A model for determining optimum process mean in the presence of inspection errors by considering the cycle time

Document Type : Original Manuscript


1 College of Engineering, Yazd University, Yazd, Iran

2 Industrial engineering department , Yazd university


Any production process should be adjusted based on a target value. The problem of process mean determination in a production system with two markets is investigated. An absorbing Markov chain is employed to formulate the flow of items. All items are inspected and if the value of the quality characteristic falls below a lower limit then the item is scrapped and when it falls above an upper limit then the item is reworked. Since some items are reworked thus the cycle time of production is computed in the presence of the inspection errors. Numerical studies are performed to analyze the results


  • Considering two markets for the sale of items.
  • Considering the process cycle time in objective function. Due to the use of reworking loops in the production process, one item may be processed several times that leads to increase the cycle time of production.
  • Considering inspection errors in the model along with analyzing their effects on the sales and the total profit of manufacturer.
  • Considering loss functions in the model. The costs of quality are usually analyzed by reworking cost or scrapping cost. However, Taguchi considered cost to customers. Since after sale of the


Abbasi, B., Niaki, STA., Arkat, J. (2006). Optimum Target Value for Multivariate Processes with Unequal Non-Conforming Costs. Journal of Industrial Engineering International. 2(3), 1-12.
Al-Sultan, K.S., Pulak, M.F.S. (2000). Optimum target values for two machines in series with 100% inspection. European Journal of Operational Research, 120(1), 181-189.
Bisgaard, W., Hunter, L., Pallensen, L. (1984) Economic selection of quality of manufacturing products. Journal of Quality technology, 26(1), 9-18.
Boucher, T., Jafari, M. (1991). The optimum target value for single filling operations with quality sampling plans. Journal of Quality Technology, Vol. 23(1), 44-47.
Bowling, S.R., Khasawneh, M.T., Kaewkuekool, S., and Cho, B.R.(2004). A Markovian approach to determining optimum process target levels for a multi-stage serial production system. European Journal of Operational Research. 159, 638-650.
Chen, C.H., Lai, T. (2007). Determination of optimum process mean based on quadratic loss function and rectifying inspection plan. European Journal of Operational Research.182 (2), 755-763.
Chung, H.C., Hui, K.S. (2009). The determination of optimum process mean and screening limits based on quality loss function. Expert systems with applications.36 (3), 7332-7335.
Darwish, M. A. (2010). A mathematical model for the joint determination of optimal process and sampling plan parameters. Quality in Maintenance Engineering. 16, 181-189.
Duffuaa, S.O., Gaaly, A.EL. (2012). A multi-objective mathematical optimization model for process targeting using %100 inspection policy.  Applied mathematical modeling, 37(3), 1-8.
Duffuaa, S.O., Gaaly, A.EL. (2013). A multi-objective optimization model for process targeting using sampling plans. Computers & Industrial Engineering,  64(1), 309-317.
Fallahnezhad, M.S., Hosseininasab, H. (2012). Absorbing Markov Chain Models to Determine Optimum Process Target Levels in Production Systems with Dual Correlated Quality Characteristics. Pakistan Journal of Statistics and Operation Researches, 8(2), 205-212.
 Fallahnezhad, M.S., Niaki, S.T.A. (2010). Absorbing Markov Chain Models to Determine Optimum Process Target Levels in Production Systems with Rework and Scrapping. Journal of Optimization in Industrial Engineering, 4, 1-6.
 Fallahnezhad, M.S, Ahmadi, E. (2014). Optimal Process Adjustment with Considering Variable Costs for uni-variate and multi-variate production process. International Journal of Engineering, 27(4), 561-572.
Hong, S. H., Elsayed, E. A. (1999). The optimum mean for processes with normally distributed measurement error. Journal of Quality technology, 31(3), 338-344.
Hong, S. H. (1999). Optimum mean value and screening limits for production processes with multi-class screening. International Journal of Production Research, 37(1) , 155-163.
Hunter, W., Kartha, C., (1977). Determining the most profitable target value for a production process. Journal of Quality technology, 9(4), 176-181.
Jinshyang, R., Lingua, G., Kwiei, T. (2000). Joint determination of process mean, production run size and material order quantity for a container-filling process. Production economics. 63(3), 303-317.
Lee, M.K., Elsayed, E. A. (2002). Process and mean screening limits for filling process under two-stage screening procedure. Operational research, 138(1), 118-126.
Lee, K., Kwon, M.M., Hong, S.H., and Kim, Y. J. (2007). Determination of the optimum target value for a production process with multiple products. Production Economics, 107(1), 173-178.
Park, T., Kwon, H.M., Hong, S.H., and Lee, M.K. (2011). The optimum common process mean and screening limits for a production process with multiple products. Computers & Industrial Engineering.  60 (1), 158- 163.
Pillai, V.M., Chandrasekharan, M.P. (2008). An absorbing Markov chain model for production systems with rework and scrapping. Computers & Industrial Engineering. 55(3), 695-706.
Shokri, S.Z., Walid, K.Z., (2011). Optimal means for continuous processes in series. European Journal of Operational Research.  210(3), 618-623.
 Springer, C. (1951). A method for determining the most economic position of a process mean. Quality Control.  8, 36-39.
Taguchi G., Elsayed, E. A., and Hsiang, T. (1989). Quality Engineering in Production Systems. McGraw-Hill.
Wang, Z., Wu, Q., Chai, T. (2004). Optimal-setting control for complicated industrial process and its applications study. Engineering Practice. 12, 65-74.
Zilong, L., Enriuedel, C. (2006) Setup adjustment under unknown process parameters and fixed adjustment cost. Statistical Planning and Inference, 136, 1039-1060.