UDK 519.6
SILHOUETTE CRITERION FOR AUTOMATIC GROUPING ALGORITHM OF SPACESHIP ELECTRONIC COMPONENTS
V. I. Orlov, L. A. Kazakovtsev, I. S. Masich
Reshetnev Siberian State Aerospace University 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660037, Russian Federation
Due to the development of the space industry, expansion of functions of spacecrafts and increasing its service life, matter of its reliability are becoming very important. Therefore, it is necessary to provide a high quality of electronic components in space production and pay attention to the homogeneity of its specifications to ensure a high level of consistency of its work as the part of the device. This requires a complex control system, testing and automatic classification of arriving components, which aims to select components manufactured within the same production batch from providing components. Besides, the results of the selective destroying physical analysis can be extended to all batches of components, only being confident in homogeneity of this batch. This paper is devoted to one aspect of such a system – the definition of the estimated number of production batches in a composite party of components. The task of determination of number of groups is one of the most difficult aspects of data classification. There is significant amount of various criteria for evaluation of expected number of groups in literature today. We studied the effectiveness of various criteria, and concluded that the method based on the Silhouette criterion is very effective to solve the problem of automatic grouping, particularly for grouping of spacecraft electronic components on homogeneous production batches. We paid special attention to the “outliers” – elements, which characteristics are far from the characteristics of the major amount of classified elements. We made experimental verification of the method on real data and showed that the maximum of Silhouette criterion corresponds to the actual number of production batches in the examination selection, representing the combined batch collected from the elements made as a part of several homogeneous production lots. The proposed method for estimating the number of production lots is based on the test data from a specialized test center and does not require additional testing. Thus, this method is suitable for implementation in manufacturing process to improve the quality of spacecraft electronic components without considerable expenses. Keywords: silhouette criterion, clustering algorithm, electronic components, automatic grouping.
Keywords: silhouette criterion, clustering algorithm, electronic components, automatic grouping.
References

1. Kazakovtsev L. A., Antamoshkin A. N., Masich I. S. Fast deterministic algorithm for EEE components classification problems. IOP Conference Series: Materials Science and Engineering. 2015, Vol. 94. Article ID 012015. Doi: 10.1088/1757-899X/94/1/012015.

2. Fedosov V. V., Orlov V. I. [Minimal necessary extent of examination of microelectronic products at inspection test stage]. Izvestiya Vuzov. Priborostroenie. 2011, Vol. 54(4), P. 62–68 (In Russ.).

3. Kharchenko V. S., Yurchenko Yu. B. [Rating of faulttolerant onboard complexes frames at usage electronic components industry]. Tekhnologiya I konstruirovanie v elektronnoy apparature. 2003, No. 2, P. 3–10 (In Russ.).

4. Hamiter L. The History of Space Quality EEE Parts in the United States. ESA Electronic Components Conf., ESTEC (Noordwijk, The Netherlands, 12–16 Nov 1990 ESA SP-313).

5. Kirkconnell C. S. et al. High Efficiency Digital Cooler Electronics for Aerospace Applications Proc. SPIE 9070, Infrared Technology and Applications XL 90702Q (June 24, 2014).

6. Kuklin V. I, Orlov V. I., Fedosov V. V. [Results of operations of quality assurance of domestic electronic components for on-board equipment of spacecrafts in the period from January 2008 to June 2008]. VIII Rossiyskaya nauchno-tekhnicheskaya konferentsiya. Elektronnaya komponentnaya baza kosmicheskikh sistem [VIII Russian scientific and technical conference. Electronic components in space industry]. Moscow, 2009, P. 64–66 (In Russ.).

7. Fedosov V. V., Kuklin V. I., Orlov V. I., Islyaev Sh. N. Tekhnicheskiy otchet. Kosmicheskiy apparat “SESAT” so srokom aktivnogo funktsionirovaniya 10 let. Printsipy, metody i rezul’taty komplektatsii apparatury elektroradioizdeliyami. [Technical report. The SESAT spacecraft with a 10-year lifetime. Principles, methods and results of the electronic components complication]. FGUP “NPO PM im. akademika Reshetneva”, 1999, 408 p.

8. Perechen’ TsK-1/96. Izdeliya elektronnoy tekhniki, dopuskaemye dlya primeneniya v apparature kosmicheskogo apparata “Yamal” s 10-letnim srokom aktivnogo sushchestvovaniya [The list TsK-1/96. Electronic components, permitted for use in the Yamal spacecraft with a 10-year lifetime]. AO ITTs “Tsiklon” Publ., 1997, 90 p.

9. Reshenie № SST-TP-97006 o kvalifikatsii elektroradioizdeliy na sootvetstvie trebovaniyam kosmicheskogo apparata s 10-letnim srokom aktivnogo sushchestvovaniya (Redaktsiya 1-97) [Resolution № SST-TP-97006 – suitability qualification of electronic components
 for the spacecraft with the 10-year lifetime (Issue 1-97)]. AO ITTs “Tsiklon” Publ., 1997, 108 p.

10. Vernov S. N. (ed.) Model’ okolozemnogo kosmicheskogo prostranstva [Model of a near-earth space]. Moscow, MGU Publ., 1983, Vol. 3, 133 p.

11. Stoykost’ izdeliy elektronnoy tekhniki k vozdeystviyu faktorov kosmicheskogo prostranstva i elektricheskikh impul’snykh peregruzok: Spravochnik. T. XII. Termovakuumnye i elektricheskie vozdeystviya [Resistance of electronic components to the effects of space factors and electrical pulse overloads: A Handbook. Vol. XII. The thermal vacuum and electrical effects]. VNII “Elektronstandart” Publ., 1990, 162 p.

