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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What is tolerance technique that use to deal missing data?

Current administrations of processing missing data can be approximately divided into three categories: tolerance, ignoring and imputation-based procedures. i- Missing data ignorance often refers to ...
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Indexing set in a probability measure [duplicate]

Reading a book I've noticed the following statement: If over the (sample) space $X$ there exists a class of probability measures, we denote a member of this class by $P^\theta_X(A)$ where $\theta$ ...
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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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statistical tolerance

My request is: I have data (sums of money) and someone calculated tolerance limits for the data. I want to validate these tolerance limits with statistical methods/arguments. Does anyone know ...
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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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about degree of precision and how to select randomly a sample by using minitab or spss

I have a data set which contains dependent variable Y,and independent variable X. and Population size is N = 270 I want to choose sample from this data set with simple random sampling. What should I ...
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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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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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266 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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Some clear range and interval definitions

What is your or an offical (please provide link to citation) definition of range AND interval _? Or perhaps put in another way: what is the major important difference between the two terms _? My ...
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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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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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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 ...