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Questions tagged [tolerance-interval]

A tolerance interval is an interval that contains $p\%$ of a population with $(1-\alpha)$ confidence. A TI is distinct from (but sometimes confused with) prediction intervals & confidence intervals.

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Confidence intervals for non-parametric statistics

I have a positive random variable $X$ (say, price or latency or energy) and I want to be able to say something like I am 95% confident that $P(X<42)>0.9$ (percentile) or $P(X<22)\ge\frac12$ (...
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Accounting for unobserved variability in interval estimation

My work involves estimating the strength of materials. Essentially, a manufacturer has samples of a material tested for strength, and then we use that data to compute tolerance intervals. However, ...
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Confidence Interval For Values

Confidence Intervals help construct a range where you expect the true mean of a population of values to be, given some arbitrary sample. I'm curious if there is an equivalent function you can use, ...
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How do I find the probability of interference of a shaft and a bearing given their nominal diameter values and their standard deviations?

The exact question is as follows: An assembling of shaft and bearing is made out of shaft manufactured to a specification of 30.00 ± 0.09 mm and bearings are manufactured to a specification of 30.10 ±...
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Question related to Wald and Wolfowitz paper on tolerance limits

I have a question regarding Wald and Wolfowitz paper on tolerance limits for a normal distribution. There paper can be found here Wald and Wolfowitz denote the root of the equation: $ A(\bar{x},s,\...
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How is the equation for minimum sample size when using maximum and minimum sample values for nonparametric two-sided tolerance interval derived?

So the equation in question is $1-\alpha = 1-np^{(n-1)}+(n-1)p^n$ I have seen it in multiple textbooks but none of them shows how it's derived.
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95% limits of a normally distributed parameter

How do I find the 95% limits of the population distribution of a normally distributed parameter? I've taken the mean and SD from 10 different readings of the parameter. Will the 95% limits be mean +/-...
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Creating a tolerance range for measuring performance

Apologies for my ignorance, I've been trying to find an answer to my question but I think my understanding of statistical analysis is so rudimentary it has been confusing. I want to use a statistical ...
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How to derive a nonparametric minimum volume tolerance region from a random sample?

Given only a sample of IID variables with unknown density $f$, is there a way to derive a nonparametric tolerance region $T$ that contains at least a specified proportion $p$ of the population with at ...
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How do I know whether future samples will remain below a threshold?

I have N samples of quantity x (N=40 or 50 or so; I illustrate 7 of them here). ...
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90 views

Tolerance interval and significant probability

Let's take for simplicity an iid sample from a Gaussian random variable $Y \sim \mathcal{N}(\mu, \sigma^2)$. Let $y_0 \in \mathbb{R}$. The $(1-\alpha, p)$-bound of the lower one-sided (i.e. right-...
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Sample size calculation for non-normal data

I have a dataset that is not normally distributed - trying to prove 99.7% reliability of it being less than spec (spec=250). We typically would've used tolerance intervals if the data was normal for ...
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2-sided tolerance interval

Is there a way to find out which percentiles are being bounded by the interval? Say I calculate a 2-sided tolerance interval for 95% of the population with 95% confidence interval. How do I find out ...
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Tolerance interval for Poisson

I am an R user and need to figure out how to compute a tolerance interval for a Poisson distribution with lambda = 120. I would like to get a 1-sided upper tolerance interval with alpha = 0.05 and ...
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2answers
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Assessing model prediction performance using tolerance interval coverage

I am trying to assess a model's prediction performance, and one metric I look at is the percentage of new observations that fall within the 95% tolerance interval, and see whether or not it is ...
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Tolerance Interval for a Non-Random Sample

I have a sample of measurements representing the number of defects at a certain time point. I have 74 measurements over the past year. In addition, I have a limit of the maximum number of defects ...
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standard error about the mean apply to other values?

Does the standard error (SE) estimate of the mean (SE = sigma/sqrt(n)) only apply to the mean, or can it be applied to any value in the fit normal distribution? For example, if estimated 95th ...
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Making a forecast: Confidence/Prediction/Tolerance Interval?

I understand the the difference between these three types of intervals but I will summarize briefly: Confidence Interval: an interval that will contain the true mean value say, 95%, of the time. ...
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Conditioning within definition explanation

I have a doubt on the meaning of a conditioning within a definition. In a book I've found the following definition of upper tolerance limit: $P(P(X<\bar X+kS|\bar X, S)>p)=1-\alpha$ where $X$ ...
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Tolerance interval vs Prediction interval, which one is wider?

