Analysis of Tolerance Levels of Resistors

Rob Jackson, Gayashan Ediriweera, and Rocky Gray

Recently, we purchased a set of 860 resistors with 86 different values from Joe Knows Electronics for a senior design project. Joe Knows claims that these particular resistors have a 1% tolerance rating. We’ve tested a few resistors and they seemed to be within the tolerance rating. However, we purchased these resistors at an extremely low price and were actually expecting a 5% tolerance rating. We think that a relatively high percentage of the resistors (about 15%) will . So, we would like to test whether or not Joe really does know electronics.
Resistors are a key component used when constructing any type of circuit, whether it is simple or complex. The current that flows through a resistor is in direct proportion to the voltage across the resistor's two terminals. Thus, the ratio of the voltage applied across a resistor's terminals to the intensity of current through the circuit is called resistance.
With our experience with resistors as computer engineers an extremely important component included with resistors is the tolerance level that it maintains. Many resistors are built based with a tolerance level that varies from .1% to 10%. For example a pack of 12 resistors could be built to have 100 ohms flow through it with a 1% tolerance level. This means that any resistor with a value of 99 to 101 ohms would be acceptable. This understanding of tolerance levels leads us to the basis of our experiment, whether our 860 resistors are within the tolerance level of 1%.
Our first job will be to collect data about the resistors. There are 86 different values within the 860 resistors, so there will be 10 resistors per value. We will test the resistance of the resistors within their respective groups and calculate the variance with respect to the expected values. This will help us determine whether or not the set of resistors are within the 1% tolerance level of their respective value. We will then find, as a whole, how many of the 860 resistors are actually within the 1% tolerance level.
Our hypothesis is that the tolerance level of the set of resistors is greater than 1%. If we set H0 : µ=1% and Ha: µ > 1%, then we’d shift the burden of proof on ourselves. But we want to shift the burden of proof over to Joe Knows so we would set H0: µ = 1% and Ha: µ < 1%, however, this would not confirm our hypothesis; it would only enable us to reject the claim that the tolerance is less than 1%, but what if it is exactly 1% (which would still mean their claim is valid)? We are still researching how to set up our hypothesis test.
By using our confidence intervals and hypothesis tests we should be able to figure out if Joe truly knows electronics. It will also help us to figure out how large the range of values for resistors actually is. Since these are integral pieces to all circuits they affect all electronic devices that people use. As computer engineers we also want to know if the tolerance level actually does affect our circuits or if its just used as a means of covering up discrepancies in manufacturing.