Engineers have used safety margins for centuries to protect their companies and customers from the consequences of product degradation and failure. Sometimes the safety margins are fairly obvious (e.g., maximum-load limits posted in elevators), and other times they’re not.

Design margins are often hidden from view. For example, some computers have cooling fans that are used to reduce the CPU’s failure rate. A heat sensor in the computer automatically increases the fan’s speed, which increases air flow and cools the CPU, thus reducing the failure rate of this expensive computer component.

In quality engineering there are some popular statistics that have less-than-obvious safety margins included. Consider the process capability index Cpk, which is defined for a stable normal process as:

Cpk = min{(USL – mean), (mean – LSL)}/ 3 sigma

where sigma is the within the rational subgroup estimate of variation.

Because the minimum is used, the metric reflects only half the distribution, and hence the fraction nonconforming for the distribution can range from p to 2p, where p corresponds to the tail area of the minimum distance of the mean to the specification limits for a normal distribution.

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