Một phương pháp thống kê mới cho thiết kế và phân tích độ dung sai thành phần

Journal of Industrial Engineering International - Tập 13 - Trang 59-66 - 2016
Mohammad Mehdi Movahedi1, Mohsen Khounsiavash2, Mahmood Otadi3, Maryam Mosleh3
1Department of Management, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran
2Department of Electrical, Biomedical, and Mechatronics Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran

Tóm tắt

Việc xác định độ dung sai do các kỹ sư thiết kế thực hiện để đáp ứng nhu cầu của khách hàng là điều kiện tiên quyết để sản xuất các sản phẩm chất lượng cao. Các kỹ sư thường sử dụng sách hướng dẫn để thực hiện xác định độ dung sai. Trong khi việc sử dụng các phương pháp thống kê cho độ dung sai không phải là điều mới, các kỹ sư thường sử dụng các phân phối đã biết, bao gồm cả phân phối chuẩn. Tuy nhiên, nếu phân phối thống kê của biến số nhất định là không rõ, một phương pháp thống kê mới sẽ được áp dụng để thiết kế độ dung sai. Trong bài báo này, chúng tôi sử dụng phân phối lambda tổng quát để thiết kế và phân tích độ dung sai thành phần. Chúng tôi sử dụng phương pháp phần trăm (PM) để ước lượng các tham số phân phối. Các phát hiện cho thấy rằng, khi phân phối của dữ liệu thành phần không rõ ràng, phương pháp được đề xuất có thể được sử dụng để thúc đẩy thiết kế độ dung sai thành phần. Hơn nữa, trong trường hợp các bộ lắp ghép, có thể áp dụng độ dung sai rộng hơn cho mỗi thành phần với cùng hiệu suất mục tiêu.

Từ khóa

#độ dung sai #phương pháp thống kê #phân tích thành phần #phân phối lambda tổng quát #phương pháp phần trăm

