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A tolerance interval is a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls.
A tolerance 16296-6 can be seen as a statistical version of a probability interval. The tolerance interval is less widely known than the confidence interval and prediction intervala situation some educators have lamented, as it can lead to misuse of the other intervals where a tolerance interval is more appropriate.
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The tolerance interval differs from a confidence interval in that the confidence interval bounds a single-valued population parameter the mean or the variancefor example with some confidence, while the tolerance interval bounds the range of data values that includes a specific proportion of the population. Whereas a confidence interval’s size is entirely due to sampling errorand will approach a zero-width interval at the true population parameter as sample size increases, a tolerance interval’s size is due partly to sampling error and partly to actual variance in the population, and will approach the population’s probability interval as sample size increases.
The tolerance interval is related to a prediction interval in that both put bounds on variation in future samples. The prediction interval only bounds a single future sample, however, whereas a tolerance interval bounds the entire population equivalently, an arbitrary sequence of future samples.
In other words, a prediction interval covers a specified proportion of a population on averagewhereas a tolerance interval covers it with a certain confidence levelmaking the tolerance interval more appropriate if a single interval is intended to bound multiple future samples.
Tolerance interval – Wikipedia
So consider once again a proverbial EPA mileage test scenario, in which several nominally identical autos of a particular model are tested to produce mileage figures y 1y 2.
Such an interval, would however, not be of much help to a person renting one of these cars and wondering whether the full gallon tank of gas will suffice to carry him the miles to his destination. For that job, a prediction interval would be much more useful.
Another example is given by: It was noted that the log-transformed lead levels fitted a normal distribution well that is, the data are from a lognormal distribution.
We note that exp mu is the median air lead level. A confidence interval for mu can be constructed the usual way, based on the t -distribution ; this in turn will provide a confidence interval for the median air lead level. Now suppose we want to predict the air lead level at a particular area within the laboratory. A two-sided prediction interval can be similarly computed.
The meaning and interpretation of these intervals are well known. A prediction interval has a similar interpretation, and is meant to provide information concerning a single lead level only. The confidence interval and prediction interval cannot answer this question, since the confidence interval is only for the median lead level, and the prediction interval is only for a single lead level. What is required is a tolerance interval; more specifically, an upper tolerance limit.
One-sided normal tolerance intervals have an exact solution in terms of the sample mean and sample variance based on the noncentral t -distribution. From Wikipedia, the free encyclopedia. Not to be confused with Engineering tolerance. This section needs expansion with: You can help by adding to it.
YoungBook Reviews: Ryan 22 June Retrieved 22 February Determination of statistical tolerance intervals”. A tutorial on tolerance intervals for ordinary least-squares regression”. Chemometrics and Intelligent Laboratory Systems. Theory, Applications, and Computation. John Wiley and Sons. Journal of Statistical Software.
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