In the manufacture of metal pieces which require at least moderate precision (say, ball bearings, or valves, but not roofing nails or door hinges), what is a typical error rate? I only need an order of magnitude estimate. For example, if a factory makes a million balls for use in ball bearings, how many will be defective?
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$\begingroup$ None. Every single one should be in tolerance for something. If not, you have some improvements to be made to your process. Ball bearings might be a poor example though- it really depends on the part. $\endgroup$– AbelCommented Feb 2 at 3:42
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$\begingroup$ Any part failing a tolerance check will get recyled back to the start. $\endgroup$– Solar MikeCommented Feb 2 at 9:15
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$\begingroup$ two categories: defects that escape to customer, and defects that are caught (i.e. 1-yield). For first category, determined by what market will accept. Something like a bearing is a special case, because subtle failure modes over time. My gut feel for something like valve or industrial electrical cables: "mid-value" brands ~= 0.2% defective, and the market seems to tolerate this, willing to test and catch it at the next level of integration ; "top" brands ~= 0.02% defective. Pay more for high confidence. The other category, defects caught in QC, I'd expect tremendous variation $\endgroup$– Pete WCommented Feb 2 at 15:11
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$\begingroup$ also depends on use. the impact of a part failure goes up with the cost/complexity of the machine into which you install it. The possibility of a 0.1% part defect rate in manufacturing a small 100-part benchtop product is probably not a concern at all, the QC needed to detect, find, and fix it would be reasonable. A 0.1% defect rate in a bespoke 50,000 part industrial machine, with low production volume, would have much more cost impact to detect, find, and fix it... so the latter likely to pay more for high grade parts with much lower defects $\endgroup$– Pete WCommented Feb 2 at 15:14
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2$\begingroup$ this is so broad as to be unanswerable. The rates will vary by orders of magnitude depending on the part and the manufacturing process. Even ball bearings will vary. Bearings are used in everything from children's toys and kitchen appliances to jet engines and space satellites. The former have loose requirements (thus low scrap rates) while the later need precision (thus high scrap rates, even with expensive manufacturing process). You really need to narrow down the question. For example, "what is the error rate for a CNC mill manufacturing a part to a 0.005 inch tolerance" is answerable. $\endgroup$– Daniel KCommented Feb 5 at 0:03
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The most common measure of a high quality process these days is "six sigma." This means a process whose variability as measured in standard deviations is six standard deviations from the spec limit (upper and lower). Six sigma mathematically is .002 defects per million opportunities. That said, Motorola, which mostly developed this methodology, expected setpoint drift of 1.5 sigma, so the true expected defect rate of a "6 sigma process" is actually 4.5 sigma, or 3.4 million defects per million opportunities. Industries such as airlines may have processes that have even lower expected failure rates than this due to the catastrophic consequences of failure. I suggest that the key learning of Six Sigma is that high quality processes (those with few defects) save money. The old adage was that you could choose two from fast, cheap, or good has been retired by modern methods.
Now, your process in hand may be much much worse than this. All of this is relative to your specification limits. Back when Toyota was launching Lexus, they set very demanding spec limits for the weight of engine components, such that they had to create new manufacturing methods to meet the specs. The result was an engine that ran much smoother than the competition. If you were familiar with car panel fit in American cars in the 70s, my guess is the spec was +/- .25 inches (6 mm) and they may have had very few failures relative to that sad spec. Japan came along and showed that the right spec was much lower, and put US manufacturers to shame. Now if you decide (like a certain electric car manufacturer's CEO) that all components must be built to a +/- 10 micron spec, my guess is you will have a 1 sigma or less process until you figure out how to do it, give up, or go bankrupt trying.
You can spend a career becoming expert on these issues. My knowledge is via Statistical Process Control, Total Quality Method, and Six Sigma training. My description here is a drop in the ocean of the knowledge that exists on the subject.
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$\begingroup$ Thank you so much. This is just what I was looking for. I grew up in Detroit in the 1970s, so know something of the American car panels you speak of…. $\endgroup$ Commented Feb 6 at 2:56