Reliability of Electronic Devices at Early Stages of Life Cycle

In the paper, early stages of existence of electronic devices are considered: design stage and stage of early failures. At the design stage of electronic devices, various actions are carried out: choice of circuit and structural decisions; choice of parts of devices, components and elements; performance of programs on maintaining reliability [1, 2]. Among programs on maintenance of reliability, important role is attributed to evaluation works related to reliability of various variants of structure of electronic devices [3]. At evaluation of reliability of devices, help data manufacturers components and elements (further – components) are used [4]. The stage of early failures is usually related to the beginning of technological running–in of electronic devices. At this stage, failures of both devices, parts of devices and components are revealed. In general, the reason of the given failures is industrial lacks. To organize works on revealing early failures in a rational way is possible having estimated reliability of electronic devices for the given stage [3, 5, 6]. In the article, the method of forecasting of reliability of components applied at a design stage of electronic devices is analyzed. Models of reliability of electronic devices for the stage of early failures are considered. Methods of evaluation of parameters of considered models and method of evaluation of conformity of models with statistical data on failures, are offered.


Introduction
In the paper, early stages of existence of electronic devices are considered: design stage and stage of early failures.At the design stage of electronic devices, various actions are carried out: choice of circuit and structural decisions; choice of parts of devices, components and elements; performance of programs on maintaining reliability [1,2].Among programs on maintenance of reliability, important role is attributed to evaluation works related to reliability of various variants of structure of electronic devices [3].At evaluation of reliability of devices, help data manufacturers components and elements (further -components) are used [4].
The stage of early failures is usually related to the beginning of technological running-in of electronic devices.At this stage, failures of both devices, parts of devices and components are revealed.In general, the reason of the given failures is industrial lacks.To organize works on revealing early failures in a rational way is possible having estimated reliability of electronic devices for the given stage [3,5,6].
In the article, the method of forecasting of reliability of components applied at a design stage of electronic devices is analyzed.Models of reliability of electronic devices for the stage of early failures are considered.Methods of evaluation of parameters of considered models and method of evaluation of conformity of models with statistical data on failures, are offered.

Forecasting of reliability of components of electronic devices
Works of calculation of reliability are carried out at various stages of life cycle of electronic devices.At early stages of life cycle this usually is the counting of indexes of reliability of devices.The given evaluations are based on the information by manufacturers on reliability of components.The information on reliability of components of electronic devices is specified in various sorts of directories.The important question is definition of failure rate of components during the moments of time further from time of publication of help data.
Let's consider a time interval from the moment of publication of help data for which the manufacturer specifies reduction of failure rate of components.Then, for the certain type of components, it can be written down: where t -the moment of time of a considered interval; for the moments of time i t .It is easy to show that based on the method of the least squares, values of coefficient A in (2) can be determined from expression For example, the manufacturer specifies reduction of failure rate of the certain type of components within the first three years from the moment of publication of help data:

Models of reliability of electronic devices at a stage of early failures
For a stage of early failures, it is first necessary to choose a kind of the dependence describing change of mean value of a failure rate (further -failure rate) of devices in the course time.
For the device the density of a distribution of time from the beginning of technological running-in to first failure, and between other consecutive failures can be presented as superposition of two exponential distributions with parameters   where 1 b , 2 b -coefficients depending on a parity between two kinds of failures of the device, described by failure rate 1  and 2  , with . The following dependence (regression) of failure rate of the device on time can also be used: where t t -duration of technological running-in of the device.

Evaluation of parameters of models of reliability of electronic devices based on statistical data on failures
The following issue to be solved is determining values of coefficients 1  , 0  , 0  in regression (4) and coefficients *  , 1  in regression (8).As it may be seen from ( 4) and ( 8), considered regressions are nonlinear.
where i r -quantity of the failures that have arisen during interval The method of the least squares can be applied for definition of coefficients of regression ( 4) and ( 8) [6].If random errors of supervision are independent and are subordinate to normal distribution, the given method provides evaluation of unknown coefficients with the least dispersion.Thus, the received estimations are efficient [7].Otherwise, other methods leading to steady estimations can be applied [7,8].
On the basis of method of the least squares, coefficients To find 1  , 0  , 0  , according to (11), it is necessary to carry out differentiation of the left part (11) according to 1  , 0  , 0  and to equate derivatives to zero: where Considering that regression (4) is nonlinear it is not possible to solve the system of the equations (13) in analytical way.In this view, we shall stop on numerical methods.
Let's use a method of search on a grid.Let's consider area of possible values 0  with limits min 0  and max 0


can be determined considering requirements of the method of the least squares, under formulas: Values 0  , 1  and 0  can be considered as required values of coefficients at which l S satisfies the following equation ,..., ,..., , min where For unbiased estimate of square deviation 0  , it will be fair

Values of coefficients *
 and 1  in regression (8) shall also define based on the requirement of the method of the least squares: For finding *  and 1  according to (22) it is necessary to solve the following system of the equations: Regression ( 8) is also nonlinear.In this case, definition of values of coefficients *  and 1  is possible by using the logarithm or numerical methods.At transformation of regression (8) by using the logarithm, coefficients 1  also *  can be received in an analytical way: The unbiased estimation of square deviation 1


for regression (8) will be as follows As a numerical method for regression (8), it is also possible to use the above-considered method of search on a grid.Let's allocate q values in the field of

Definition of consistency of models of reliability of electronic devices with statistical data on failures
Let's consider the issue of check of validity of judgments on a kind of regression   t  .Let's consider a zero hypothesis that dependence of failure rate on time corresponds to (4).
Let's consider that 0 Value of statistics 2  , calculated by (30), can satisfy one of following conditions: where  percentage point of 2  distribution with 0  degrees of freedom;  -significance level of criterion.
At performance of (31), follows that the stated hypothesis about regression of kind (4) has been approved as not contradicting to statistical data.At performance of (32) or (33), hypothesis about regression of kind ( 4) is rejected with significance level  .Except for that, at performance of (32) it is possible to consider that the number of coefficients of regression   t  of kind ( 4) is overestimated.At performance of (33), it is possible to consider that the number of coefficients of considered regression is underestimated.
Check of conformity to available statistical data of regression of kind ( 8) is the same as above.In this case, statistics 2   1  with   the manufacturer.3. The method of forecasting of reliability of components is offered.The method considers data by the manufacturer on change of failure rate of components during the moments of time after publication of help data.4. The stage of early failures of electronic devices is considered.Two models of dependence of failure rate on time for the given stage are offered.5. Methods of estimation of parameters of considered models and a method of estimation of conformity of models with statistical data on failures are offered.6. Models of reliability of electronic devices are nonlinear, numerical method of finding the parameters of models is therefore considered.The method provides carrying out of computing experiment.
value of failure rate of component of the device; 0  -help value of failure rate of component of the device; reduction coefficient of component of the device.Let's analyze a case when the manufacturer specifies certain values

1  2 
characterizes failure rate of parts of the device and components due to industrial lacks.Parameter characterizes failure rate without taking into account the mentioned lacks.Then dependence (regression) of failure rate of the device on time will be as follows

where 1 
-value of a failure rate, caused, basically, by defects of manufacture of the device, parts of the device and components; 0  -the established value of failure rate; 0  -coefficient describing speed of revealing of defects of manufacture during running-in.Between coefficient 1


of regression (4) can be determined in view of following requirements:

Conclusions 1 .
Early stages of existence of electronic devices are analyzed: design stage and stage of early failures.2. At the design stage the important question is definition of failure rate of components during the moments of time further from time of publication of help data by