factory-local standards (for example, [7][8][9]).
Initial data for durability prediction using methods of this standard are the element's durability characteristics which are detailed and systematized in the handbook [10]. The handbook is an official publication and it gives a list of such experimentally obtained element's durability characteristics: -gamma-percentile life; -minimum operating time. Fig. 1 shows a fragment of a Hand Book's table of resistor's durability characteristics.
However, minimum operating time values are detailed only for elements which have been produced under modern requirements. If an element is missing from the reference book, it has to be calculated using standard's [5] formula: 1 . .
As implied by (3) methods of standard [5] assume that life of an element is a normally distributed random value: Clearly, the number 0.15 in formula (3) represents variation coefficient of life: It should be noted that in the document [7] value of ν is 0.25, and in the document [8] -0.21.
On top of that each of those documents assumes that the value of ν stays the same for every element when calculating durability characteristics. Therefore, if one elements has the same γ value as some another element, but one of the elements has greater Т р.γ value, other durability characteristics (Т р.m и T н.м ) will also be greater.  So, if variation coefficients of life differ between elements, it can happen that one element has Т р.m greater than another, and Т р.γ , in contrast, lesser.
To combat this, in [11] it has been suggested to use mean value of variation coefficient of life: But neither documents [7,8] nor monograph [11] detail evaluation of error, which is based on assumption of ν n values equality.
Thus, one of the ways to increase durability prediction of equipment is using not determinate, but probabilistic characteristics of elements life.

MATERIALS AND METHODS
In order to resolve this problem a method of statistical modeling was used. This method is "a universal method of calculation for objects of any structure, for any distributions of operating time between failures and restoration times, for any strategies and methods of restoration and preventive maintenance…" [12].
-Performing simulation modeling: -Calculating life realization for each element (using Box-Muller transform); -Calculating life realization for equipment using limiting state criterion (К LS ). The limiting state criterion in standard [5] is interpreted as reaching operating life limit by a defined percentage of total count of equipment. Us-ing this limiting state criterion for equipment's life realization means life realization's vector is aligned in ascending order. A value with number k is chosen from this vector: where k is Obviously, if the limiting state criterion is formulated as "reaching lifespan by any element", then, with this limiting state criterion: where l is This method was implemented and included in ASONIKA-K-D system of ASONIKA-K software package [13]. Fig. 3 shows results of modeling operating life of Р1-1 resistor, which has T н.м = 25 thousand of hours, Т р.γ = 50 thousand of hours (γ = 95%), amount of simulation experiments -10 6 . As seen in Fig. 3, statistically modelled value of resistor's 95% operating life (49.956 thousands of hours) almost coincides with predetermined one.

EXPERIMENTS
To evaluate the influence of variation coefficient of life a number of calculations inside ASONIKA-K-D system was carried out. Case 1. Equipment contains 5 elements with Т р.m = 50 thousands of hours (ν = 0.25) and 5 elements with Т р.m = 40 thousands of hours (ν = 0.1), К LS = 0%.
Case 2. Equipment contains 5 elements with Т р.m = 50 thousands of hours and 5 elements with with Т р.m = 40 thousands of hours, К LS = 0%. The variation coefficient for each element equals ν m, which is calculated using formula (6).
To evaluate the accuracy of calculations using a method described in standard [5], a 95% operating life calculation example was chosen.
The equipment consists of 101 resistors, 34 nonelectrolytic capacitors, 28 electrolytic capacitors, 22 silicon diodes, 14 low-powered silicon transistors, 5 highpowered transistors, 37 microchips with low degree of integration, black and white kinescope and 2 lowfrequency transformers. limiting state criterion: "No more than 20% of elements should have their operating life used up".
Since standard [5] does not include types of elements, they were chosen match standard's [5] example. That means choosing elements in a way that makes the count of elements with 95% life's value to fit with the standard's [5] example. Formed data is summarized in Table 1.

RESULTS
Results of calculating 95% life's value for case 1 are shown in Fig. 4a. Calculations were performed using ASONIKA-K-D system with a number of simulation experiments M = 10 6 . Fig. 4 b shows Results of calculating 95% life's value for case 2.
Results of calculating 95% life's value for case 1 are shown in Fig. 5. Calculations were performed with a number of simulation experiments M = 10 6 . Fig. 6a illustrates results of calculating 95% life's value calculated using ASONIKA-K-D system with a number of simulation experiments M = 10 6 for К LS = 20%. Fig. 6b shows results of calculating equipment's 95% life's value for К LS = 0%.

