Normal Tolerance Interval Procedures in the tolerance Package

Young, Derek S.

doi:10.32614/rj-2016-041

Cited by 10 publications

(12 citation statements)

References 21 publications

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“…where the random variables Z and v 2 in equation (5) are the same as those in equation (4). The R package tolerance 24,25 can be used to compute c 5 . Figure 3 that c 5 is considerably larger than c 1 in order that RR 5 contains 100 P ð Þ% of the population with a pre-specified large confidence c about the randomness in the sample.…”

Section: Tolerance Intervalsmentioning

confidence: 99%

“…15 A formula for values of c 6 is available 11 and can be computed using the function K.factor of the R package tolerance. 24,25 This interval can be viewed as a c confidence simultaneous lower confidence bound on quantile l À z ð1þPÞ=2 r and upper confidence bound on quantile l þ z ð1þPÞ=2 r. 26 It is clear that comprising the central 100 P ð Þ% of the population ½l À z ð1þPÞ=2 r; l þ z ð1þPÞ=2 r implies containing 100 P ð Þ% of the population. Hence the equal-tailed RR 6 satisfies a more stringent requirement than RR 5 and, as a result, c 6 is larger than c 5 .…”

Section: Equal-tailed Tolerance Intervalsmentioning

confidence: 99%

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Reference range: Which statistical intervals to use?

Liu

Bretz

Cortina‐Borja

2020

Stat Methods Med Res

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Reference ranges, which are data-based intervals aiming to contain a pre-specified large proportion of the population values, are powerful tools to analyse observations in clinical laboratories. Their main point is to classify any future observations from the population which fall outside them as atypical and thus may warrant further investigation. As a reference range is constructed from a random sample from the population, the event ‘a reference range contains [Formula: see text] of the population’ is also random. Hence, all we can hope for is that such event has a large occurrence probability. In this paper we argue that some intervals, including the P prediction interval, are not suitable as reference ranges since there is a substantial probability that these intervals contain less than [Formula: see text] of the population, especially when the sample size is large. In contrast, a [Formula: see text] tolerance interval is designed to contain [Formula: see text] of the population with a pre-specified large confidence γ so it is eminently adequate as a reference range. An example based on real data illustrates the paper’s key points.

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Section: Tolerance Intervalsmentioning

confidence: 99%

Section: Equal-tailed Tolerance Intervalsmentioning

confidence: 99%

Reference range: Which statistical intervals to use?

Liu

Bretz

Cortina‐Borja

2020

Stat Methods Med Res

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show abstract

“…Fig. 1 The critical value z p for a standard normal distribution The exact solution for the two-sided k 2 factor can be obtained by solving the following implicit nonlinear integral equation [21,22]:…”

Section: Methodsmentioning

confidence: 99%

Quantifying and Qualifying Alloys Based on Level of Homogenization: A U-10Mo Alloy Case Study

Wang

Fagan

et al. 2019

Journal of Engineering Materials and Technology

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Homogenization heat treatment is performed to attain uniformity in microstructure which is helpful to achieve the desired workability and microstructure in final products and, eventually, to gain predictive and consistent performance. Fabrication of low-enriched uranium alloys with 10 wt% molybdenum (U-10Mo) fuel plates involves multiple thermomechanical processing steps. It is well known that the molybdenum homogeneity in the final formed product affects the performance in the nuclear reactor. To ensure uniform homogenization, a statistical method is proposed to quantify and characterize the molybdenum concentration variation in U-10Mo fuel plates by analyzing the molybdenum concentration measurement data from scanning electron microscopy energy dispersive spectroscopy line-scan. Statistical tolerance intervals (TI) are employed to determine the qualification of the U-10Mo fuel plate. We formulate an argument for the minimum number of independent samples to define fuel plate qualification if no molybdenum measurement data are available in advance and demonstrate that the given TI requirements can be equivalently reduced to a sample variance criterion in this application. The outcome of the statistical analysis can be used to optimize casting design and eventually increase productivity and reduce fabrication costs. The statistical strategy developed in this paper can be implemented for other applications especially in the field of material manufacturing to assess qualification requirements and monitor and improve the process design.

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“…(10), a comparison is conducted by solving the true solutions calculated from Eq. (9) using the R package developed in (Young 2016). The relative error between approximation and true solution is defined as 1 − 2 ( ) 2 ( ) .…”

Section: Methodsmentioning

confidence: 99%

Quantifying and Qualifying Alloys Based on Level of Homogenization: A U–10 wt% Mo Alloy Case Study

Wang

Fagan

et al. 2019

View full text Add to dashboard Cite

Normal Tolerance Interval Procedures in the tolerance Package

Cited by 10 publications

References 21 publications

Reference range: Which statistical intervals to use?

Reference range: Which statistical intervals to use?

Quantifying and Qualifying Alloys Based on Level of Homogenization: A U-10Mo Alloy Case Study

Quantifying and Qualifying Alloys Based on Level of Homogenization: A U–10 wt% Mo Alloy Case Study

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