12. Pease R. L., Johnston A. H., Azarevich J. L. Radiation testing of semiconductor devices for space electronics. Proceeding of the IEEE. 1988, Vol. 76, Iss. 11. P. 1510–1526. Doi: 10.1109/5.90110.

13. Radiatsionnaya stoykost’ bortovoy apparatury i elementov kosmicheskikh apparatov. I Vsesoyuznaya nauchno-tekhnicheskaya konferentsiya. Materialy konferentsii [Radiation resistance of on-board equipment and the elements of the spacecraft. 1 All-Union Scientific and Technical Conference. Conference proceedings]. Tomsk, 1991, 257 p.

14. Sidorov N. A., Knyazev V. K. (eds.) Radiatsionnaya stoykost’ materialov radiotekhnicheskikh konstruktsiy: Spravochnik [Radiation resistance of radiotechnical material: Handbook]. Moscow, Sovetskoe radio Publ., 1976, 567 p.

15. Malyshev M. M., Malinin V. G., Kulikov I. V., Torgashov Yu. N, Uzhegov M. V. Metodologiya otsenki radiatsionnoy nadezhnosti IET v usloviyakh nizkointensivnykh ioniziruyushchikh izlucheniy. Sb. st. Radiatsionnonadezhnostnye kharakteristiki izdeliy elektronnoy tekhniki v ekstremal’nykh usloviyakh ekspluatatsii [Evaluation methodology of radiation resistance of electronic components at a low-intensity ionizing radiation. Dig. Radiation reliability of electronic products in extreme operating conditions.]. St. Petersburg, RNII “Elektronstandart” Publ., 1994, 96 p.

16. Myrova L. O., Chepizhenko A. Z. Obespechenie stoykosti apparatury svyazi k ioniziruyushchim i elektromagnitnym izlucheniyam [Ensuring stability of communications equipment to the ionizing and electromagnetic radiation]. Moscow, Radio i svyaz’ Publ., 1988, 296 p.

17. Kononov V. K., Malinin V. G., Ospishchev D. A., Popov V. D. Otbrakovka potentsial’no-nenadezhnykh integral’nykh mikroskhem s ispol’zovaniem radiatsionnostimuliruyushchego metoda Sb. st. Radiatsionno-nadezhnostnye kharakteristiki izdeliy elektronnoy tekhniki v ekstremal’nykh usloviyakh ekspluatatsii ekspluatatsii [Culling potentially unreliable integrated circuits using a radiation-stimulating method. Dig. Radiation reliability of electronic products in extreme operating conditions]. St. Petersburg, RNII “Elektronstandart” Publ., 1994, 96 p.

18. Kazakovtsev L. A., Antamoshkin A. N., Fedosov V. V. Greedy heuristic algorithm for solving series of EEE components classification problems. IOP Conference Series: Materials Science and Engineering. 2016, Vol. 122. Article ID 012011. Doi: 10.1088/1757-899X/122/1/012011.

19. Kazakovtsev L. A., Orlov V. I., Stupina A. A. [On distance metric for the system of automatic classification of the EEE devices by production batches]. Programmnye produkty i sistemy. 2015, No. 2, P. 124–129. Doi: 10.15827/0236-235X.110.124-129.

20. Davies D. L., Bouldin D. W. A Cluster Separation Measure. IEEE Transaction on Pattern Analysis and Machine Intelligence. 1979, PAMI-1 (2), P. 224–227.

21. Calinski T., Harabasz J. A dendrite method for cluster analysis. Communications in Statistics. 1974, Vol. 3, P. 1–27. Doi: 10.1080/03610927408827101.

22. Krzanowski W., Lai Y. A criterion for determining the number of groups in a dataset using sum of squares clustering. Biometrics. 1985, No. 44, P. 23–34.

23. Hartigan J. A. Clustering Algorithms. New York: Wiley, 1975, 369 p.

24. Tibshirani R., Walther G., Hastie T. Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society. 2001, Vol. 63, P. 411–423. Doi: 10.1111/1467-9868.00293.

25. Schwarz G. Estimating the Dimension of a Model. Annals of Statistics. 1978, Vol. 6 (2), P. 461–464. Doi: 10.1214/aos/1176344136.

26. Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control. 1974, Vol. 19 (6), P. 716–723. Doi: 10.1109/TAC.1974.1100705.

27. Rousseeuw P. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics. 1987, Vol. 20, P. 53–65.

28. Kaufman L. Finding groups in data: an introduction to cluster analysis. New York: Wiley, 1990, P. 368.

29. Koplyarova N. V., Orlov V. I. [About research of radio-electronic equipment diagnostics computer system on the basis of experimental data]. Vestnik SibGAU. 2014, No. 1(53), P. 24–30 (In Russ.).

30. Zinov’ev A. Yu. Vizualizatsiya mnogomernykh dannykh [Visualization of multidimensional data]. Krasnoyarsk, KGTU Publ., 2000, 168 p. (In Russ.).


Orlov Viktor Ivanovich – Cand. Sc., doctoral student, Department of System analysis and operations research,

Reshetnev Siberian State Aerospace University. E-mail: ttc@krasmail.ru.

Kazakovtsev Lev Aleksandrovich – Cand. Sc., docent, Department of System analysis and operations research,

Reshetnev Siberian State Aerospace University. E-mail: levk@bk.ru.