Basic Principles of the Methodology for Determining the Economic Efficiency of Radiation Defectoscopy
Abstract Generated abstract
The paper develops methodological principles for evaluating the economic efficiency of radiation defectoscopy, particularly inspection methods using accelerators, in industrial quality control. It distinguishes between selecting the least costly interchangeable inspection method and assessing whether inspection is justified by reductions in rejects, preservation of products, longer service life, or improved reliability. The authors propose reduced-cost criteria and a set of formulas that account for inspection costs, capital investments, machining losses, repairable scrap, product life, and emergency repair savings. The contribution is a structured calculation framework for identifying economically effective applications of radiation inspection under comparable production and quality conditions.
Full Text
Basic Principles of a Methodology for Determining the Economic Efficiency of Radiation Defectoscopy
L. M. Dobner, V. A. Berdonosov, Yu. S. Prokof'ev
(Presented by the scientific seminar of the Department of Industrial Economics and Enterprise Organization)
In recent years, radiation methods of inspection have been gaining ever wider use in the country’s industry; these methods involve the use, as radiation sources, not only of radioactive isotopes and X-ray apparatuses, but also of various kinds of accelerators (betatrons, linear accelerators, etc.). In this connection, the problem of identifying the areas in which the corresponding inspection methods can be applied economically effectively is becoming important. To establish these areas, a correct approach is needed to the methodological questions of determining the economic efficiency of inspection methods.
The methodological questions of determining the economic efficiency of using accelerators for product-quality inspection should be considered in two aspects: first, from the standpoint of choosing the most effective of several interchangeable methods; second, for establishing the expediency of inspection (with the aid of accelerators) for the purpose of preventing (reducing) rejects and increasing the durability and reliability of the products being inspected.
In the first case, the choice of the most effective inspection variant should be made according to the minimum of reduced costs \(c_{\text{p}}\):
\[ c_{\text{p}} = c_{\text{k}} + e_{\text{n}} k_{\text{k}} \to \min, \tag{1} \]
where \(c_{\text{k}}\) is the cost of defectoscopic inspection, rubles/item;
\(e_{\text{n}}\) is the norm of efficiency of additional capital investments,
\[ \frac{\text{rubles/year}}{\text{ruble}}; \]
\(k_{\text{k}}\) is the specific capital investment caused by performance of the inspection operation,
\[ \frac{\text{rubles}}{\text{item/year}}. \]
The composition of the costs \(c_{\text{k}}\) to be taken into account when determining the cost of the inspection operation depends, to a certain extent, on the method of detecting defects in the item being inspected.
The cost of the inspection operation when defects are recorded by the photographic method may be represented as the sum of costs:
\[ c_{\text{k}} = c_{\text{pr}} + c_{\text{pl}} + c_{\text{rs}} \ \text{rubles/item}, \tag{2} \]
where \(c_{\text{pr}}\) is the cost of radiographing the items;
\(c_{\text{pl}}\) is the cost associated with the purchase and processing of film;
\(c_{\text{rs}}\) is the cost of interpreting the radiograph.
With the scintillation method, the cost of the inspection operation will include only the costs of radiographing the product, \(c_{\mathrm{k}} = c_{\mathrm{pr}}\), which are the sum of the following costs:
\[ c_{\mathrm{pr}} = c_{\mathrm{z}} + c_{\mathrm{a}} + c_{\mathrm{r}} + c_{\mathrm{e}} + c_{\mathrm{osn}} + c_{\mathrm{zd}} + c_{\mathrm{or}} \ \text{rubles/item}, \tag{3} \]
where \(c_{\mathrm{z}}\) is the wages of inspectors (operators) engaged in performing inspection operations; \(c_{\mathrm{a}}\) is the cost of depreciation of equipment (inspection, lifting-and-transport, and power equipment) attributable to the product; \(c_{\mathrm{r}}\) is the cost of current repairs of equipment; \(c_{\mathrm{e}}\) is the cost of electric power; \(c_{\mathrm{osn}}\) is the cost of operating the tooling; \(c_{\mathrm{zd}}\) is the cost of maintaining the premises attributable to the product; \(c_{\mathrm{or}}\) is general plant overhead.
Capital investments caused by performance of the inspection operation, \(k_{\mathrm{k}}\), include capital costs for inspection equipment and devices, for lifting-and-transport and power equipment, and for buildings, structures, and tooling.
The calculation of cost and capital investments should be carried out only for those cost elements and components of capital investment that differ in the compared inspection variants. It is assumed here that the compared methods and means of inspection must be identical in terms of production volume, product composition, and product quality. The latter condition, in particular, presupposes identity of the compared variants with respect to the degree of defect detectability.
If inspection (with the aid of accelerators) is a means of reducing losses from rejects and increasing the durability and reliability of the inspected products, then the additional costs of inspection operations must be commensurated with the economic effect achieved as a result of improving product quality. In this case, defectoscopy of products (cast, forged, rolled) makes it possible: 1) to detect rejects before subsequent machining operations and, consequently, to prevent unproductive costs; 2) to detect rejects (which are usually revealed in the course of machining), establish their limits, and determine the possibilities of correction—in other words, to preserve finished products; 3) to eliminate defects (which may not be detected in the course of subsequent processing) and thereby increase the durability and reliability of the inspected product during its operation.
