What is required is a tolerance interval; more specifically, an upper tolerance limit.
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The tolerance interval is related to a prediction interval in that both put bounds on variation in future samples.
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What the engineer really needs is a tolerance interval for a fraction p = . 99 of mileages of such autos.
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A tolerance interval bounds this variance by introducing a confidence level \ gamma, which is the confidence with which this interval actually includes the specified proportion of the population.
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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 ).
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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 variance, for example ) with some confidence, while the tolerance interval bounds the range of data values that includes a specific proportion of the population.
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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 variance, for example ) with some confidence, while the tolerance interval bounds the range of data values that includes a specific proportion of the population.
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In other words, a prediction interval covers a specified proportion of a population " on average ", whereas a tolerance interval covers it " with a certain confidence level ", making the tolerance interval more appropriate if a single interval is intended to bound multiple future samples.
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In other words, a prediction interval covers a specified proportion of a population " on average ", whereas a tolerance interval covers it " with a certain confidence level ", making the tolerance interval more appropriate if a single interval is intended to bound multiple future samples.
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For a normally distributed population, a z-score can be transformed into a " " k " factor " or "'tolerance factor "'for a given \ gamma via lookup tables or several approximation formulas . " As the degrees of freedom approach infinity, the prediction and tolerance intervals become equal ."
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