Economic-statistical Design of NP Control Chart with Variable Sample Size and Sampling Interval

Authors

Department of Industrial Engineering, Yazd University, Yazd, Iran

Abstract

The control charts are graphical tools and proven techniques to improve the performance of a process. Usually, the processes are not naturally controlled, so the use of control charts will help to reduce the variability and increase the stability of the process. In the traditional approach, control charts with fix sample size and constant sampling intervals were used to identify the changes in the process. While, control charts can be examined from different statistical and economical directions using different sampling schemes for achieving a better result. In past studies, it has been shown that np control charts show better results in detecting shifts by using variable sampling schemes but it is also important to consider how the cost of using variable sampling schemes will be, since the cost of a process depends on the parameters of the control chart. In this paper, the economic-statistical design of np control chart with variable sample size and sampling interval (VSSI) is formulated and then we compare and analyze the resulted obtained with other schemes. Results show significant improvement in terms of economic and statistical performance.

Keywords


1.     Yang, S.-F. and Chen, W.-Y., "Monitoring and diagnosing dependent process steps using vsi control charts", Journal of Statistical Planning and Inference,  Vol. 141, No. 5, (2011), 1808-1816.
2.     Reynolds, M.R., Amin, R.W., Arnold, J.C. and Nachlas, J.A., "Charts with variable sampling intervals", Technometrics,  Vol. 30, No. 2, (1988), 181-192.
3.     Reynolds, M.R., Amin, R.W. and Arnold, J.C., "Cusum charts with variable sampling intervals", Technometrics,  Vol. 32, No. 4, (1990), 371-384.
4.     Vaughan, T.S., "Variable sampling interval np process control chart", Communications in Statistics-Theory and Methods,  Vol. 22, No. 1, (1992), 147-167.
5.     Liu, J., Xie, M., Goh, T., Liu, Q. and Yang, Z., "Cumulative count of conforming chart with variable sampling intervals", International Journal of Production Economics,  Vol. 101, No. 2, (2006), 286-297.
6.     Faraz, A., Chalaki, K. and Moghadam, M., "On the properties of the hotelling’s t 2 control chart with variable sampling intervals", Quality & Quantity,  Vol. 45, No. 3, (2011), 579-586.
7.     Prabhu, S., Runger, G. and Keats, J., "X chart with adaptive sample sizes", The International Journal of Production Research,  Vol. 31, No. 12, (1993), 2895-2909.
8.     Zimmer, L.S., Montgomery, D.C. and Runger, G.C., "Evaluation of a three-state adaptive sample size x control chart", International Journal of Production Research,  Vol. 36, No. 3, (1998), 733-743.
9.     He, D., Grigoryan, A. and Sigh, M., "Design of double-and triple-sampling x-bar control charts using genetic algorithms", International Journal of Production Research,  Vol. 40, No. 6, (2002), 1387-1404.
10.   Prabhu, S.S., Montgomery, D.C. and Runger, G.C., "A combined adaptive sample size and sampling interval x control scheme", Journal of Quality Technology,  Vol. 26, No. 3, (1994), 164-176.
11.   Mahadik, S.B. and Shirke, D.T., "A special variable sample size and sampling interval chart", Communications in Statistics—Theory and Methods,  Vol. 38, No. 8, (2009), 1284-1299.
12.   Noorossana, R., Deheshvar, A. and Shekary, M., "A modified variable sample size and sampling interval controlchart", The International Journal of Advanced Manufacturing Technology,  Vol. 84, No. 5-8, (2016), 1303-1312.
13.   Zhou, M., "Variable sample size and variable sampling interval shewhart control chart with estimated parameters", Operational Research,  Vol. 17, No. 1, (2017), 17-37.
14.   Amiri, H.S.a.A., "The effect of measurement errors on the performance of variable sample size and sampling interval xbar control chart", International Journal of Engineering,  Vol. 30, No., (2017), 995-1004.
15.   Duncan, A.J., "The economic design of x charts used to maintain current control of a process", Journal of the American Statistical Association,  Vol. 51, No. 274, (1956), 228-242.
16.   Lorenzen, T.J. and Vance, L.C., "The economic design of control charts: A unified approach", Technometrics,  Vol. 28, No. 1, (1986), 3-10.
17.   Montgomery, D.C., "The economic design of control charts: A review and literature survey", Journal of Quality Technology,  Vol. 12, No. 2, (1980), 75-87.
