Q 632. What is a Tolerance Interval? How is it different from Confidence Interval? Provide some examples of usage of tolerance intervals.

 

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A tolerance interval is a set of upper or lower limits with specified confidence that a given percentage of the process output falls in. A confidence level and a minimum percentage of the population must be specified in order to develop tolerance intervals. Tolerance intervals can be either one-sided, which means that one limit is either positive or negative infinity, or two-sided, that means that there are minimum and maximum values in the range.

 

Confidence Interval is the interval where the population mean is projected to fall. In all hypothesis testing, Confidence Intervals are calculated as we make conclusions about the population from the data set. It is a range of probabilities that is calculated by taking a set of observed data and using a confidence level (95%) to forecast where a population parameter eg. Mean is likely to fall. As Confidence Intervals are forecast for means, they are smaller and have less chances of going wrong.

 

 

Examples:

1.) Tolerance intervals may also be employed to identify process variance. Tolerance intervals are used to determine when product variation is excessive by comparing customer needs to tolerance limits covering a given percentage of the population.

2.) A customer care company would aim to make sure that, when calling customer support, 95% of its clients wait less than five minutes. Tolerance intervals allow the business to calculate the range of wait times that, with a certain degree of confidence, probably consists of 95% of future customer calls.

 

Tolerance interval is the range of values which contains certain proportion of a population. The width is normally determined by the sampling error and the variance in population itself. The difference between tolerance interval and confidence interval is confidence interval bounds a single valued population parameter with some confidence where as tolerance interval bounds the range of data values that includes a specific proportion of population. Usage of tolerance level will be visible in packaging industries where the weight or volume will have a tolerance limit. For example, a 1 Litre of Milk packet might contain 990 ml - 1010 ml of milk 

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.

 

Correct answers from all respondents. Muth Abraham has provided the best answer to this question. Well done!