Let say we have a 95% prediction interval, versus 95%/99% tolerance interval, which one is wider? A. PI always wider than TI B. TI always wider than PI C. Depends on sample you get Thanks!
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Difference between gaussian and lognormal

I have to study tolerance intervals for a distribution of a random variable Z that is given by the difference of a normal X minus a (independent) lognormal Y. To begin with I tried to get an ...
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Statistical tolerance interval for half-normal or folded normal

I've a half-normal distribution with its $\theta$ parameter defined and I would need to compute a tolerance interval for a certain proportion of this population with a certain level of confindence. Do ...
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Spatial correlation and tolerance limits

I have previously studied the problem of defining tolerance limits for normal distributions for a given small sample of observations. Now I would like to take into consideration the fact that the ...
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One Sigma error and 68% tolerance interval

I have first a clarifying question, and second, a question asking about how to do something, depending on the answer to the first question. Suppose you have a set of data of some PDF which is non-...
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Reverse function to tolerance interval, using R

Given a data set and a min/max range, I want to know (with given alpha value) what portion of the population will be in it. This is the opposite of the tolerance interval, as I see it.
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Combining info from two population coverage levels from a tolerance interval

I have some existing product data from which I've calculated a tolerance interval with a 95% confidence level with at least 95% of population covered. I would like to use this tolerance interval as a ...
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Nonparametric tolerance intervals for discrete variables

Suppose you have a bunch of people rate how much they liked a movie on a discrete scale from 1 to 10, and you would like an interval [l, u] such that with (at least) 95% confidence, (at least) 90% of ...
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Use daily production as a check on whether monthly production goal is likely to be met

This is a real small business problem, not a homework problem. A monthly production goal is 60000. We want to be sure that say 95% of months meet this goal. The goal is a minimum, so we want to be ...
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How to obtain a confidence interval for a percentile?

I have a bunch of raw data values that are dollar amounts and I want to find a confidence interval for a percentile of that data. Is there a formula for such a confidence interval?
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Joint pdf of functions of order statistics

Let $ Y_1 < Y_2 <\ldots <Y_{10}$ be the order statistics of a random sample from a continuous type distribution with cdf $F(x)$. How would I begin to show that the joint distribution of $V_1=...
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Normality Testing - Choose the transformation that makes the data “most normal”?

Background: I have conducted some testing on a random sample of n=20 parts. The data is variable and I know nothing about the population statistics. I would like to use the data from this sample to ...
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207 views

Decision rule using tolerance intervals

I'm testing a new instrument with the traditional instrument and taking measurements on the same subject using both instruments. I want to be able to make a statement that "at least 95% of the ...
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313 views

One sided dist-free tolerance intervals and testing

I am involved in writing a standard where test labs are trying to decide sample sizes for a new device. The suggestion has been that using ISO 16269-6: Table F.1 ("sample size for a proportion p at ...
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Tolerance bound for a normalized variable

Based on a sample $(x_i) \sim_{\text{iid}} {\cal N}(\mu, \sigma^2)$, how can you get an exact or a well-approximated upper tolerance bound (i.e. an upper confidence bound of a quantile of the ...
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Tolerance interval for Deming regression

I am trying to derive (one-sided) tolerance intervals related to the Deming regression model: $$ x_i=x^*_i + \epsilon_i$$ $$ y_i = (\alpha+\beta x^*_i) + \epsilon'_i$$ where the $x^*_i$'s are ...
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686 views

What is the equivalent of a standard deviation when considering a least squares fit line?

I am calculating a tolerance interval following http://www.itl.nist.gov/div898/handbook/prc/section2/prc253.htm but this says to multiply the k value by the standard deviation of the sample. I have a ...
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Prediction and Tolerance Intervals

I have a couple of questions for prediction and tolerance intervals. Let's agree on the definition of the tolerance intervals first: We are given a confidence level, say 90%, the percentage of the ...
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482 views

Prediction vs. tolerance interval

I want to predict a factor and also get an upper bound for my prediction. It seems that what I want is prediction interval. but prediction interval only specifies the bound for one next prediction not ...