Problem statement

As discussed in the previous chapters, the problem considered in this research is mainly to determine an optimal inspection plan so as to minimize total manufacturing cost for a given serial multistage production system (MPS) to obtain a desired quality level of final products. Through an inspection plan, considering a part with an initial set of quality characteristics, three main simultaneous decisions should be made including: (i) which quality characteristics should be inspected, (ii) what type of inspection should be performed for the selected quality characteristics, and (iii) where these inspections should be performed. There would be also another decision like how to inspect that usually corresponds to selection of the inspection tool. Although there is a vast number of characteristics belongs to a part, but only a few of them are key characteristics that represent the quality level of the part.

Accordingly, there is no need to potentially consider all the characteristics, while some of them can be filtered. So, the initial set is better to contain the most important characteristics. There are different techniques in the literature to select the key characteristics but the most recent work by Mirdamadi (2014) can be applied to provide the initial set of quality characteristics. Therefore, the results of the work of Mirdamadi (2014) could be an input for the problem that is addressed by this thesis.

The specific features of the production system include the number of different quality characteristic, the number of manufacturing stages, the failure rate of each stage in producing nonconforming items, inspection errors for each quality characteristic, the inspection strategy (i.e., no inspection, full inspection, sampling inspection) and the costs associated with manufacturing and inspection activities.

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As an example for such production systems, consider a MPS as Figure 3.1 with k quality characteristic, i type of inspection and n processing stages. Initially, it is checked that whether inspection is needed for quality characteristic k. The part may be transferred to the next stage or to the final customer unless at least one quality characteristic needs inspection. Next, at least one type of inspection (i.e., CI and MI) is performed. Not important what type of inspection is performed, in-process parts must wait until the inspection is finished. After inspection, items are sent to the next stage in the case of no nonconformance in terms of items or processing features. In presence of any nonconformity in the items, different decisions may be made including: (a) they may be reworked and undergo the inspection again, (b) they may be repaired and be transferred to the next stage as downgraded products; or (c) they may be scrapped.

In this thesis, the operation of a conformity inspection may involve errors of two types: misclassification of a conforming item as non-conforming (error type I) and nonconforming one as conforming (error type II). For more information about these errors, please read the Appendix 2.

Although planning an inspection process in a MPS constitutes an additional cost, but in imperfect manufacturing systems, specific level of inspection will decrease total cost of manufacturing as well as increase the customer satisfaction. In such cases, the associated cost of inspection will be covered by the benefits realized through the detection of nonconforming products.

It must be noted that although considering inspection after every manufacturing stage will decrease the scrap, reworking, and downgrading costs and prevent nonconforming products from reaching the customers, but on the other hand, unnecessary and often too inspections constitute huge cost of equipment, staff, time, and space as well as interrupt the overall process that might lead to extra work in-progress (WIP) and flow. Accordingly, if inspections are performed unnecessarily, then greater total costs will incur.

In a MPS as Figure 3.1, after the processing stage i, there is a possibility to inspect the quality characteristics that have been realized by previous stages and have not been inspected before. It is noteworthy that inspection of each quality characteristic can be performed only in some specific allowed stages.

The above-mentioned problem is solved to obtain the optimal inspection plan with the objective of minimizing the total manufacturing cost. This cost includes production cost, fixed and variable costs of inspection, scrap cost, and penalty cost of nondetected nonconforming products that reach the customers. The difference between this problem and those of in the literature is that not only almost all of the papers have considered the inspection as a general term and have not specified different quality characteristics, but also they have not considered the possibility of inspecting the quality characteristics in different stages.

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Figure 3.1. Inspection of quality characteristics in a serial MPS

This thesis also tries to generalize the classic inspection planning into more complex and more realistic multi-product MPS with machine and inspection tool allocation (PSMIA). In PSMIA, other important objectives raise beside to manufacturing cost including customer satisfaction and manufacturing time. It is noteworthy that minimum manufacturing cost is ideal for manufacturer, while maximum customer satisfaction and minimum manufacturing time are desired for customers. Although manufacturers eager to cost less, but reaching acceptable quality level as well as producing items in lower time to satisfy the customers forces manufacturers to cost more. Accordingly, these objectives are in conflict where higher customer satisfaction needs higher manufacturing cost; lower manufacturing time needs higher manufacturing cost; and lower manufacturing cost may lead to lower quality (i.e., lower manufacturing time may need to ignore time-consuming inspection activities and this event leads to lower quality and consequently lower customer satisfaction).

As enumerated in Section 3.1, due to uncertainty in environmental production parameters, a percent of the manufactured products do not conform design specifications and their processes are sensitive to manufacturing variations.

Accordingly, manufacturers are interested in robust processes, which are relatively insensitive to alteration of uncertain parameters.

Summarized, this chapter first proposes a single-objective inspection planning model for the Main Problem. Next, the Extended Problem is modeled. In addition, the robustness of both Main and Extended problems are investigated.

Input

Stage i

Input for Stage i-1 Stage i+1

Inspection Station Manufacturing Stage

….…. ….…. ^Output

Stage 1

Stage 1 ^Stage Stage ii Stage Stage ii+1+1 ^Stage Stage NN

Q_Ch of Stage 1

? Q_Ch of Stage 2

? ?

Q_Ch of Stage n<i

?

Q_Ch of Stage i

Inspection Activities

Q-Ch : Quality Characteristic

Output of Stage i+1

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