Queuing Analysis

#### Optimization Models

Drive/Structure

Models

Subassemblies

 Process Flow Analysis - Example: Processing Printed Circuit Boards

 The principal features of the production system are defined using process flow charts illustrated by this example and others throughout these pages. In a system with multiple products there is a chart for each product. The example illustrated here has three products labeled A, B and C. The example process chart for product A is shown below. The analysis assumes that the process is in the tree form with raw materials combining to form a single product. The flow of material is from left to right. This process is making printed circuit boards. For product A, 50% of the boards are SMT (surface mount technology). These boards are the raw material for operation 1. 50% of the boards are TH (through hole) entering the system at operation 3. The proportions are shown on the arcs entering operation 5. Each operation has a processing time measured in hours and a defect rate. For example, operation 1 takes 0.03 hours per part and makes 10% of the parts passing through it defective. This is a pull system because the flow through the system is determined by the amount of product pulled from the last operation, Insp. 4.

The numbered circles in the figure are production operations that perform some activity on the product. Operations 1 and 3 are respectively the SMT line and the TH line. Each operation has two parameters placed within parentheses near the circle. The first parameter is the processing time per unit of product. The second parameter is the defect rate for the operation. Our models assume that defects introduced by an operation pass through the downstream operations and are not discovered until an inspection station is encountered. For this example each operation is followed immediately by an inspection, so defects are discovered immediately after they are produced.

The rectangles are inspection stations. Inspections discover defective items and remove them from the flow. Again, an inspection station has two parameters. The first is the time for inspecting a single unit. For the example, we use 0 for the inspection time indicating that the operator of each operation inspects his/her own work. The time for inspection is included in the operation time. The second parameter is the proportion of defective items that are not discovered. In the case of the example these are 0, indicating that the inspection operations find all defects. For the example, inspection takes place after each operation; however, this is not necessary. One use for the models is to find the most effective locations for inspections in the process.

The flows from the SMT and TH lines merge after inspection to pass through the remainder of the process. In the example, 50% of the flow is to be from the SMT line and 50% from the TH line. After passing through one of these lines, the product passes through a run-in test in operation 5, an inspection in operation 6, packing in operation 7 and a final inspection in operation 8.

The example considers three products. Product A is described above. Products B and C are similar products that differ only with regard to the proportions of product passing through the SMT and TH lines. For product B, 90% of the units pass through the SMT line and 10% pass through the TH line. For product C, all the units pass through the SMT line. Although the three products use the same operations, we represent them with separate processes. This allows the quantities produced of the products to be set independently. It also allows the operation parameters to be different for the different products.

Operations Management / Industrial Engineering
Internet
by Paul A. Jensen