ECONOMIC-STATISTICAL DESIGN OF CUSUM CONTROL CHARTS UNDER EXPONENTIAL SHOCK MODEL

Faezeh Najafi; Mohammad  Bameni Moghadam; Farzaneh  Najafi

Faezeh Najafi Allameh Tabataba’I University
Mohammad Bameni Moghadam Allameh Tabataba’I University
Farzaneh Najafi Sharif University of Technology

Keywords: Economic statistical design. Cumulative control chart. Exponential shock model.

Abstract

In a wide range of industrial applications, it is desirable that processes result in fault-free products. The manufacturing process must have limited variability around the target value for the product. In a process where a non-random factor leads to a change in the process under control, the out-of-control process is said to be the result of a process out of control of a defective product. Random agents are also caused by the accumulation of a number of small and unavoidable deviations that in the statistical quality control process, the random factor-affected process is usually considered as the process under control. The control chart discussed in this article is a cumulative control chart that is plotted by summing the pre-self statistical samples and comparing the result with the permissible control boundary detects how the process status is used to identify cost variables. Waiting time is the unit of time and cost of identifying the cause deviation as well as the decision variables that include sample size, sampling interval, and cumulative control chart decision distance, and reference value, economic statistical design. In this paper, the econometric design of control charts is performed under the cost model of Lorenzen and Vance.This paper deals with the economic performance of the cumulative control chart and compares it with the Schuharti control chart. The economic performance of the cumulative assembly control charts is more appropriate. It is necessary to explain the distribution mechanism of the exponential distribution process failure and all calculations are programmed with R software.

Author Biographies

Faezeh Najafi, Allameh Tabataba’I University

Master Student of Socio-Economic Statistics, Allameh Tabataba’I University, Tehran, Iran.

Mohammad Bameni Moghadam, Allameh Tabataba’I University

Professor, Department of statistics Faculty of Mathematical Science and Computer, Allameh Tabataba’I University.

Farzaneh Najafi, Sharif University of Technology

Bachelor Student of Computer Science at Sharif University of Technology, Tehran, Iran.

References

Aghabeig D. and Moghadam M. (2014). “Economic design of -control charts under generalized exponential shock models with uniform sampling intervals,” European Online Journal of Natural and Social Sciences, vol. 2, no. 3, 2014.

Albloushi T., Suwaidi A., Zarouni N., Abdelrahman A., and Shamsuzzaman M. (2015). “Design of and R control charts for monitoring quality of care for hypertension,” in Proceedings of the 5th International Conference on Industrial Engineering and Operations Management (IEOM '15), pp. 1–5, Dubai, United Arab Emirates, March 2015.

Caballero-Morales S. O. (2013). Economic statistical design of integrated X-bar- S control chart with preventive maintenance and general failure distribution,” PLoS ONE, vol. 8, no. 3, Article ID e59039, 2013.

Crosier, R.B. (1986). A new two-sided cumulative sum quality control scheme. Technometrics, 28, 187–194.

Duncan, A. J. (1956). The economic design of X charts used to maintain current control of a process , Journal of the American Statistical Association, 51, 228–242.

Faraz A. and Saniga E. (2013). “Multi objective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an Application to X and S2 Charts,” Quality and Reliability Engineering International, vol. 29, no. 3, pp. 407–415, 2013.

Haq A., Brown J. & Moltchanova E. (2014). “New exponentially weighted moving average control charts for monitoring process mean and process dispersion”, Quality and Reliability Engineering International, Vol. 31(8), pp. 1587-1610, 2014.

Heydari A.A., Bameni Moghadam M. and Eskandari F (2016). An Extension of Banerjee and Rahim Model in Economic and Economic-Statistical Designs for Multivariate Quality Characteristics under Burr XII Distribution. Communications in Statistics -Theory and Methods,DOI:10.1080/03610926.2016.1140782.

Ho, C. (1994). Economic design of control charts: a literature review for 1981-1991, Journal of Quality Technology, 26, 39–53.

Kasarapu V. and Vommi B. (2013). “Economic design of chart using differential evolution,” International Journal of Emerging Technology and Advanced Engineering, vol. 3, no. 4, pp. 541–548, 2013.

Katebi, M., Seif A. and Faraz A. (2016). Economic and Economic-Statistical designs of the T2 control charts with SVSSI sampling scheme. Communications in Statistics -Theory and Methods. 46 (20):10149-10165, DOI:10.1080/03610926.2016.1231823.

Keats, J.B. and Simpson, J.R. (1994) Comparison of the X and the CUSUM control charts in an economic model. Economic Quality Control, 9, 203–220.

Lai M., Chen C. and Hariguna T. (2017). A bivariate optimal replacement policy with cumulative repair cost limit for a two-unitsystem under shock damage interaction,Brazilian Journal of Probability and Statistics, 2, 353-372.
Lorenzen T. J. and Vance L. C. (1986). The Economic Design of Control Charts: A Unified Approach, Technometrics, 28(1), 3-10. Roberts, S.W, (1959). Control chart tests based on geometric moving averages, Technometrics, 42(1), 97–102.

Mahadik S. B. (2013). Variable sample size and sampling interval 𝑋̅ charts with runs rules for switching between sample sizes and sampling interval lengths, Quality and Reliability Engineering International, 29(1):63-76.
Mahadik S. B. (2013). 𝑋̅ Charts with Variable Sample Size, Sampling Interval, and Warning Limits, Quality Reliability Engineering International, 29(4):535-544.

Rafiey S.R., Ghaderi M.M., and Bameni Moghadam M. (2016). A Generalized Versionof Banerjee and Rahim Model In Economicand Economic Statistical Designs of Multivariate Control Charts under Generalized Exponential Shock Model, Communications in Statistics -Theory and Methods.DOI:10.1080/03610926.2016.1171354.

Ridwan A. Sanusi, Mu'azu Ramat Abujiya , Muhammad Riaz , Nasir Abbas (2017). Combined Shewhart CUSUM charts using auxiliary variable. Journal of Computers and Industrial Engineering archive, 105(C), 329-337.

Saniga, E.M. (1977). Joint economically optimal design of X and R control charts. Management Science, 24, 420–431.

Seif, A. Faraz, and E. Saniga. (2015). Economic statistical design of the VP X control charts for monitoring a process under non-normality,” International Journal of Production Research, vol. 53, no. 14, pp. 4218–4230, 2015.

Shamsuzzaman M., Alsyouf I., and Ali A. (2015). “Optimization design of Xfi & EWMA control chart for minimizing mean number of defective units per out-of-control case,” in Proceedings of the IEEE International Conference on Industrial Engineering and Engineering Management, IEEM 2015, pp. 391–395, Singapore.

Shrivastava D., Kulkarni MS.,Vrat P. (2016). “Integrated design of preventive maintenance and quality control policy parameters with CUMSUM chart”, Int J Adv Manuf Technolgy, Vol. 82(9),pp. 2101-2112, 2016.

Sultana I., Ahmed I., Azeem A. & Sarkar N. (2016). “Economic Design of Exponentially Weighted Moving Average Chart with Variable Sampling Interval at Fixed Times Scheme incorporating Taguchi Loss Function”, international Journal of Industrial and Systems Engineering, 2016.