Calculate the costs of adding inspection to a test strategy

Choosing an inspection system to incorporate into a manufacturing line is primarily an engineering decision—you need to find a system with the capabilities that match your needs. Adding an inspection system to an apparently already effective test strategy, however, often represents more of an economic decision than an engineering one.

SIDEBAR: General Assumptions

Consider a company making complex microprocessor-based boards in relatively high mix in a single manufacturing facility. The existing strategy consists of in-circuit test, functional test, system assembly, and system test. In the hope of finding more faults earlier—before defective products undergo expensive testing steps—you are considering adding an automated optical inspection (AOI) system prior to in-circuit test. How can you justify the purchase to management?

Any economic-justification model consists of three classes of costs:

• Fixed costs. Fixed costs occur only once in the model. They include the price of the inspection system, any site preparation (such as concrete platforms or installation of power conduits), and initial training costs. For simplicity, you can lump any items that come with the machine—spares kits, for example—with the purchase price.
• Recurring costs. These costs occur periodically, but not constantly. For example, maintenance costs fall into the recurring-cost category, as does the cost of spares to replace any parts consumed during equipment repair and any unanticipated downtime. Fixture and programming costs usually fall into this category. But with an AOI system, fixtures are primarily platforms that hold boards of various sizes, so their purchase can be considered a one-time cost, and in this case, I suggest bundling them with the system purchase price under “fixed costs.” Because AOI system programs generally come from CAD files or by learning from known-good boards, you can assume either that the programming cost is small enough to ignore or that any programming cost at AOI is offset by savings at functional test.
• Ongoing costs. These costs are essentially continuous. Labor charges are calculated in cost per hour, but you can also state them as cost per half hour, cost per day, and so on. Board troubleshooting and repair at each step falls into this category, as does board scrap.

In creating an economic justification that compares alternatives, you need to include only costs (and benefits) that change significantly depending on your final action. In adding inspection, the goal is to find more faults and find them sooner (and less expensively). You can assume that adding inspection will not change the boards’ fault spectra or the failure rates out of manufacturing and that no failure caught by the existing strategy will escape the new arrangement. Also, because you should assume that any repairable boards are sent back through the system, the only products that result from the new process are good boards and scrap.

In essence, the existing process appears as a “black box” fed by manufacturing or by the new inspection step and generating output that ships to customers. Most costs from the existing process remain constant.

You can also ignore any costs associated with your analysis that do not depend on whether you add the inspection system. Evaluating your process with and without inspection is not free, nor is comparing costs and features of available inspection equipment, but you spend that money regardless of how you proceed.

In analyzing costs that could matter, you must separate likely effects from less likely ones that only complicate the model. For example, if adding an inspection step doesn’t require building or moving to a new factory, then the aggregate facility (fixed) cost doesn’t change. Your company may allocate such costs as mortgage, property taxes, and building security to each process based on the amount of floor space it occupies, but that breakdown is merely an accounting convenience. At the end of the day, the entire factory can neither expand nor contract in response to adding or removing process steps, so the overall cost remains constant.

Adding a piece of capital equipment like an AOI system will undoubtedly increase the facility’s energy consumption, and therefore the overall utility cost for the entire factory. That cost tends to be small compared with other associated costs, and in many cases you can ignore it. If you expect the effect to be significant, however, include only the anticipated additional cost in your analysis. Baseline energy use does not change.

Similarly, include only the additional labor costs that the extra step requires. Labor costs for the existing process remain constant, and are therefore irrelevant for this purpose. The cost of devices consumed during board repair doesn’t change because the fault spectrum doesn’t change, and you can ignore that as well.

The sidebar summarizes the general and cost-related assumptions, while Table 1 presents the primary costs that remain.

To see how adding an inspection system could save your company money over time, consider the following example. Suppose a manufacturer ships 100,000 boards per year with a manufacturing cost of $600. The existing process produces 1% or 1000 scrap boards per year worth $600,000 and therefore requires building 101,000 boards altogether. (These numbers are rounded for simplicity; a 1% scrap would actually require the manufacture of 101,010 boards to yield 100,000 good boards.)

Actual yield from in-circuit test (the actual number of good boards) before adding inspection is 94.4%, which means the tester is passing 5656 bad boards (including the 1000 that will be scrapped). Functional test yields 99.4% of the 100,000 boards that will actually be shipped, therefore excluding the scrap. This means that 4056 boards are repaired at functional test, and 600 bad boards will move on to system test, where they will get repaired.

Assume that you are planning to add an inspection system to a line with an anticipated three-year life. The AOI system costs $150,000 (including lumped costs). The addition of two operators at $20/hr (including benefits) adds another $83,200 per year. Training operators to use the system costs $15,000, which is allocated at $5000 per year. You could estimate annual maintenance and spares at 10% of the system purchase price (a common cost for a maintenance contract), or $15,000, and estimate extra downtime at 2% per year, or $3000. Thus, inspection will add $106,200 per year to the production cost, not counting the capital outlay itself.

Suppose the new strategy reduces scrap by half, to 500 boards, saving $300,000 per year, and therefore requires only 100,500 board starts to ship 100,000 boards. A 96.5% yield out of in-circuit test sends 3518 bad boards to functional test, compared to 5656 without inspection, which means that an additional 1638 are getting repaired at the AOI/ICT stage. A 99.9% yield of the shippable 100,000 boards at functional test (again, excluding the scrap) sends only 100 boards to be repaired at system test.

Repairing each board after either inspection or in-circuit test costs $15, rising to $25 after functional test and $75 after system test. As Table 2 shows, the inspection system, in theory, reduces aggregate annual test costs by more than $235,000.

Actual results are a bit less rosy. The savings is subject to income tax. Assuming a corporate 35% tax rate, the result is a still-considerable $152,000. The tax code also permits depreciating the equipment over five years (irrespective of the anticipated three-year life for the project), reducing the part of the benefit subject to tax by $30,000 per year and therefore adding 35% (the tax) of $30,000, or $10,500, to the after-tax benefits. So, the original $150,000 cost of the system would generate $163,367 of actual annual savings, a justifiable expense to any corporate manager, since the system would pay for itself in less than a year.

Other factors, such as the opportunity cost (the cost to borrow the money for the equipment or the “interest rate” it would earn on another project) and the cost of false failures would add to the analysis, but this calculation serves as a first approximation.

Knowing that you want to make a capital purchase will not generally convince your company comptroller to sign the check. A justification showing the bottom-line impact of the expenditure will likely elicit a more favorable reaction.