Journal of Mechanical Science and Technology

  • 제16권1호
  • /
  • Pages.60-74
  • /
  • 2002
  • /
  • 1738-494X(pISSN)
  • /
  • 1976-3824(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
권호 표지

An Attempt to Model Distributions of Machined Component Dimensions in Production

  • Cogun, Can (Mechanical Engineering Department, Gazi University) ;
  • Kilinc, Biinyamin (Mechanical Engineering Department, Gazi University)
  • 발행 : 2002.01.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, normal, log-normal, triangular, uniform. Weibull, Erlang and unit beta probability density functions are tried to represent the behaviour of frequency distributions of workpiece dimensions collected from various manufacturing firms. Among the distribution functions, the unit beta distribution function is found to be the best fit using the chi-square test of fit. An attempt is made for the adoption of the unit beta model to x-bar charts of quality control in manufacturing. In this direction, upper and lower control limits (UCL and LCL) of x-bar control charts of dimension measurements are estimated for the beta model, and the observed differences between the beta and normal model control limits are discussed for the measurement sets.

키워드

참고문헌

  1. Bai, D. S. and Chois, I. S., 1995, 'Xbar-Control and R-Control Charts for Skewed Populations,' Journal of Quality Technology, 27, (2), 120-131
  2. Bain, L. J., 1978, 'Statistical Analysis of Reliability and Life Testing,' Marcel Dekker, New York
  3. Balakrishnan, N. and Kocherlakota, S., 1986, 'Effects of Non-normality on Xbar Charts-Assignable Cause Model,' Sankhya-The Indian Journal of Statistics Series B, 48, 439-444
  4. Bennet, G., 1964, 'The Application of Probability Theory to the Allocation of Engineering Tolerances,' Ph. D. Thesis, University of New South Wales, Australia
  5. Bjorke, Q., 1978, 'Computer Aided Tolerancing,' Tapir Publishers, Trondheim, Norway
  6. Borror, C. M., Montgomery, D. C. and Runger, G. C., 1999, 'Robustness of the EWMA Control Chart to Non-Normality,' Journal of Quality Technology, 31, (3), 309-316
  7. Bury, K. V. , 1975, 'Statistical Models in Applied Science,' John Wiley, New York
  8. Burr, I. W., 1958, 'Some Theoretical and Practical Aspects of Tolerances for Mating Parts,' Quality Control, 15, (3), 18
  9. Chan, L. K., Hapuarachi, K. P. and MacPherson, B. D., 1988, 'Robustness of Xbar and R-Charts,' IEEE Transactions on Reliability, 37, (1), 117-123 https://doi.org/10.1109/24.3728
  10. Choobineh, F. and Ballard, J. L., 1987, 'Control Limits of QC Charts for Skewed Distributions Using Weighted Variance,' IEEE Transactions on Reliability, 36, (4), 473-477 https://doi.org/10.1109/TR.1987.5222442
  11. Cooke, P., 1979, 'Statistical Inference For Bounds of Random Variables,' Biometrica, 66, 367-374 https://doi.org/10.1093/biomet/66.2.367
  12. Crafts, J. W., 1952, 'Assembly Tolerance Problem,' Engineer (London), 206, 918-928
  13. Doyle, L. E., 1951, 'Statistical Aids for Tool Engineers,' Tool Engineer, 26, (1), 48-51
  14. Fortini, E. T., 1956, 'Dimension Control in Design,' Machine Design, 28, (28), 82-89
  15. Fortini, E. T., 1967, Dimensioning For Interchangeable Manufacture, Industrial Press Inc., New York
  16. Gibson, J., 1951, A New Approach to Engineering Tolerances, The Machinery Publishing Co. Ltd., Brighton and London
  17. Gladman, C. A., 1959, 'Techniques For Applying Probability to the Tolerancing of Machined Dimensions,' C. S. I.R. D. Australian National Std. Lab. Tech. Paper No.11
  18. Gladman, C. A., 1980, 'Applying Probability in Tolerance Technology,' The Institution of Engineers, 5, (2), 82-88
  19. Haridy, A. M. A. and El-Shabrawy, A. Z., 1996, 'The Economic Design of Cumulative Sum Charts Used to Maintain Current Control of Non-Normal process Means,' Computers in Industrial Engineering, 31, (3-4), 783-790 https://doi.org/10.1016/S0360-8352(96)00242-2
  20. He, J. R., 1991, 'Estimating the Distributions of Manufactured Dimensions With the Beta Probability Density Fuction,' Int. J. Mach. Tools Manuf., 31, (3), 383-396 https://doi.org/10.1016/0890-6955(91)90083-F
  21. Ishikawa, K., 1976, 'Guide to Quality Control,' Asia Productivity Organisation, Tokyo, 9
  22. Kilinc, B., 1999, 'Computer Aided Statistical Investigation on the Variation of Dimensions of Workpieces Machined Under the Same Machining Conditions,' M. Sc. Thesis, Gazi University, Ankara
  23. Lashkari, R. S. and Rahim, M. A., 1982, 'An Economic Design of Cumulative Sum Charts to Control Non-Normal Process Means,' Computers in Industrial Engineering, 6, (1), 1-18 https://doi.org/10.1016/0360-8352(82)90021-3
  24. Mansoor, E. M., 1960, 'The Dimension Analysis of Engineering Designs,' M. Sc. Thesis, University of Melbourne
  25. Mansoor, E. M., 1964, 'The Application of Probability to Tolerances Used in Engineering Designs,' Proc. Instn. Mech. Engrs., 178, (1), 29-51 https://doi.org/10.1243/PIME_PROC_1963_178_007_02
  26. Nelson, P. R., 1979, 'Control Charts for Weibull Processes with Standards Given,' IEEE Transactions on Reliability, 28, (4), 283-288 https://doi.org/10.1109/TR.1979.5220605
  27. Nelson, L. S., 1984, 'The Shewhart Control Chart: Tests For Special Causes,' J. of Quality Technology, 16, (4), 237-239
  28. Padget, W. J. and Spurrier, J. D., 1990, 'Shewhart Type Charts for Percentiles of Strength Distributions,' Journal of Quality Technology, 22, (4), 283-288
  29. Shainin, D., 1949, 'Cost-cutting Chance Laws Can Control Design Tolerances,' Machine Design, 21, (6), 130-140
  30. Shilling, E. G. and Nelson, P. R., 1976, 'The Effect of Non-Normality on the Control Limits of X-bar Charts,' Journal of Quality Technology, 8, (4), 183-188
  31. Shore, H., 1998, 'A New Approach to Analysing Non-Normal Quality data with Application to Process Capability Analysis,' Int. J. Prod. Res., 36, (7), 1917-1933 https://doi.org/10.1080/002075498193039
  32. STATGRAF, 1993, Statistical Graphics System by Statistical Graphics Corporation (STSC Inc.)-Plus Ware Product, ver. 5.0
  33. Zhang, H. C. and Huq, M. E., 1992, 'Tolerancing Techniques: The State-of-the-Art,' Int. J. Prod. Res., 30, (9), 2111-2135 https://doi.org/10.1080/00207549208948140