Method for calculating gamma-percentile time to failure and failure rate of resistive position sensors of control systems

Aim. Traditionally, the dependability indicators of resistive position sensors based on wire-wound potentiometers used in various control systems are confirmed by means of appropriate dependability tests or tests of comparable products. For cases of non-availability of comparable products test data or significant changes in the product’s design and materials, a method for short-term dependability testing and dependability indicators forecasting is required. Calculations of dependability indicators are to be based on statistical information on the variations of properties and parameters over the course of dependability testing along with research findings regarding the physical patterns, descriptions of process kinetics that cause such variations.

Methods. The analysis of physical processes that cause catastrophic changes in resistive position sensors has shown that under electrical loads thermal and electrical fields form that cause electrokinetic, thermoelectric, thermo-diffusion effects. In all cases the rates of physical and chemical processes are functions of material temperature, have temperature dependence and are described with the Arrhenius equation. The conducted research allowed establishing that variations of the position sensors’ impedance are largely defined by the processes occurring in the resistive element. The temporal dependence of impedance can be described with a logarithmic, exponential or polynomial dependence.

Results. Mathematical models that describe physical and chemical processes occurring in resistive position sensors in operation allowed developing a scientifically grounded calculation and experimental method for short-term reliability testing. The method includes the description of thermal and electrical modes, durability testing conditions and timing. It is shown that the results of such tests are used in subsequent statistical processing for the purpose of forecasting dependability values. Gamma-percentile time to failure and failure rate are evaluated by means of forecasting the degradation of the acceptance criterion values. The dependence of acceptance criteria values acquired in the course of the tests is approximated by a straight line, exponential curve or a polynomial equation. The form of the approximating line for forecasting the value of gammapercentile time to failure and failure rate is defined analytically based on the adopted model that describes the physical and chemical processes occurring in potentiometers in operation. The value of acceptability criteria of gamma-percentile time to failure required by the performance specifications and technical regulations is identified through extrapolation of the approximating line as a continuation of the chosen approximating curve (straight line).

Conclusions. The provided test data for short and long-term reliability corresponds to the calculated values of dependability indicators, which confirms the applicability of the developed calculation method. The application of the proposed method allows reducing the scope and duration of costly dependability tests.

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