Development Optimization Model of a Zero-Defect Single Sampling Plan

Document Type : Research Paper


1 Department of Industrial Engineering, Yazd University, Yazd, Iran.

2 Department of Industrial Engineering, Yazd University, Yazd, Iran

3 Department of Industrial Engineering, Science and Art University, Yazd, Iran.

4 Department of Industrial Engineering, University of Bojnord, Bojnord, Iran


One way to control the quality of products is to inspection the lot inputs. The focus of this paper is on a non-linear integer programming model for determining an optimal single sampling plan for inspecting different parts so that the total cost of the quality control is minimized and we try to improve the quality of inputs to the assembly line by applying a rectifying inspection policy. The optimization model includes the cost of inspection, the cost of non- conforming items entering the assembly line and the cost of rejecting the items. In this research, it is assumed that the inspection is perfect and zero acceptance number policy is employed for inspection. If a non- conforming item is found in the sample, the total lot is rejected. Each part is different in the risk of non- conforming items, the cost of non- conforming items, the size of the lot and the cost of inspection. In the practical example, it can be seen that the rate of defective items, followed by the cost of defective items and the cost of lot rejection, have been greatly reduced following the proposed methods and minimized the cost of quality control.


[1]Montgomery, Douglas, C. “Statistical Quality Control”, Noorossana, R., Iran University of Science and Technology, (2013), (In Persian)
[2] Wetherill, G.B., and Chiu, W.K. “A review of acceptance sampling schemes with emphasis on the economic aspect”, International Statistical Review, 43, pp. 191-210, (1975).
[3] Hald, A. “Statistical theory of sampling inspection by attributes”, Academic Press, New York, U.S.A, (1981).
[4] Lieberman, G, I. and Resnikov, G.J. “Sampling plans for inspection by variables”, Journal of the American Statistical Associative, 50, pp. 457-516 (1955).
[5] Bennett, G.K.; Schmidt, J.W.; Case, K.E. “The choice of variables sampling plans using cost effective criteria”, AIIE Transactions, 6, pp. 178-184 (1974).
[6] Schmidt, J.W.; Bennet, G.K.; Case, K.E. “Three action cost model for acceptance sampling by variables”, Journal of Quality Technology, 16(3), pp. 10-18 (1980).
[7] Taguchi, G. “Quality evaluation for quality assurance”, American supplier institute, Romulus, Michigan, U.S.A, (1984).
[8] Zlatan Hamzic, Elizabet A. Cudney, and Ruwen Qin. “Development of an optimization model to determine sampling levels”, Missouri University of science and technology (2013).
[9] Ruwen Qin, Elizabet A. Cudney, Zlatan Hamzic. “An optimal plan of zero-defect single-sampling by attributes for incoming inspections in assembly lines”, European Journal of Operational Research 246 (2015) 907–915, (2015).
[10] Willemain, T. R. “Estimating the population median by nomination sampling”, Journal of the American Statistical Association, 75(372), 908-911, (1980).
[11] Ferrell W.G. and Choker jr.A. “Design of economically optimal acceptance sampling plane with inspection error”, Computer & Operations Research, Vol.29, pp. 1283-1300, (2002).
[12] Niaki, S. A., Nezhad, M. F. “Designing an optimum acceptance sampling plan using Bayesian inferences and a stochastic dynamic programming approach”, Scientia Iranica Transaction E-Industrial Engineering, 16(1), 19-25, (2009).
[13] Nezhad, M. S. F., Nasab, H. H. “Designing a single stage acceptance sampling plan based on the control threshold policy. International Journal of Industrial Engineering”, 22(3), 143-150, (2011).
[14] Hsu, L. F., Hsu, J. T. “Economic design of acceptance sampling plans in a two-stage supply chain”, Advances in Decision Sciences, (2012).
[15] Fallah Nezhad, M. S., Akhavan Niaki, S. T. “A new acceptance sampling policy based on number of successive conforming items”, Communications in Statistics-Theory and Methods, 42(8), 1542-1552, (2013).
[16] Fallahnezhad MS, Aslam M. “A New Economical Design of Acceptance Sampling Models Using Bayesian Inference”, Accreditation & Quality Assurance, Vol. 18, pp. 187-195, (2013).
[17] Li, M. H. C., Al-Refaie, A., Tsao, C. W. “A Study on the Attributes Sampling Plans in MIL-STD-1916”, Lecture Notes in Engineering and Computer Science, 2190, (2011).
[18] Champernowne, D. G. “The economics of sequential sampling procedures for defectives”, Applied Statistics, 118-130, (1953).
[19] Barnard, George A. “Sampling inspection and statistical decisions”, Journal of the Royal Statistical Society. Series B (Methodological), 151-174, (1954).
[20] Hamaker, H. C. “Some basic principles of sampling inspection by attributes”, Applied Statistics, 149-159, (1958).
[21] Calvin, T. “Quality Control Techniques for Components, Hybrids, and Manufacturing Technology”, IEEE Transactions on components, hybrids and manufacturing technology, 6(3), 323-328, (1983).
[22] Salameh, M. K., and Jaber, M. Y. “Economic production quantity model for items with imperfect quality”, International journal of production economics, 64(1), 59-64, (2000).
[23] Maddah, B., Jaber, M. Y. “Economic order quantity for items with imperfect quality”, Revisited. International Journal of Production Economics, 112(2), 808-815, (2008).
[24] Taghipour, S., and Banjevic, D. “Periodic inspection optimization models for a repairable system subject to hidden failures”, Reliability, IEEE Transactions on, 60(1), 275-285, (2011).
[25] Taghipour, S., Banjevic, D., and Jardine, A. K. “Periodic inspection optimization model for a complex repairable system”, Reliability Engineering & System Safety, 95(9), 944-952, (2010).
[26] Shi, J., and Zhou, S. “Quality control and improvement for multistage systems: A survey”, IIE Transactions, 41(9), 744-753, (2009).
[27] Starbird, S.A. “Acceptance sampling, imperfect production, and the optimality of zero defects”, Naval Research Logistics (NRL), 44(6), 515–530, (1997).
[28] Dodge, H.F., Romig, H.G. “Sampling inspection tables: single and double sampling”, (2nded.).New York: John Wiley, (1998).
[29] Arturo J. Fernández. “Economic lot sampling inspection from defect counts with minimum conditional value-at-risk”, European Journal of Operational Research 258, 573–580, (2017).
[30] Arturo J. Fernández. “Optimal attribute sampling plans in closed-forms”, Computers & Industrial Engineering 137,106066, (2019).
[31] Lu Cui, Lanju Zhang, Bo Yang. “Optimal adaptive group sequential design with flexible timing of sample size Determination”, Contemporary Clinical Trials 63, 8–12, (2017).
[32] Andreas Sommer, Ansgar Steland. “Multistage acceptance sampling under nonparametric dependent sampling designs”, Journal of Statistical Planning and Inference 199, 89–113, (2019).
[33] Jafar Ahmadi, Elham Basiri, S.M.T.K. MirMostafaee. “Optimal random sample size based on Bayesian prediction of exponential lifetime and application o real data”, Journal of the Korean Statistical Society 45, 221–237, (2016).
This article