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.

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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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## Comments

## Ill-used, anyway...

I've been doing some research for a paper on this subject. Michael Harry originally conceived the 1.5-sigma shift as a

designmargin. He told his engineers to run their simulations with all the critical component metrics shifted 1.5 sigmain the worst-case direction,to simulate the potential effects on the system of a worst-case tolerance stack nightmare. This makes a lot of sense, from a robust-design perspective.What doesn't make sense is that for whatever reason, this idea ended up being extrapolated to an assumption that a process could somehow sustain an undetected 1.5-sigma shift indefinitely (or, at least, over a statistically stable production run of 1,000,000). That absurd claim is probably the worst of several fundamentally flawed assumptions for the "Process Sigma Table" in most Six Sigma training materials, and its claim that a process operating at "Six Sigma" levels of quality produce no more than 3.4 defects per million opportunities.

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