Optimum Process Adjustment Under Inspection Errors with Considering the Cycle Time of Production and Two Markets for the Sale of Goods

Abstract

 This paper is devoted to the study of determining optimal process mean in system production with the two markets for the sale of goods. In this paper, we developed an absorbing Markov chain model in production systems where all items are inspected %100 for conformance with their specification limits. When the value of the quality characteristic of an item falls below a lower limit, the item is scrapped. If it falls above an upper limit, the item is reworked (reprocessed). Products items conformance with specification limits sold in a primary market or a secondary market. Flow of material through the production system can be modeled in an absorbing Markov chain. We included cycle time of production line in model. Also effects of inspection errors are investigated. Numerical examples are given to demonstrate the application of the proposed model.

Keywords


 

[1] Darwish. M.A., S.O. Duffuaa, (2010), A mathematical model for the joint determination of optimal process and sampling plan parameters, Journal of Quality in Maintenance Engineering 16: 181 – 189.

[2] Duffuaa, S.O., Gaally, A.EL. (2012). A multi-objective mathematical optimization model for process targeting using %100 inspection policy. Journal of applied mathematical modeling, 37 (3), 1-8.

[3] Springer.C, (1951), A method for determining the most economic position of a process maen, Ind. Journal of Quality Control 8 36-39.

[4] Hunter. W, C. Kartha, (1977), determining the most profitable target value for a production process, Journal of Quality Technol. 9 176-181.

[5] Bisgaard, w. Hunter, L. Pallensen, (1984), Economic selection of quality of manufacturing products, Journal of Quality Technol. Metrics 26 9-18.

[6] Boucher. T, Jafari. M, (1991), The optimum target value for single filling operations with quality sampling plans, Journal of Quality Technol. 23 44-47.

[7] Lee, M.K., Elsayed, E. A., (2002). Process and mean screening limits for filling process under two-stage screening procedure. European journal of operational research 138: 118-126.

[8] 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: 181–189.

[9] Zilong, L., Enriuedel, C., (2006). Setup adjustment under unknown process parameters and fixed adjustment cost. Journal of Statistical Planning an Inference: 136, 1039 – 1060.

 [10] Jinshyang. R, Lingua, G., Kwiei, T., (2000). Joint determination of process mean, production run size and material order quantity for a container-filling process. International journal of production economics, 63: 303-317.

[11] Wang, Z., Wu, Q., Chai, T., (2004). Optimal-setting control for complicated industrial process and its applications study. Journal of Engineering Practice, 12: 65-74.

 [12] Chen.C. H. Chen, T. Lai, Determination of optimum process mean based on quadratic loss function and rectifying inspection plan, Eur. J. Oper. Res. 182 (2007) 755–763.

 [13] Shokri, S.Z., Walid, K.Z., (2011). Optimal means for continuous processes in series. European Journal of Operational Research, 210: 618-623.

[14] Park, T., Kwon, H.M., Hong, S.H., Lee, M.K., (2011). The optimum common process mean and screening limits for a production process with multiple products. Computers & Industrial Engineering, 60: 158-163.

 [15] Chung, H.C., Hui, K.S., (2009). The determination of optimum process mean and screening limits based on quality loss function. Expert systems with application, 39: 7332-7335.

[16] Lee, K., Kwon, M.M., Hong, S.H., Kim, Y. J., (2007). Determination of the optimum target value for a production process with multiple products. Int. J. Production Economics, 107: 173-178.

[17] Bowling, S.R., Khasawneh, M.T., Kaewkuekool, S., 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: 636–650.

[18] 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.

[19] 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 Industrial Engineering, Qazvin Islamic Azad University, 4 (6),1-6.

[20] Pillai, V.M., Chandrasekharan, M.P. (2008). An absorbing Markov chain model for production systems with rework and scrapping. Computers & Industrial Engineering, 55: 695–706.

[21] Duffuaa S.O, El-Gaally A,(2013). A multi-objective optimization model for process targeting using sampling plans, Journal of Computers & Industrial Engineering, 64:309-317.