Developing two variables sampling plans considering the compliance rate with the ideal OC curve

Document Type : Research Paper


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

2 Department of Industrial Engineering, Shahed University, Tehran, Iran.


An essential tool for examining the quality of manufactured products is acceptance sampling. This research applies the concept of minimum angle method to extend two variables sampling plans including the variables multiple dependent state (VMDS) sampling plan and the variables repetitive group sampling (VRGS) plan on the basis of the process yield index Spk. Optimal parameters of acceptance sampling plans can be determined by solving a non-linear optimization model with the following conditions: 1) The objective function of the plan is to minimize the average sample number. 2) Constraints are set in a way that the compliance rate will be satisfied with the ideal operating characteristic (OC) curve as well as the producer’s and costumer’s risks. The assessment of the proposed plans reveals that by increasing the rate of convergence to the ideal OC curve, the proposed VRGS plan performs better than the proposed VMDS plan in terms of the average sample number. A numerical example is considered to reveal the applicability of the proposed acceptance sampling plans.


Main Subjects

Arizono, I., Miyazaki, T., & Takemoto, Y. (2014). Variable sampling inspection plans with screening indexed by Taguchi’s quality loss for optimising average total inspection. International Journal of Production Research, 52(2), 405-418.
Aslam, M., Balamurali, S., & Jun, C. H. (2019). A new multipl dependent state sampling plan based on the process capability index. Published online in Communications in Statistics-Simulation and Computation, doi: 10.1080/03610918.2019.1588307.
Aslam, M., Yen, C. H., Chang, C. H., & Jun, C. H. (2014). Multiple dependent state variable sampling plans with process loss consideration. The International Journal of Advanced Manufacturing Technology, 71(5-8), 1337-1343.
Balamurali, S., & Jun, C. H. (2006). Repetitive group sampling procedure for variables inspection. Journal of Applied Statistics33(3), 327-338.‏
Balamurali, S., & Jun, C. H. (2007). Multiple dependent state sampling plans for lot acceptance based on measurement data. European Journal of Operational Research, 180(3), 1221-1230.‏
Boyles, R. A. (1994). Brocess capability with asymmetric tolerances. Communications in Statistics-Simulation and Computation, 23(3), 615-635.
Fallahnezhad, M. S., & Yazdi, A. A. (2016). A new optimization model for designing acceptance sampling plan based on run length of conforming items. Journal of Industrial and Systems Engineering, 9(2), 67-87.‏
Lee, J. C., Hung, H. N., Pearn, W. L., & Kueng, T. L. (2002). On the distribution of the estimated process yield index . Quality and Reliability Engineering International, 18(2), 111-116.
Lee, A. H., Wu, C. W., & Wang, Z. H. (2018). The construction of a modified sampling scheme by variables inspection based on the one-sided capability index. Computers & Industrial Engineering, 122, 87-94.
Liu, S. W., Lin, S. W., & Wu, C. W. (2014). A resubmitted sampling scheme by variables inspection for controlling lot fraction nonconforming. International Journal of Production Research, 52(12), 3744-3754.
Nezhad, M. S. F., Saredorahi, F. Z., Owlia, M. S., & Zad, M. A. V. (2018). Design of economically and statistically optimal sampling plans. Hacettepe Journal of Mathematics and Statistics, 47(3), 685-708.
Niaki, A., & Nezhad, F. (2012). A new markov chain based acceptance sampling policy via the minimum angle method. Iranian Journal of Operations Research, 3(1), 104-111.‏
Pearn, W. L., & Wu, C. W. (2007). An effective decision making method for product acceptance. Omega, 35(1), 12-21.
Sherman, R. E. (1965). Design and evaluation of a repetitive group sampling plan. Technometrics, 7(1), 11-21.
Soundararajan, V., & Christina, A. L. (1997). Selection of single sampling variables plans based on the minimum angle. Journal of Applied Statistics, 24(2), 207-218.
Tamirat, Y., & Wang, F. K. (2019). Acceptance sampling plans based on EWMA yield index for the first order autoregressive process. Journal of the Operational Research Society, 70(7), 1179-1192.
Wang, Z. H., & Wu, C. W. (2019). An improved sampling plan by variables inspection with consideration of process yield and quality loss. Published online in Statistical Computation and Simulation, 89(13), 1-15.
Wu, C. W., Aslam, M., Chen, J. C., & Jun, C. H. (2015). A repetitive group sampling plan by variables inspection for product acceptance determination. European Journal of Industrial Engineering, 9(3), 308-326.
Wu, C. W., & Chen, J. T. (2019). A modified sampling plan by variable with an adjustable mechanism for lot sentencing. Published online in Journal of the Operational Research Society, doi:10.1080/01605682.2019.1657366.
Wu, C. W., & Liu, S. W. (2018). A new lot sentencing approach by variables inspection based on process yield. International Journal of Production Research, 56(12), 4087-4099.
Wu, C. W., Liu, S. W., & Lee, A. H. (2015). Design and construction of a variables multiple dependent state sampling plan based on process yield. European Journal of Industrial Engineering, 9(6), 819-838.
Wu, C. W., & Wang, Z. H. (2017). Developing a variables multiple dependent state sampling plan with simultaneous consideration of process yield and quality loss. International Journal of Production Research, 55(8), 2351-2364.
Volume 12, Issue 4 - Serial Number 4
November 2019
Pages 242-251
  • Receive Date: 19 December 2019
  • Revise Date: 23 February 2020
  • Accept Date: 26 March 2020
  • First Publish Date: 24 July 2020