inner ring heat treatments are increased together." "Remembering that bearings like this one have been made for decades, it is at first surprising that it could take so long to discover so important an improvement. A likely explanation is that, because most engineers have, until recently, employed only one factor at a time experimentation, interaction effects have been missed." Example The simplest factorial experiment contains two levels for each of two factors. Suppose an engineer wishes to study the total power used by each of two different motors, A and B, running at each of two different speeds, 2000 or 3000 RPM. The factorial experiment would consist of four experimental units: motor A at 2000 RPM, motor B at 2000 RPM, motor A at 3000 RPM, and motor B at 3000 RPM. Each combination of a single level selected from every factor is present once. This experiment is an example of a 22 (or 2×2) factorial experiment, so named because it considers two levels (the base) for each of two factors (the power or superscript), or #levels#factors, producing 22=4 factorial points. Designs can involve many independent variables. As a further example, the effects of three input variables can be evaluated in eight experimental conditions shown as the corners of a cube. This can be conducted with or without replication, depending on its intended purpose and available resources. It will provide the effects of the three independent variables on the dependent variable and possible interactions. Notation The notation used to denote factorial experiments conveys a lot of information. When a design is denoted a 23 factorial, this identifies the number of factors (3); how many levels each factor has (2); and how many experimental conditions there are in the design (23 = 8). Similarly, a 25 design has five factors, each with two levels, and 25 = 32 experimental conditions. Factorial experiments can involve factors with different numbers of levels. A 243 design has five factors, four with two levels and one with three levels, and has 16 × 3 = 48 experimental conditions. To save space, the points in a two-level factorial experiment are often abbreviated with strings of plus and minus signs. The strings have as many symbols as factors, and their values dictate the level of each factor: conventionally, for the first (or low) level, and for the second (or high) level. The points in this experiment can