Muhamad Safiih Lola, Nurul Hila Zainuddin, Mohd Noor Afiq Ramlee, Hizir Sofyan


The bootstrap approach on control limit has provided a solution in solving uncertainty estimation problem in control chart performance. However, the limitation of this standard chart has shown to be less efficient and invalidation at certain magnitude shift, especially the monitored sample data is assumed from skewed family distribution. Thus, in this study, a double bootstrap base-model and its control limit is developed in order to improve the efficiency and decrease the invalidation chart performance. In order to test the performance of proposed model, a simulation study using Average Run Length (ARL) and Type II Error rate were implemented. The result has shown that the proposed chart is sensitive and effective in detecting the shift process for small and medium size of skewed sample data. Also, it has found that the proposed chart shown to has better performance on large magnitude shift. The performance of the proposed model was investigated further using sukuk volatility data at Bursa Malaysia. The result revealed that the double bootstrap control chart is sensitive to small shifts process when it can detect changes in the volatility faster. In other words, it is efficient in monitoring the shifts process. Thus, the proposed model could help the traders in making a new decision, for example, either save/hold for a certain period, sell or buy the sukuk certificate.  


Double bootstrap, estimation, control chart, simulation, sukuk

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Nembhard, D. A. and Nembhard, H. B. 2000. A Demerits Control Chart for Autocorrelated Data. Quality Engineering. 13(2): 179-190.

Khoo, M. B. C., Teh, S. Y., Chew, X. Y. &Teoh, W. L. 2015. Standard Deviation of the Run Length (SDRL) and Average Run Length (ARL) Performance of EWMA and Synthetic Charts. International Journal of Engineering and Technology. 7(6): 513-516.

Koshti, V. V. and Kalgonda, A. A. 2011. A Study of Robustness of the Exponentially Weighted Moving Average Control Chart: A Simulation Approach. International Journal of Advanced Scientific and Technical Research. 1(2): 519-525.

Shao, Y. E. and Hou, C. D. 2011. A Combined MLE and EWMA Chart Approach to Estimate the Change Point of a Gamma Process with Individual Observations. International Journal of Innovative Computing, Information and Control. 7(5): 2109-2122.

Castagliola, P. and Tsung, F. 2005. Autocorrelated SPC for Non-normal Situations. Quality and Reliability Engineering International. 21: 131-161.

Maravelakis, P., Panaretos, J. and Psarakis, S. 2005. An Examination of the Robustness to Non-normality of the EWMA Control Charts for Dispersion. Communication in Statistics-Simulation and Computation. 34: 1069-1079.

Khoo, M. B. C and Atta, A. M. A. 2008. An EWMA Control Chart for Monitoring the Mean of Skewed Populations using Weighted Variance. Proceedings of the IEEE International Conference on Industrial Engineering and Engineering Management, Singapore. 218-223.

Yourstone, S. A. and Zimmer, W. J. 1993. Non-normality and the Design of Control Charts for Averages. Decision Sciences. 23: 1099-1113.

Edopka, I. W. and Ogbeide, E. M. 2013. Bootstrap Approach Control Limit for Statistical Quality Control. International Journal of Engineering Science Invention. 2(4): 2319-6734.

Abbasi, B. and Guillen, M. 2013. Bootstrap Control Chart in Monitoring Value at Risk in Insurance. Expert System with Application. 40: 6125-6133.

Chatterjee, S. and Qiu, P. 2009. Distribution-free Cumulative Sum Control Charts Using Bootstrap-based Control Limits. The Annals of Applied Science. 3(1): 349-369.

Z. Nurul Hila and L. Muhamad Safiih. 2016. The Performance of BB-MCEWMA Model: Case Study on Sukuk Rantau Abang Capital Berhad, Malaysia. International Journal of Applied Business and Economic Reserach. 14(2): 639-653.

Z. Nurul Hila, L. Muhamad Safiih and K. Nur Shazrahanim. 2015. The Performance of BB-MCEMA Model: Case Study on Normal and Non-normal Data. Social Sciences Reserach Journal. 4(2): 155-163.

L. Muhamad Safiih and Z. Nurul Hila. 2016. Monitoring Volatility Point of Sukuk Ijarah Using a Hybrid MCEWMA Control Chart: Double Bootstrap Approach. Middle-East Journal of Scientific Research. 24(6): 1907-1912.

Z. Nurul Hila, L. Muhamad Safiih. 2016. The Accuracy of Two-sided Confidence Interval Algorithm: An Alternative of Double Bootstrap Approach. International Mathematical Forum. 11(170: 845-851.

