Sensor Technologies is a small manufacturing company located in Schenectady, New York. They produce a variety of motion and light detectors to be used in a wide range of settings. Sensor Technologies does not manufacture the electronic components contained within their sensor, but rather buys them from large scale electronics manufacturers and assembles their own products. Katrina Brown, the head of purchasing for Sensor Technologies, needs to acquire the new electrical components for an upcoming production run of the Model Z-62 motion sensor. The production plan is to produce 50,000 units.

For the primary sensor chip for the Model Z-62, Katrina has a couple of options. She can buy the units from AMG Electronics. AMG Electronics is a well-established electronics manufacturing firm that has a great reputation for customer service, and guarantees that all of their sensor chips have been tested and are 100% defect free. If Katrina buys from AMG, she is sure of getting defect-free chips, and she has been quoted a price of $2.62 per chip. Her other option is to buy the chips from Tech Relectronics. Tech Relectronics buys the production overruns from various chip manufacturers, then tries to resell the chips to other manufacturers who can use the chips. Since Katrina does not know who manufactured the chip, there is some risk that the chips bought from Tech Relectronics are faulty. Past experience with Tech Relectronics has shown that the defect rates have either been around 10% or around 20%. Assume that Sensor Technologies policy is that they will only buy in lots of 50,000 and if they find a defective chip, they replace it with a good chip from AMG (which they have in stock), and that there is no additional cost to replace a chip other than the cost of the chip itself.

Suppose Tech Relectronics is offering to sell 50,000 chips to Katrina at a price of $2.18 per chip. Furthermore, the sales representative for Tech Relectronics realizes that there is some risk associated with buying her chips. So she offers to send Katrina a random sample of 200 chips for her to inspect and test. Katrina turns to you for advice. Devise a sampling plan for her to use when testing these chips. For example, If the number of defects in the sample of 200 is greater than x dont buy the chips. If the number of defects in the sample of 200 is less than or equal to x, buy the chips. Justify your answer. Keep in mind that your sampling plan could result in two different types of mistakes; you can buy the chips from Relectronics when in fact you should not have, or you could not buy the chips from Relectronics when in fact you should have. The probabilities of these two types of mistakes should drive your sampling plan.