Functional mathematical definition of dependability indicators and establishment of the dependency between the integrated indicator and the unique indicators at the stage of manufacture and recovery of components that define the reliability of a machine

Abstract

. As of today, the dependability of machines in the process of their operation and repair is considered as a whole, while the norms and specifications of GOST 27.002-2015, reference and scientific/technical literature do not provide any strict mathematical definitions of dependability indicators of primary elements/components. At the same time, the parametric dependability of a machine is based on the paradigm of evaluation of dependability indicators over the whole operation period from the stage of manufacture to end of service life subject to possible repairs. Aim. Given the above, the aim of this paper is to evaluate the effect of unique dependability indicators on the integrated indicator ID(efficiency retention coefficient) at the stage of manufacture and recovery of machine components. Methods . The paper is based on the mathematical device for the identification of linear dependency between the integrated indicator and unique indicators that involves the identification of the integrated indicator when the unique indicator under consideration changes its value from the basic (first) level to the high (forth) level, while all the other unique indicators remain at the basic level, which rules out the correspondence between the unique indicator under consideration and the other indicators in the process of integrated indicator calculation. Results. Calculations show that the optimal option for increasing ID is to increase the unique indicators according to their priorities. Thus, coordinated increase at the stage of manufacture and recovery of only three unique indicators in some instances ensures 75 percent growth of the integrated indicator. Conclusions. It is suggested to classify machine components into three groups based on the value of reliability indicator of the initially installed machine component: ones that define the life until discarding (IR1>1); ones that define machine service life (IR1=1) and ones that define machine reliability (IR1<1). The identification of the dependability indicators of the components in each group is based on the provisions of GOST 27.002-2015, but each group has its own unique features that must be taken into consideration in the functional mathematical definition of the dependability indicators of components in relation to the dependability of machines as a whole. For the components of the third group functional mathematical definitions were developed, dependencies and priorities between the unique indicators and increased integrated indicator were identified. Using a specific example, the economic feasibility of increasing the integrated indicator was calculated. It was established that the most promising solution would be a coordinated increase of the integrated indicator at the stages of manufacture and recovery that enables a more that a double reduction of costs, while ensuring 61 percent profitability.