Vinod, H. D. 1995. Double Bootstrap for Shrinkage Estimators. Journal of Econometrics. 68: 287-302.

Efron, B. 1990. More Efficient Bootstrap Computations. Journal of the American Statistical Association. 85(409): 79-89.

Martin, M. A. 1990. On the Double Bootstrap. Technical Report No. 347.

Hall, P. and Martin, M. A. 1998. On Bootstrap Resampling and Iteration. Oxford Journa. 75(4): 661-671.

Bisgaard, S. and Kulachi, M. 2005. Quality Quandaries: The Effect of Autocorrelation on Statistical Process Control Procedures. Quality Engineering. 17(3): 481-489.

Neubauer, A. S. 1997. The EWMA Control Chart: Properties and comparison with Other Quality-control Procedures by Computer Simulation. Clinical Chemistry. 43(4): 594-601.

Margario, T. M., Conerly, M. D., Woodall W. H. and Drake L. G. 1995. Alarm Rates for Quality Control Chart. Statistic and Probability Letters. 24: 219-224

Lucas, J. M. &Saccucci, M. S. 1990. Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements. Technometrics. 32(1): 1-12.

Ramjee, R., Crato, N. & Ray, B. K. 2002. A Note Moving Average Forecasts of Long Memory Processes with an Application to Quality Control. International Journal of Forecasting. 18: 291-297.

Cox, D. R. 1961. Prediction by Exponentially Weighted Moving Averages and Related Methods. Journal of the Royal Statistical SocietySeries B (Methodological). 23(2): 414-422.

Psarakis, S. and Papleonida, G. E. A. 2007. SPC Procedures for Monitoring Autocorrelated Processes. Quality Technology and Quantitaive Management. 4(4): 501-540.

Apley, D. W. and Lee, H. C. 2003. Design of Exponentially Weighted Moving Average Control Charts for Autocorrelated Process with Model Uncertainty. Technometrics. 45(3): 187-198.

Nembhard, H. B. and Mastrangelo, C. M. 1998. Integrated Process Control for Startup Operations. Journal of Quality Technology. 30(3): 201-211.

Efron, B. and Tibshirani, R. J. 1993. An Intoduction to the Bootstrap. Chapman & Hall., New York .

Efron, B. 1979. Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics. 7(1): 1-26

Lola, M. S. and Zainuddin, N. H. 2016. The Performance of Double Bootstrap Method for Large Sampling Sequence. Open Journal of Statistics. 6: 805-813.

Akhmad, F., N. A. Ibrahim, Isa D. and Mohd. Rizam, A.B. 2003. Interval Selisih Rata-Rata DenganMetode Bootstrap Persentil. JurnalTeknikIndustri. 8(4): 110-117.

Aparisi, F. and García-Díaz, J. 2007. Design and Optimization of EWMA Control Charts for In-control, Indifference and Out-of-control Regions. Computers and Operations Research. 34: 2096-2108.

Ye, N., Vilbert, S. and Chen, Q. 2003. Computer Intrusion Detection Detection Through EWMA for Autocorrelated and Uncorrelated Data. IEEE Transaction on Reliability. 52(1): 75-82.

Knoth, S. 2005. Accurate ARL Computation for EWMA-S2 Control Chart. Statistics and Computating. 15: 341-352.

Fu, J. C., Spiring, F. A. and Xie, H. 2002. On the Average Run Lengths of Quality Control Schemes using a Markov Chain Approach. Statistics and Probability Letters. 56: 360-380.

Tosasuku, J. Budsaba, K. and Volodin, A. 2009. Dependent Bootstrap Confidence Intervals for a Population Mean. Thailand Statistician. 7(1): 43-51.

Serel, D. A. and Maskowitz, H. 2008. Joint Economic Design of EWMA Control Charts for Mean and Variance. European Journal of Operational Research. 184: 157-168.

Lola, M. S., Alwi, W.S.W. and Zainuddin, N. H. 2016. Sample Selection Model with Bootstrap (BPSSM) Approach: Case Study of the Malaysian Population and Family Survey. Open Journal of Statistics. 6: 741-748.

Lola, M. S. 2013. Fuzzy Parametric Sample Selection Model: Monte Carlo Simulation Approach. Journal of Statistical Computation and Simulation. 83(6): 992-1006.

Okpara, G. C. 2010. Stock Market Prices and the Random Walk Hypothesis: Further Evidence from Nigeria. Journal of Economics and International Finance. 2(3): 049-057.

Shafi, M. 2014. Testing of Market Efficiency in the Weak-Form Taking CNX NIFTY as a Benchmark Index: A Study. Researchjournali’s Journal of Finance. 2(2): 1-20.



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