The Lyapunov Exponent Variance of an Electronic Manufacturing Enterprise’s Daily Qualified Rate Time Series by Improved Small Data Sets Approach

Abstract:

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.

• Periodical: Applied Mechanics and Materials (Volume 197)
• Pages: 271-277
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.197.271
• Online since: September 2012
• Authors: Zhu Ping Gong
• Keywords: Daily Qualified Rate, Lyapunov Exponent, Small Data Sets, Time Series

References

[1] Wolf A, Swift J B, Swinney H L, et al. Determining lyapunov exponents from time series. Physica D, 1985, 16 (2) : 285-371.

DOI: 10.1016/0167-2789(85)90011-9

[2] Ground F, Diebner H H, Sahle S. A robust, locally interpretable algorithm for Lyapunov exponents. Chaos, Solitions and Fractals, 2003, 16 (5): 841-852.

DOI: 10.1016/s0960-0779(02)00479-4

[3] Snao M, Sawada Y. Measurement of lyapunov spectrum from a chaotic time series. Physical review Letters, 1985, 55 (10): 1082-1085.

DOI: 10.1103/physrevlett.55.1082

[4] Rosenstein M T, Collins J J, and De luca C. J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D, 1993, 65: 117-134.

DOI: 10.1016/0167-2789(93)90009-p

[5] Hai-feng Liu, Zheng-hua Dai, Wei-feng Li, Xin Gong, Zun-hong Yu. Noise rebust estimates of the largest Lyapunov exponent. Physics Letters A 341 (2005): 119-127.

DOI: 10.1016/j.physleta.2005.04.048

[6] Fraser A. M, Swinney H L. Independent coordinates for strange attractors from mutual information. Physical Review A, 1986, 33 (2): 1134-1140.

DOI: 10.1103/physreva.33.1134

[7] Kraskov A, Stogbauer H, Grassberger P. Estimating mutual information. Physical Review E, 2004, 69 (9): Art No. 066138 Part 2.

DOI: 10.1103/physreve.83.019903

[8] Grassberger P, Procaccia I, Estimation of the Kolmogorov entropy from a chaotic signal. Physical Review A, 1983, 28: 2591-2593.

DOI: 10.1103/physreva.28.2591

[9] Grassberger P. An optimized box-assisted algorithm for fractal dimensions. Physics Letters A, 1990, 148: 63-68.

DOI: 10.1016/0375-9601(90)90577-b

[10] Grassberger P. On the Hausdorff dimension of fractal attractors. Stat J Phys, 1981, 26: 173-179.

DOI: 10.1007/bf01106792