18.   Fallahnezhad, M. and Ahmadi, E., "Optimal process adjustment with considering variable costs for uni-variate and multi-variate production process", International Journal of Engineering, Transactions A: Basics,  Vol. 27, No. 4, (2014), 561-572.
19.   Katebi, M., Seif, A. and Faraz, A., "Economic and economic-statistical designs of the t2 control charts with svssi sampling scheme", Communications in Statistics-Theory and Methods,  Vol. 46, No. 20, (2017), 10149-10165.
20.   Fallahnezhad, M. and Golbafian, V., "Determining the sample size for estimation of the ccc-r control chart parameters based on estimation costs".
21.   Woodall, W.H., "Weaknesses of the economic design of control charts", Technometrics,  Vol. 28, No. 4, (1986), 408-409.
22.   Saniga, E.M., "Economic statistical control-chart designs with an application to and r charts", Technometrics,  Vol. 31, No. 3, (1989), 313-320.
23.   Amiri, F., Noghondarian, K. and Safaei, A.S., "Evaluating the performance of variable scheme x-bar control chart: A taguchi loss approach", International Journal of Production Research,  Vol. 52, No. 18, (2014), 5385-5395.
24.   Jahantigh, F.F. and Safaeia, A., "Bi-objective economic statistical design of the joint xbar and s charts incorporating taguchi loss function", Journal of Industrial and Systems Engineering,  Vol. 9, No. 1, (2016), 1-16.
25.   SHERBAF, M.A., Amiri, A. and Bashiri, M., "Multi-objective economic-statistical design of cumulative count of conforming control chart", (2014).
26.   Faraz, A. and Saniga, E., "Economic statistical design of a t2 control chart with double warning lines", Quality and Reliability Engineering International,  Vol. 27, No. 2, (2011), 125-139.
27.   Amiri, A. and Jafarian-Namin, S., "Evaluating multi-objective economic-statistical design of attribute c control charts for monitoring the number of non-conformities", International Journal of Quality Engineering and Technology,  Vol. 5, No. 2, (2015), 145-161.
28.   Lupo, T., "Economic-statistical design approach for a vssi x-bar chart considering taguchi loss function and random process shifts", International Journal of Reliability, Quality and Safety Engineering,  Vol. 21, No. 02, (2014), 1450006.
29.   Nezhad, M.S.F. and Shamstabar, Y., "Economical-statistical design of one-sided ccc-r control chart based on analytical hierarchy process", Journal of Industrial and Systems Engineering,  Vol. 9, No. 3, (2016), 127-145.
30.   Luo, H. and Wu, Z., "Optimal np control charts with variable sample sizes or variable sampling intervals", Economic Quality Control,  Vol. 17, No. 1, (2002), 39-61.
31.   Wu, Z. and Luo, H., "Optimal design of the adaptive sample size and sampling interval np control chart", Quality and Reliability Engineering International,  Vol. 20, No. 6, (2004), 553-570.
32.   Montgomery, D.C., Heikes, R.G. and Mance, J.F., "Economic design of fraction defective control charts", Management Science,  Vol. 21, No. 11, (1975), 1272-1284.
33.   Chiu, W., "Economic design of np charts for processes subject to a multiplicity of assignable causes", Management Science,  Vol. 23, No. 4, (1976), 404-411.
34.   Chung, K.-J., "Economic designs of attribute control charts for multiple assignable causes", Optimization,  Vol. 22, No. 5, (1991), 775-786.
35.   Wang, R.-C. and Chen, C.-H., "Economic statistical np-control chart designs based on fuzzy optimization", International Journal of Quality & Reliability Management,  Vol. 12, No. 1, (1995), 82-92.
36.   Kooli, I. and Limam, M., "Economic design of an attribute np control chart using a variable sample size", Sequential Analysis,  Vol. 30, No. 2, (2011), 145-159.
37.   Kooli, I. and Limam, M., "Economic design of attribute np control charts using a variable sampling policy", Applied Stochastic Models in Business and Industry,  Vol. 31, No. 4, (2015), 483-494.
38.   Bashiri, M., Amiri, A., Asgari, A. and Doroudyan, M., "Multi-objective efficient design of np control chart using data envelopment analysis", (2013).
39.   Cinlar, E., "Introduction to stochastic processes, Courier Corporation,  (2013).
40.   Faraz, A. and Moghadam, M., "Hotelling’s t 2 control chart with two adaptive sample sizes", Quality & Quantity,  Vol. 43, No. 6, (2009), 903.
41.   Costa, A.F., "X chart with variable sample size and sampling intervals", Journal of quality technology,  Vol. 29, No. 2, (1997), 197.