Tài liệu tham khảo

Armillotta A, Hartmann W (2015) Force analysis as a support to computer-aided tolerancing of planar linkages. Mech Mach Theory 93:11–25 Bigerelle M, Najjar D, Fournier B, Rupin N, Iost A (2006) Application of lambda distribution and bootstrap analysis to the prediction of fatigue lifetime and confidence intervals. Internet J Fatigue 28:223–236 Chandra MJ (2001) Statistical quality control. CRC Press LLC, 5–53 Delaney HD, Vargha A (2000) The effect on non-normality on student’s two-sample t-test. The annual meeting of the American educational research Association, New Orlean Dengiz B (1988) The generalized lambda distribution in simulation of m/m/1 queue systems. J Fac Eng Arch Gazi Univ 3:161–171 Devor RE, Tsong-How Chang, Sutherland JW (2007) Statistical quality design and control. Pearson Prentice hall, Upper saddle river, pp 366–404 Devroye L (1996) Random variant generation in one line of code. In: Charnes JM, Morrice DJ, Brunner DT, Swain JJ, eds. Proceedings of the Winter Simulation Conference. San Diego, CA, USA, December 8–11. Association for Computing Machinery, NY, pp 265–272 Filliben JJ (1975) The probability plot correlation coefficient test for normality. Technometrics 52:111–117 Fournier B, Rupin N, Bigerelle M, Najjar D, Iost A (2006) Application of the generalized lambda distribution in a statistical process control methodology. J Process Control 16:1087–1098 Fournier B, Rupin N, Bigerelle M, Najjar D, Iost A, Wilcox R (2007) Estimating the parameters of a generalized lambda distribution. Comput Stat Data Anal 51:2813–2835 Freimer M, Mudholkar S, Kollia G, Lin TC (1988) A study of the generalized Tukey Lambda family. Common Stat Theor Methods 17:3547–3567 Ganeshan R (2001) Are more supplier better? Generating the Gau and Ganeshan procedure. J Oper Res Soc 52:122–123 George J. Kaisarlis. (2012). A systematic approach for geometrical and dimensional tolerancing in reverse engineering, reverse engineering. Recent Advances and Applications Gilchrist W (2000) Statistical Modeling with Quantile Function. CRC Press, Boca Raton Ginsberg Robert H (2013) Outline of tolerancing from performance specification to toleranced drawings. Hughes Aircr Co Opt Eng 20(2):175–180 Harrell FE, Davis CE (1982) A new distribution free quantile estimator. Biometrika 69:635–640 Hasenauer D (2013) Optical design tolerancing, a key to product cost reduction. Synopsys, Inc. 700 East Middlefield Road, Mountain View, CA 94043, www.synopsys.com Hoaglin DC (1975) The small-sample variance of the Pitman location estimators. J Am Stat Assoc 52:880–888 Hoecke AV (2016) Tool risk setting in statistical tolerancing and its management in verification, in order to optimize customer’s and supplier’s risks. 14th CIRP Conference on Computer Aided Tolerancing (CAT), Procedia CIRP, 43, 250–255 Jean-Marc J (2016) Process Tolerancing: a new approach to better integrate the truth of the processes in tolerance analysis and synthesis. 14th CIRP Conference on Computer Aided Tolerancing (CAT), Procedia CIRP, 43, 244–249 Joiner BL, Rosenblatt JR (1971) Some properties of the range in samples from Tukey’s symmetric lambda distribution. J Am Stat Assoc 66:394 Karian ZA, Dudewicz EJ (1999) Fitting the generalized lambda distribution to data: a method based on percentiles. Commun Stat Simul Computat 28:793–819 Karian ZA, Dudewicz EJ (2000) Fitting statistical distributions. The generalized lambda distribution and generalized bootstrap methods. CRC Press, Boca Raton Korn EL, Miothorne D, Graubard BJ (1997) Estimating interpolated percentiles from grouped data with large samples. J Off Stat 13:385–399 Lam H, Bowman KO, Shenton LR (1980) Remarks on the generalized Tukey’s lambda family of distributions. In: Proc. ASA, Statist. Comput. Sec. Houston, Texas, August, 11–14, 134–139 Macko M, Ilić S, Jezdimirović M (2012) The influence of part dimensions and tolerance size to trigger characteristics. Strojniški vestnik J Mech Eng 58(6):411–415 Movahedi MM, Lotfi MR, Nayyeri M (2013) A solution to determining the reliability of products: using generalized lambda distribution. Res J Recent Sci 2(10):41–47 Najjar D, Bigerelle M, Lefebvre C, Lost A (2003) A new approach to predict the pit depth extreme value of a localized corrosion process. Isij 43:720–725 Nasser A, Aljazar L (2005) Generalized lambda distribution and estimation parameters. The Islamic University of Gaza, Deanery of Higher Studies, Faculty of Science, Department of Mathematics, Master of Science thesis, Supervised by Professor: Mohammed S. Elatrash Nili Ahmadabadi M, Farjami Y, Bameni Moghadam M (2012) A process control method based on five-parameter generalized lambda distribution. Qual Quant, Springer Science + Business Media B.V. 46, 1097–1111 Ozturk A, Dale RF (1982) A study of fitting the generalized lambda distribution to solar radiation data. J Appl Meteorol 21:995–1004 Ramberg J, Schmeiser B (1974) An approximate method for generating asymmetric random variables. Commun ACM 17(2):78–82 Ramberg J, Dudewicz E, Tadikamalla P, E. Mykytka, E. (1979) A probability distribution and its uses in fitting data. Techno metrics 21(2):201–214 Rochan R, Upadhyay Ofodike A, Ezekoye (2008) Treatment of design fire uncertainty using quadrature method of moments. Five Saf J 43:127–139 Sampath Kumar R, Alagumurthi N, Ramesh R (2009) Optimization of design tolerance and asymmetric quality loss cost using pattern search algorithm. Int J Phys Sci 4(11):629–637 Sarabia JM (1996) A hierarchy of Lorenz curves based on generalized Tukeys lambda distribution. Econom Rev 16:305–320 Schmeiser BW, Deutsch SJ (1977) Quantile estimation from grouped data: the cell midpoint. Commun Stat Simul Computat 6:221–234 Shannon RR (2013) Tolerancing techniques. Optical Sciences Center University of Arizona Tucson, Arizona, pp 36.1–36.12 Shapiro SS, Wilk MB (1965) An analysis of variance test for normality (complete samples). Biometrika 52:591–611 Tarsitano A (2005) Estimation of the Generalized Lambda Distribution Parameters for Grouped Data. Taylor & Francis Inc, Commun Stat Theory Methods 34:1689–1709 Tukey JW (1962) The future of data analysis. Ann Math Stat 33(1):1–67 Wadsworth HD, Stephens KS, Godfrrey AB (2002) Modern methods for quality control and improvement. Wiley, New York, pp 311–337 Weckenmann A, Hartmann W (2015) A model- and simulation-based approach for tolerancing and verifying the functional capability of micro/nano-structured workpieces. Measurement 76:70–79 Wheeler DL, Cavalier TM, Lehtihet EA (1999) An implicit enumeration approach to probabilistic tolerance allocation under conventional tolerance control. Int J Prod Res 37:3773 Zhang HC, Hook ME (1992) Tolerancing technique: the state-of-the art. Int J Prod Res 30:2111