Economic Single-Sampling Plans Based on Different Probability Distributions Considering Inspection Errors

Document Type : Research Paper


1 university of yazd

2 Kermanshah University of Technology

3 University of Science & Art

4 Department of industrial Engineering, Yazd University, Yazd, Iran



As a traditional statistical quality control method, acceptance sampling plans are widely applied for quality assurance. In a sampling plan, with the aim of acceptance or rejection of a lot of martial, inspection is carried out to determine adherence to standards. Usually, it is assumed that the inspection of the items is error-free. In the present study, this assumption is relaxed. Using Bayesian inferences and considering inspection errors, three mathematical models are developed for the economic single-sampling plans. First, the model is developed based on Binomial distribution. Regarding the application of Poisson model in approximating Binomial distribution, the second model is developed based on Poisson distribution. The third model is presented considering Negative binomial (which is also known as Pascal Distribution). The models determine the sample size and acceptance number to minimize the expected inspection costs incurred during sampling. A numerical example is presented and sensitivity analyses are carried out.


Chattinnawat. W (2013). Investigating design of zero acceptance number single sampling plans with inspection errors. International Journal of Quality & Reliability Management, 30(6), 662-674.
Duffua, S. O (1996). Impact of inspection errors on performance measures of a complete repeat inspection plan. International Journal of Production Research, 34(7), 2035-2049.
Fallahnezhad M.S., Ayeen S., Sahmatkesh.F., Rasay.H, (2018 a). Optimal process adjustment under inspection errors considering the cycle time of production. Journal of Quality Engineering and Production Optimization, article in press, 10.22070/JQEPO.2018.2680.1053.  
Fallahnezhad. M.S, Qazvini.E, Abbesi.M, (2018 b). Designing an economical acceptance sampling plan in the presence of inspection errors based on maxima nomination sampling method. Scientia Iranica Transactions E: Industrial Engineering, 25(3), 1701-1711.
Fallahnezhad M.S, Hosseini Nasab H, (2011). Designing a single stage acceptance sampling plan based on the control threshold policy. International Journal of Industrial Engineering & Production Research, 22, 143–150.
Fallahnezhad, MS, Aslam M. (2013). A new economical design of acceptance sampling models using Bayesian inference. Accreditation and Quality Assurance, 18 (3), 187-195.
Fallahenzhad. M.S, Golbafian.V, Rasay. H and Shamstabar. Y, (2017). Economic-statistical design of a control chart for high yield process when the inspection is imperfect. International Journal of Industrial Engineering and Production Research, 28(3), 241-249.
Jamkhaneh. E.B, Gildeh. B.S, Yari.G, (2011). Inspection error and its effects on single sampling plans with fuzzy parameters. Structural and Multidisciplinary Optimization, 43(4), 555-560.
Khan, M., & Duffuaa, S. O (2002). Effect of inspection errors on the performance of inspection plans in quality control system. In The Sixth Saudi Engineering Conference, 14-17.
Khamseh, A. A., Ghomi, S. F., & Aminnayyeri, M. (2008). Economical design of double variables acceptance sampling with inspection error. Journal of Algorithm and Computation, 41(7), 959-967.
Markowski, E. P., & Markowski, C. A. (2002). Improved attribute acceptance sampling plans in the presence of misclassification error. European Journal of Operational Research, 139(3), 501-510.
Montgomery, D., (2009). Introduction to Statistical Quality Control, John Wiley & Sons Inc., Hoboken, NJ.
Fallahnezhad, M. F., & Hosseini Nasab, H. H. (2012). A new Bayesian acceptance sampling plan considering inspection errors. Scientia Iranica, 19(6), 1865-1869.
Rasay. H, Pourxarib.M, Fallahnezhad. M.S. (2018). Sequential Sampling Plan in the Truncated Life Test for Weibull Distribution. Journal of Testing and Evaluation, 46(2), 693-703.