Title

Fréchet分配產品的壽命績效指標在逐步型II設限下之統計檢定程序

Translated Titles

A testing procedure for the lifetime performance index of products with Fréchet distribution under progressive type II censoring

DOI

10.6846/TKU.2015.00422

Authors

張文瑞

Key Words

逐步型II設限 ; Fréchet分配 ; 最大概似估計量 ; 製程能力指標 ; 檢定程序 ; progressive type II censoring ; Fréchet distribution ; maximum likelihood estimator ; process capability index ; testing procedure

PublicationName

淡江大學統計學系應用統計學碩士班學位論文

Volume or Term/Year and Month of Publication

2015年

Academic Degree Category

碩士

Advisor

吳淑妃

Content Language

繁體中文

Chinese Abstract

近年隨著時代的進步,科技產業的快速發展,使得高科技的產品不斷推陳出新,更由於市場的高度競爭,所以對於產品品質的要求也不斷提高,因此,提升產品品質變得相對重要。在實務上,製程能力指標(process capability indices, PCIs)被廣泛應用在評估製程的績效,進而不斷地提升產品品質及製程能力。 本研究假設產品服從Fréchet分配時,在逐步型II設限下,提出一些樞紐量,以對參數做區間估計,並使用壽命績效指標之最大概似估計量,探討其精確分配,在規格下限已知的情況下,發展出一個新的假設檢定程序,以判定壽命績效指標是否達到預定的能力水準。最後,我們用兩個數值實例去說明如何使用本研究提出的區間估計和檢定程序。

English Abstract

In recent years, the development of technology industry is pretty fast, and the high-tech products are also innovated quickly. Due to the highly competitive commercial market, the requirement of high quality products becomes much more important. In practice, process capability indices (PCIs) have been widely used to assess the performance of the process, and then continue to improve the product quality and process capability. This research is focusing on the lifetime of products which follow the Fréchet distribution. Some pivotal quantities are proposed to construct the interval estimation of parameters. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type II censored sample, and we use this estimator to develop the hypothesis testing algorithmic procedure for the process capability index in the condition of known lower specification limit. Finally, two practical examples are given to illustrate the proposed interval estimation and the testing algorithmic procedure to determine whether the process is capable.

Topic Category 基礎與應用科學 > 統計
商管學院 > 統計學系應用統計學碩士班
Reference
  1. [1] Balakrishnan, N. and Aggarwala, R. (2000), Progressive Censoring: Theory, Methods and Applications, Birkhauser Publisher, Boston.
    連結:
  2. [2] Boyles, R. A. (1991), The Taguchi capability index, Journal of Quality Technology, 23(1), pp. 17-26.
    連結:
  3. [3] Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988), A new measure of process capability: Cpm, Journal of Quality Technology, 20(3), pp.162-175.
    連結:
  4. [4] Cohen, A. C. (1963), Progressively Censored Samples in Life Testing, Technometrics, 5(3), pp. 327-339.
    連結:
  5. [5] Fisher, R. A. and Tippett, L. H. C. (1928), Limiting forms of the frequency distribution of the largest or small member of a sample, Proc. Cambridge Phil. Soc., 24, pp.180-190.
    連結:
  6. [7] Gill, M. H. and Gastwirth, J. L. (1978), A scale-free goodness-of-fit Test for the Exponential Distribution Based on the Gini Statistic, Journal of the Royal Statistical Society, Series B(Methodological), 40, pp. 350-357.
    連結:
  7. [9] Hong, C. W., Wu, J. W. and Cheng, C. H. (2008), Computational procedure of performance assessment of lifetime index of Pareto lifetime businesses based on confidence interval, Applied Soft Computing , 8(1), pp. 698-705.
    連結:
  8. [11] Kane, V. E. (1986), Process capability indices, Journal of Quality Technology, 18, pp. 41-52.
    連結:
  9. [12] Lawless, J. F. (2003), Statistical Models and Methods for Lifetime Data, 2nd Edition, John Wiley, New York.
    連結:
  10. [13] Mann, N. R. (1971), Best linear invariant estimation for Weibull parameters under progressive censoring, Technometrics, 13(3), pp.521-533.
    連結:
  11. [15] Pearn, W. L., Kotz, S. and Johnson, N. L. (1992), Distributional and inferential properties of process capability indices, Journal of Quality Technology, 24(4), pp. 216-231.
    連結:
  12. [16] Tong, L. I., Chen, K. S. and Chen, H. T. (2002), Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution, International Journal of Quality & Reliability Management, 19(7), pp. 812-824.
    連結:
  13. [17] Viveros, R. and Balakrishnan, N. (1994), Interval estimation of parameters of life from progressively censored data, Technometrics, 36(1), pp.84-91.
    連結:
  14. [18] Wu, C. C., Wu, S. F. and Chan, H.Y. (2006), MLE and the estimated expected test time for the two-parameter Gompertz distribution under progressive censoring with binomial removals, Applied Mathematics and computation, 181(3), pp.1657-1670.
    連結:
  15. [19] Wu, J. W., Lee, H. M. and Lei, C. L. (2007), Computational testing algorithmic procedure of assessment for lifetime performance index of products with two-parameter exponential distribution, Applied Mathematics and Computation, 190, pp. 116-125.
    連結:
  16. [20] Wu, S. F. (2010a), Interval estimation for the Pareto distribution based on the progressive Type II censored sample, Journal of Statistical Computation and Simulation, 80(4), pp.463-474.
    連結:
  17. [21] Wu, S. F. (2010b), Interval estimation for the two-parameter exponential distribution under progressive censoring, Quality & Quantity, 44(1), pp.181-189.
    連結:
  18. [22] Wu, S. F., Wu, C. C., Chen, Y. L., Yu, Y. R. and Lin, Y. P. (2010), Interval estimation of a two-parameter Burr-XII distribution under progressive censoring, Statistics: A Theoretical and Applied Statistics, 44(1), pp.77-88.
    連結:
  19. [23] Wu, S. J. and Chang C. T. (2003), Inference in the Pareto distribution based on progressive Type II censoring with random removals, Journal of Applied Statistics, 30(2), pp.163-172.
    連結:
  20. [24] Wu, S. J., Chen, D. H. and Chen, S. T. (2006), Bayesian inference for Rayleigh distribution under progressive censored sample, Applied Stochastic Models in Business and Industry, 22(3), pp.269-279.
    連結:
  21. [6] Fréchet, M. (1927), Sur la loi de probabilité de l'écart maximum, Ann. de la Soc. Polonaise de Math. (Cracow), 6, pp. 93-116.
  22. [8] Gumbel, E. J. (1958), Statistics of Extremes, Columbia University press, New York.
  23. [10] Juran, J. M. (1974), Journal Quality Control Handbook, 3rd Edition, McGraw-Hill, New York.
  24. [14] Montgomery, D. C. (1985), Introduction to statistical quality control, John Wiley and Sons, New York.