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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Extreme value function in R

I have a small data set (n=25) with an unknown distribution and I'm trying to find a distribution function that is as similar as possible in order to ultimately determine tolerance limits. I used the ...
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Linear Model + tolerance intervals: How to show that when a condition is fulfilled for a tool it is also fulfilled for another related tool?

The problem Imagine that you have two different tools that produce data at given time points $t_1,...,t_m$. Suppose that we only have access to the mean and standard deviation of the data at each time ...
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When to pool batches for tolerance intervals?

Imagine that we have at disposal several batches of data from a given process and that the interval time of record of each batches can be week, months or even years. Out of these data, we would like ...
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Calculation of a nonparametric equal-tailed (central) tolerance interval for an unknown continuous distribution

Assume we have a sample of size $n$ from an unspecified continuous distribution $F(\cdot)$. We wish to construct a tolerance interval to contain $(100\,\beta)\%$ of the population with a pre-specified ...
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Bootstrapping with quantiles of data instead of SD*z?

I have recently been bootstrapping the confidence intervals of a neural network model estimated to data. I execute the following psudo-code, which seems similar to previous bootstraps I have done: ...
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Conditional Tolerance Interval

With the generous help of people here, I've recently learned about the notion of a Tolerance Interval (Confidence in a range estimate, and +- 2sigma rule of thumb). I am now working on an application ...
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Prediction Intervals and Tolerance Intervals [duplicate]

I have a question regarding interpretation of prediction intervals and confidence intervals. The definitions I've seen is: (1) A prediction interval for a single future observation is an interval ...
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How does the Empirical Rule align with Tolerance Interval

For Empirical Rule, 95% of the observed data will occur within the second standard deviation, but what is the difference between this and the 95/95 2-sided tolerance interval ? It includes 95% of ...
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Lower confidence with larger sample size? Tolerance interval for distribution-free data

I am trying to find the sample size required in order to establish a tolerance interval which contain 99% of the population, with 95% confidence. The results from Minitab for a sample size of 473 are ...
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Is it possible to estimate a specific quantile of a prediction based on the results of ordinary linear regression?

We can estimate mean value of a prediction with a specific confidence, we have an estimated value of a variance (MSE) and we also assume that prediction is a normally distributed random variable. Isn'...
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interval depending on sample size

I came across these funnel plots here and tried to reproduce something similar where I have a normally distributed population and I happen to know the true population mean (500000) and standard ...
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Tolerance Interval from the posterior predictive distribution of a ratio of two Normal distributions

I am trying to calculate a Beta-Gamma Tolerance Interval from the Posterior Predictive Distribution of a log(ratio) of two normal (no close form available). In the minimal R code below, assume ...
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tolerance interval, sample size and power

I can only find limited information on how to calculate sample sizes in respect to tolerance intervals. I have a particular problem I would appreciate any help on. If I had a normally distributed ...
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How to set the tolerance in Gradient descent?

I understand that one solution of setting the number of iterations, is to set it to a large number and then interrupt it when the gradient vector becomes tiny, so tiny that it is smaller than a ...
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Tolerance Interval of large Time Series data

I have a time series Temperature data coming from a sensor which is collected at a irregular frequency. The data size is ~100K. I have to find the Lower and Upper Bounds for this data to find the ...
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finding different value while doing regression

My question may sound unclear but I'm going to explain it in detail. I have a data set includes two-column with 50 samples. let's call the first column energy and the second column cracking. Let's ...
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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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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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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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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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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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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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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 ...
Stéphane Laurent's user avatar
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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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