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Let's first understand what each statement is saying. 1. Rework costs should be regarded as a cost of quality when the rework is caused by internal failure. 2. Prevention costs are costs that are incurred to prevent the sale and production of defective units. 3. Internal failure costs are costs of failure of machinery on the production line.

Now, let's analyze each statement: 1. Rework costs are the costs associated with fixing defects in products that are identified before they are shipped to customers. These costs are indeed considered a part of the cost of quality when they are caused by internal failure. 2. Prevention costs are the costs incurred to prevent defects from occurring in the first place. These include costs such as employee training, process improvements, and quality audits. It is correct to say that prevention costs are incurred to prevent the sale and production of defective units. 3. Internal failure costs are the costs associated with defects that are discovered before a product is shipped to customers. While the failure of machinery on the production line can be a part of these costs, it is not the only aspect. Internal failure costs also include costs of rework, scrap, and downtime caused by quality issues.

Now that we have analyzed each statement, let's examine the given options: 1. \(I, \|,\) and \(\| I\) are correct. 2. \(Il\) only is correct. 3. \(I\) and \(III\) only are correct. 4. \(I\) only is correct. Based on our analysis, Statement I and Statement II are correct. Statement III, however, is not entirely correct, as it only mentions a part of internal failure costs. Therefore, the correct answer is Option 1: \(I, \|,\) and \(\| I\) are correct.