Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32722
Design of Bayesian MDS Sampling Plan Based on the Process Capability Index

Authors: Davood Shishebori, Mohammad Saber Fallah Nezhad, Sina Seifi


In this paper, a variable multiple dependent state (MDS) sampling plan is developed based on the process capability index using Bayesian approach. The optimal parameters of the developed sampling plan with respect to constraints related to the risk of consumer and producer are presented. Two comparison studies have been done. First, the methods of double sampling model, sampling plan for resubmitted lots and repetitive group sampling (RGS) plan are elaborated and average sample numbers of the developed MDS plan and other classical methods are compared. A comparison study between the developed MDS plan based on Bayesian approach and the exact probability distribution is carried out.

Keywords: MDS sampling plan, RGS plan, sampling plan for resubmitted lots, process capability index, average sample number, Bayesian approach.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 947


[1] Wortham, A. W., Baker, R. C. (1976). Multiple deferred state sampling inspection. International Journal of Production Research. 14: 719–731.
[2] Wu, C. W. (2006). Assessing process capability based on Bayesian approach with subsamples. European Journal of Operational research. 184 (1): 207-228.
[3] Balamurali, S., Aslam, M., Chi, H. J. (2013). A New System of Skip-Lot Sampling Plans including Resampling. Scientific World Journal. Article ID 192412, 6 pages.
[4] Wu, C. W., Aslam, M., Chi, H. J. (2012). Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk, European Journal of Operational Research. 217: 560–566.
[5] Pearn, W. L., Wu, C. W. (2005). A Bayesian approach for assessing process precision based on multiple samples. European journal of Operational Research 165 (3): 685-695.
[6] Pearn, W. L., Wu, C.W. (2006). Variables sampling plans with PPM fraction of defectives and process loss consideration, J. Oper. Res. Soc. 57 (4): 450–459.
[7] Aslam, M., Azam, M., Chi, H. J. (2013). A mixed repetitive sampling plan based on process capability index, Applied Mathematical Modelling. 37(24): 10027-10035.
[8] Balamurali, S., Jun, C. H. (2007). Multiple dependent state sampling plan for lot acceptance based on measurement data. European Journal of Operational Research. 180: 1221–1230.
[9] Soundararajan, V., Vijayaraghavan, R. (1990). Construction and selection of multiple dependent (deferred) state sampling plan. Journal of Applied Statistics 17, 397–409.
[10] Vaerst, R. (1982). A procedure to construct multiple deferred state sampling plan. Methods of Operations Research. 37: 477–485.
[11] Wu, C. W., Lee, A. H. I., Chen, Y. W. (2015). A Novel Lot Sentencing Method by Variables Inspection Considering Multiple Dependent State. Qual. Reliab. Engng. Int. DOI: 10.1002/qre.1808.
[12] Sherman, R. E., (1965), Design and Evaluation of Repetitive Group Sampling Plans, Technometrics. 7: 11-21.
[13] Aslam, M., Azam, M., Chi, H. J. (2015). Various repetitive sampling plans using process capability index of multiple quality characteristics. Applied Stochastic Models in Business and Industry.
[14] Govindaraju, K., Ganesalingam, S. (1997). Sampling inspection for resubmitted lots, Communication Statistics Simulation. 26 (3): 1163–1176.
[15] Pearn, W. L., Lin, P. C. (2004). Testing process performance based on capability index Cpk with critical value. Computers and Industrial Engineering. 47:351–369.
[16] Aslam, M., Wu, C. W., Azam, M., Chi, H. J. (2013). Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items. Applied Mathematical Modelling. 37: 667–675.
[17] Aslam, M., Chi, H. J., Azam, M. (2013). Multiple Dependent State Sampling Plan Based On Process Capability Index, Journal of Testing and Evaluation. 41(2): 340–346.
[18] Balamurali, S., Jun, C. H. (2006). Repetitive group sampling procedure for variables inspection. Journal of Applied Statistics. 33: 327–338.