Muth Abraham

Tolerance intervals are used in software testing and manufacturing, particularly in machining and moulding, to show whether a component is meeting specifications and fit for its intended purpose. The question is how much deviation can be tolerated, given that the target value (e.g., the diameter of a piston being manufactured or the true value of cost) is known, but manufacturing is never exact, and computations using floating-point software have approximation problems. The tolerance level is what separates something from being unacceptable and requiring revisions or discarding it from being acceptable as is.
 
Whereas confidence interval is used to estimate a reasonable range of values within which the true value is likely to be, given some data containing unknown errors, for random data for which the true value is unknown. We are unable to confirm, though, that the true value falls inside that range. The true value is never 100% guaranteed to lie within an interval, but the wider the interval, the more likely it is to do so. However, the interval may become essentially meaningless if it is made so large that the true value is almost certainly within it. In order to achieve equilibrium and be able to state that we have 68% or 95% or whatever confidence that the true value is within this such-and-such interval,.
 
Basic Eg Tolerance Level & confidence Level
 
Tolerance interval
A range of values for a product's characteristic likely covers where a specified proportion of the population lies with a specified degree of confidence.
For example, if the 95% tolerance interval for 99% of the population for the fill volume of 375 ml bottles is 358–381 ml, you can be 95% confident that 99% of the bottles to be filled in the future will have volumes that are within this interval.
 
Confidence interval
A range of values that is likely to contain the value of an unknown population parameter, such as the mean, with a specified degree of confidence.
For example, if the 95% CI of the average fill volume of 375 ml bottles is 368–372 ml, you can be 95% confident that the true value of the process mean is within this interval.