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Errors of omission and commission — how VLSI relates to subsidies

Second choice problem involves making a choice between two solutions – both of which involve costs.

The fundamental concept behind any testing is to prevent a faulty product from reaching the end consumer. A well-designed test is the one that accurately identifies ALL types of defects in the product. Very often though, this is not possible as tests may not cover the exact range of defects that might actually exist. In that case, the suite of tests leads to the errors of commission or omissions. The interesting question, then is – which of the two errors is acceptable?

An illustration

This second problem can be explained using a fairly simple scenario from “Design-for-Testability” theory used in all integrated chip (IC) manufacturing companies. Consider a firm that makes the processor chips going into your laptops. Every single processor chip goes through a set of tests to identify if the chip is good or bad. Four scenarios result out of this exercise:

Errors of commission and omission

Errors of commission and omission

The two scenarios marked in green are the best-case scenarios. In the first of these, all the designed tests are unable to find any fault with the chip. At the same time, the chip itself does not show any defects after reaching the end consumers. When such awesomely functional chips reach your laptops, the chip making companies make profits.

In the second “green” scenario, the tests indicate that there is a problem with the chip. Further debugging (involves greater costs) concludes that this chip is actually manufactured erroneously. It is then the raison d’être of the tests to throw away these chips so that they do not reach the customers.

However, when tests are unable to identify any problem with the chip even though it is bad, we end up in the second choice problem 1 scenario or the “error of commission”. This is the scenario you encounter when your laptop crashes within a few days/weeks/years (within the guarantee period) after purchase. Obviously this makes the consumer lose trust in the product and dents the manufacturing firm’s image.

On the other hand, there is the second choice problem 2, where tests are designed so thoroughly that they start eliminating chips which are actually not dysfunctional. This is the error of omission. The cost involved with this error is that it leads to loss of revenue as many good chips are just thrown away based on faulty tests. It also lowers the confidence of the firm.

The above illustration shows the two errors that are commonly encountered in the chip manufacturing business. Which of them is tolerable is a function of the company’s image in the market, the end application of the product and the costs involved. For example, if the chip is being manufactured for use in mission-critical automobile systems like auto-braking or fuel injection, the preferable error is the error of omission as there’s a life and personal safety at stake. On the other hand, if the end application is a low-end mobile phone, the company might settle for a higher error of commission and avoid the extra costs of rejecting lots of chips.

Application – Subsidies

The above illustration can directly be applied to a subsidy case to explain the effect of identifying beneficiaries incorrectly. Using the framework above, we can visualise a subsidy program as shown in the figure below:

Subsidy conundrum

Subsidy conundrum

From the framework above, which would be your second choice? The first option would be to start with very few beneficiaries being fully aware that there will be a definite error of omission. The next step would be to work on reducing this error rate itself. The problem here will be that there might be some people who, even though needy are not attended to urgently.

Another option would be to start with a large number of beneficiaries being aware of the errors of commission. A subsequent step would be to try and reduce this error rate. The costs involved here are that the free-riders might sideline the really needy. Such schemes will also require huge sums of capital as they will start by serving a huge number of people. This is the path that most of Indian government’s subsidies follow. And schemes like Aadhaar will help in reducing this particular error.

If you were to design a subsidy scheme, which would be your second choice scenario?

 

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