Contribution of simulation to the optimization of inspection plans for multi-stage manufacturing systems A. Vaghefi, Vahid Sarhangian * Department of Industrial Engineering, Iran University of Science and Technology, PC 16844, Narmak, Tehran, Iran article info Article history: Received 20 August 2008 Received in revised form 29 May 2009 Accepted 2 June 2009 Available online 7 June 2009 Keywords: Multi-stage manufacturing systems Inspection plans Inspection errors Simulation Simulation optimization abstract In this paper we develop a new mathematical model to optimize inspection plans for multi-stage man- ufacturing systems with possible misclassification errors. The presented model minimizes total inspec- tion related costs while still assuring a required output quality. Because of the complexity of the proposed mathematical model, a simulation algorithm is presented to model the multistage manufactur- ing system subject to inspection and to estimate the resulting inspection costs. We use the popular Arena simulation software to implement our simulation algorithm and then we utilize OptQuest, Arena’s built- in optimization package, to find the optimal inspection plan. Finally, a numerical example is presented and simulation experiments are also conducted in order to examine the effects of several model parameters. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Nowadays, maintaining quality levels of products and services is vital to an organization’s business success in the competitive world. Quality assurance activities, including inspection plans play an important role to ensure that products and services meet costumer requirements properly. Manufacturing systems generally consist of several stages in which raw materials pass through various pro- cesses and eventually transform into finished products. At each stage, a number of items which were good in pervious stages may be- come defective as a result of processing. A preliminary idea to main- tain the quality level is providing an inspection station after the last stage. This is generally referred to as outgoing inspection. However, with outgoing inspection, all efforts and costs invested in producing defective items are wasted. In order to reduce the wasted efforts and costs, inspection stations should be placed immediately after each major manufacturing process. In this case, accepted items are sent forward to next stages, whereas rejected items can be either re- worked at the stage or scrapped out of the process. Inspection plans are concerned with determining the inspection parameters such as: number of total items to be inspected, deci- sion making procedure and allocation of inspection stages by con- sidering several critical factors. There are two sub-problem categories in the literature of multi-stage inspection plans. The first category deals with optimal allocation of limited inspection sta- tions within a manufacturing system. In this category, a screening or 100% inspection is widely used, in which inspections are per- formed on all produced items. In the second category, the purpose is to find optimal inspection levels by determining the sample size and acceptance number for each stage. In sampling inspection, a sample is randomly picked and inspected from the lot and based on the defective items observed in the sample, the lot can be re- jected or accepted. In this case, inspection stations are often placed after all manufacturing stages. Lindsay and Bishop (1964) showed that if the costs for inspection and scrapping are assumed to be lin- ear and the fraction of defective units for each stage is assumed to be fixed, then 100% inspection will be more efficient than sam- pling. The similar results were found by White (1969) in the case where rejected items are repaired and replaced with good items. Raz (1986) reviewed the previous researches on multi-stage inspection allocation and found out that when the inspection costs are concave, then the optimal level at each stage is either 100% or 0%. On the other hand, Montgomery (2005, p. 647) presented sev- eral situations in which sampling is most likely to be useful. For example, when the cost of 100% inspection is high and/or inspec- tions typically need destructive testing, sampling is preferred. Beightler and Mitten (1964), Woo and Metcalfe (1972), Dietrich and Saunders (1974) and Veatch (2000), have paid more attention to sampling rather than screening in multi-stage inspection. Here- dia-Langner, Montgomery, and Carlyle (2002) presented a highly constrained multi-stage inspection problem where all stages must receive sampling inspection. In their problem, sample size and acceptance number for each stage, were the decision variables. Van Volsem, Dullaert, and Van Landeghem (2007) proposed an optimal strategy for an n-stage manufacturing system with a 0360-8352/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2009.06.001 * Corresponding author. Tel.: +98 2173913024. E-mail addresses: v.sarhangian@gmail.com, sarhangian@ind.iust.ac.ir (V. Sarhangian). Computers & Industrial Engineering 57 (2009) 1226–1234 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie