Tolerance
The tolerance defines the space available to a process. It is the acceptable range within which the measured characteristics of parts or processes may vary with regard to fit, form, or function. Measured characteristics that fall within the tolerance are deemed conforming, while those that fall outside are nonconforming. To calculate the tolerance, subtract the Lower Specification Limit (LSL) from the Upper Specification Limit (USL) using the formula:
The relationship between the tolerance and a dataset of electrical resistance measurements is shown in Figure 1. Here, the USL is 5,295 and the LSL is 3,395. The tolerance associated with these specification limits is 1,900 mega ohms. Resistance measurements that fall inside the specification limits (tolerance) are conforming, while those that fall outside are nonconforming. In its current form, the process in Figure 1 is producing both conforming and nonconforming product. This is indicated by the width of the distribution being wider than the space available to the process allotted by the tolerance.
Figure 1. Capability histogram showing the specification limits (tolerance), target, and mean of the distribtuion.
To improve this process the underlying causal system must be characterized as either predictable or unpredictable using process behavior charts. If the process is characterized as unpredictable, assignable causes of exceptional variation must be eliminated. If the process is characterized as predictable, only common causes of routine variation influence process behavior. To reduce the influence of common causes new technology, new equipment, new materials, or new procedures must be introduced.
A word of warning
Producing parts inside specification (within tolerance) is generally considered good enough. This kind of thinking imbues the measured characteristics of parts and processes with the same level of uniform quality. This is epitomized by the square loss function shown in Figure 2. Here, values near the specification limits have the same quality as values near the target. Only when a value falls outside of the specification limits is the loss due to poor quality incurred. This antiquated way of thinking dates back to the earliest days of the industrial revolution.
Figure 2. Square loss function.
To avoid the trappings of a good enough, a new way of thinking is required. Luckily, this new way of thinking already exists. In September 1960, Dr. Genichi Taguchi defined world-class quality as on-target with minimum variance. This definition of quality governs the space available (tolerance) to a process with a quadratic loss function like the one shown in Figure 3. Here, measured characteristics that produced on-target are imbued with the highest quality. The further a measured characteristic diverges from the target, the larger the loss due to poor quality.
Figure 3. Quadratic loss function