DISCUSSION
To determine the cause of discrepancy between results of statistical modeling and standard's [5] example a test example was calculated ( Fig. 4) As Fig. 4a illustrates, the value of 95% life is equal to 18,788 thousands of hours. For comparison, Fig. 4b shows the value of 95% life of the same equipment with ν for each element equal to ν m , which is calculated using formula (6). As shown in Fig. 4b, the value of 95% life (23,834 thousands of hours) differs from the one with using different ν values as shown in Fig. 6a However the calculated values are substantially lower than the value of 95% life calculated using standard's [5] method (33.42 thousands of hours) A calculation of a test example was performed to identify the reason behind such results of statistical modeling (see Fig. 5). As illustrated in Fig. 5, the value of 95% life is equal to 34.068 thousands of hours, but standard's [5] result is 50 thousands of hours.
Since the ν n values in this case are same for all elements, this discrepancy is due to different elements' life values being independent random values.
When modeling independent random values (elements' lifes), for each element a random value is generated (x 1 , x 2 ,…, x N ) and it's used to calculate the life's value (t р1 , t р2 , …,t рN ) as shown in Fig. 7. Removing discrepancy between results of statistical modeling and standard's [5] method can be achieved by not only making ν n values equal, but also creating functional relation between elements of different types. That means if the first element's life realization equals to t р1 for a random value equal to x, then values of life realizations of other elements (t р1 , t р2 , …,t рN ) must be the same (illustrated in Fig. 8).
However, this is impossible in practice. It is hard to imagine skipping one type of element life verification but checking all of the others when building equipment. Specifically it has to be verification of elements life which would guarantee the element's life with probability close to 1.
Thus, if elements life are independent values, the probability of equipment's life being no lower than a certain value would decrease with increasing equipment's elements count. This can lead to calculated value of 95% equipment's life being lower than the gamma-percentile life calculated using standard's [5] method. Minimum operating time would be lower too.
It should be noted that the value γ = 99.9% in formula (3) should be considered as an approximate one. Such value is recommended in standard [5] for calculating T н.м of elements with no T н.м values given in Data Sheet. By definition, minimum operating time is a time period (life) during which limiting state of an element won't happen with a probability of 1. Which means it should be considered as a shift parameter for life distribution function (Fig. 9). To confirm this, let's find χ γ1 value using formula (3). In accordance with requirements of current standards, 95% element's life should be no lower than it's doubled minimum operating time. Let's assume Т р.γ = 2•T н.м . In this case, formula (3) will take the following form: Solving (12) for χ γ1 gives χ γ1 = 4,1568. For this value the probability is almost equal to 1 (at χ = 4.265 γ = 99.999%).
Based on this, it should be assumed that the element's life distribution function is shifted by T н.м value. In this case, statistical modeling of element's life realization should be performed using formula: With taking into account all of the correction, statistical modeling was performed for standard's [5] example.
As illustrated in Fig. 6 a, 95% equipment's life is no lower than 17.827 thousands of hours, which is 1.4 times greater than the one calculated using standard's method (13 thousands of hours).
Besides, Fig. 6b shows results of calculating 95% equipment's life for К LS = 0%. Fig. 7 b shows that 95% equipment's life is no lower than 2.457 thousands of hours, which is 2 times less than the one calculated using standard's [5] method (5 thousands of hours).
It should be noted that existence of reserved elements (reserving using additional (reserve) elements) should be taken into consideration when modeling equipment's life realizations.
For example, limiting state criterion for constantly loaded reservation is formulated as "Expending operating life of 100% of elements included in reserved group". К LS value for such reserved group will be equal to: Calculating realizations of reserved group for such К LS value is performed using following formula: ( ) -existence of reserved elements (reserving using additional (reserve) elements) should be taken into consideration when modeling equipment's life realizations.
-specialized software should be used to calculate gamma-percentile life of equipment (like ASONIKA-K-D).
In conclusion, it should be noted that aforementioned method of statistical modeling does not take into consideration elements' life dependence from equipment's operation model. Particularities of predicting life of elements whose total flow of failures consists of independent failure flows of its components. These problems are reviewed in detail in [11] and [14]. Their suggested models will be implemented with ASONIKA-K-D further development.