In the first case, the annual economic effect can be calculated by the formula:
\[ E = \left[ \left( \sum_{i=1}^{M} c_{\mathrm{obr}_i} + e_{\mathrm{n}} \sum_{i=1}^{M} k_{\mathrm{obr}_i} \right) \cdot \kappa_{\mathrm{br}_i} - \left(c_{\mathrm{k}} + e_{\mathrm{n}} k_{\mathrm{k}}\right) \right] Q_{\mathrm{g}} \ \text{rubles/year}, \tag{4} \]
where \(M\) is the ordinal number of the operation in which the reject is detected during machining; \(c_{\mathrm{obr}_i}\) is the factory cost of the \(i\)-th machining operation; \(k_{\mathrm{obr}_i}\) is the specific capital investment required to perform the \(i\)-th machining operation; \(\kappa_{\mathrm{bro}}\) is a coefficient taking into account the magnitude of final rejects detected during machining; \(Q_{\mathrm{g}}\) is the annual production program for inspected products, units/year.
The annual economic effect in the second case is expressed by the formula:
\[ E = \left\{ \left[ \left( c_{\mathrm{zag}} + \sum_{i=1}^{M} c_{\mathrm{obr}_i} - c_{\mathrm{rd}} \right) + e_{\mathrm{n}} \left( k_{\mathrm{zag}} + \sum_{i=1}^{M} k_{\mathrm{obr}_i} \right) \right] \kappa_{\mathrm{br}_i} - \left[ \left( c_{\mathrm{k}} + c_{\mathrm{isp}} \cdot \kappa_{\mathrm{br}_i} \right) + e_{\mathrm{n}} \left( k_{\mathrm{k}} + k_{\mathrm{isp}} \cdot \kappa_{\mathrm{br}_i} \right) \right] \right\} \cdot Q_{\mathrm{g}} \ \text{rubles/year}, \tag{5} \]
where \(c_{\text{zag}}\) is the factory cost of the product being inspected (castings, forgings, rolled products), rubles/item; \(c_{\text{rl}}\) is the revenue from sale of a rejected product, rubles/item; \(k_{\text{zag}}\) is the specific capital investment required for manufacturing products, \(\dfrac{\text{rubles}}{\text{items/year}}\); \(\kappa_{\text{br}_i}\) is a coefficient accounting for the amount of repairable scrap detected by means of defectoscopy; \(c_{\text{isp}}\) is the current cost of repairing defects, rubles/item; \(k_{\text{isp}}\) is the specific capital investment associated with operations for repairing defects, \(\dfrac{\text{rubles}}{\text{items/year}}\).
Finally, in the third case, when defectoscopy of products (by means of accelerators) makes it possible to detect and eliminate defects and thereby increase their service life, the annual economic effect should be calculated by the formula:
\[ \mathcal{E} = \left\{ \left[ \frac{c_{\text{izd}} + e_{\text{n}} k_{\text{izg}}}{T_{\text{sl}_1}} + e_{\text{n}}\left(c_{\text{izd}} + e_{\text{n}} k_{\text{izg}}\right) \right] - \left[ \frac{c_{\text{izd}} + c_{\text{k}} + c_{\text{isp}}\cdot \kappa_{\text{br}_i}}{T_{\text{sl}_2}} + \frac{ e_{\text{n}}\left(k_{\text{izg}} + k_{\text{k}} + k_{\text{isp}}\cdot \kappa_{\text{br}_i}\right) }{T_{\text{sl}_2}} \right] + e_{\text{n}} \left[ c_{\text{izd}} + c_{\text{k}} + c_{\text{isp}}\cdot \kappa_{\text{br}_i} + e_{\text{n}}\left(k_{\text{izg}} + k_{\text{k}} + k_{\text{isp}}\cdot \kappa_{\text{br}_i}\right) \right] \right\} Q_{\text{g}}, \ \text{rubles/year}, \]
where \(c_{\text{izd}}\) is the full cost of the product being inspected (excluding inspection costs), rubles/item; \(k_{\text{izg}}\) is the specific capital investment required for manufacturing the inspected product, \(\dfrac{\text{rubles}}{\text{items/year}}\); \(T_{\text{sl}_1}\) and \(T_{\text{sl}_2}\) are the service life of the inspected product before and after the introduction of defectoscopic inspection, respectively, years.
In cases where defectoscopy of products, along with increasing service life, makes it possible to improve their reliability, formula (6) must take into account the saving in costs resulting from a reduction in the number of emergency repairs:
\[ \mathcal{E}_{\text{r}} = \left[ A_{\text{r}_1}\left(t_{\text{r}_1}\cdot c_{\text{p}_{\text{ch}}} + c_{\text{r}_1}\right) - A_{\text{r}_2}\left(t_{\text{r}_2}\cdot c_{\text{p}_{\text{ch}}} + c_{\text{r}_2}\right) \right] Q_{\text{g}} \ \text{rubles/year}, \tag{7} \]
where \(A_{\text{r}_1}\) and \(A_{\text{r}_2}\) are the average annual number of emergency repairs, or the probability of repairs (per product), before and after the introduction of defectoscopic inspection; \(c_{\text{p}_{\text{ch}}}\) is the reduced cost attributable to operation of the equipment during one hour in which production (work) should have been performed at the moment of failure of the inspected product, rubles/hour; \(c_{\text{r}_1}\) and \(c_{\text{r}_2}\) are the average costs of carrying out one emergency repair before and after the introduction of defectoscopic inspection, rubles/repair.