Approximate two-sided tolerance interval for sample variances

Yao, Yuhui; Sarmiento, Martin G. C.; Chakraborti, S.; Epprecht, Eugenio K.

doi:10.1080/08982112.2019.1609687

Cited by 5 publications

(9 citation statements)

References 35 publications

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“…Data in Table represent the detonation times for a set of 20 shots with 14 detonators per shot. This example has been discussed in Tietjen and Johnson, in Sarmiento et al and also in Yao et al On the basis of these data, the unbiased pooled sample variance estimator of

σ^{2}

can be calculated using Equation . The variance of each shot and the estimator

S_{p}^{2}

are given in Table .…”

Section: Illustrationmentioning

confidence: 98%

“…It should be noted that the performance of the TI is measured in terms of the width of the TI, which measures the precision, and it is often of interest to find the shortest TI. Fernández minimized the width of the TI by Lagrangian multiplier to choose control‐both‐tails TIs for the exponential distribution.…”

Section: Adjusted Control‐both‐tails Tismentioning

confidence: 99%

“…Qomi and Kiapour computed the TI with the shortest width by a Monte Carlo simulation study, controlling both tails of the exponential distribution based on record values. Yao et al measured the performance of the TI by studying the distribution of width for the TI. In this section, we propose a method for constructing the shortest control‐both‐tails TI for sample variances.…”

Section: Adjusted Control‐both‐tails Tismentioning

confidence: 99%

“…Sarmiento et al presented the exact two‐sided control‐the‐center TI for sample variances, where the samples are drawn from a normal distribution with unknown parameters. Then, for the sake of convenience, Yao et al proposed a simply, approximate two‐sided control‐the‐center TI based on the method provided by Sarmiento et al Besides, Hamada provided the TI to control both tails of the distribution of sample standard deviations, whose tolerance factors were obtained by simulation. Under this background, this paper considers the exact control‐both‐tails TI for sample variances, which has not been considered previously.…”

Section: Introductionmentioning

confidence: 99%

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Exact two‐sided tolerance interval controlling tail proportions for sample variances

Guo

Zhu

Wang

et al. 2020

Quality & Reliability Eng

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Tolerance intervals (TIs) for variances are useful when we are interested in the precision of the quality characteristic. They can provide a deeper understanding of the process variability corresponding to process improvement and deterioration. In this paper, we consider the exact two‐sided TI for sample variances that simultaneously controls the proportions in each of the two tails of the distribution. The minimum number of subgroups required to achieve a specified level of precision is also computed. Moreover, we minimize the width of the TI through adjusting the tolerance factors, and the performance of the adjusted TI shows some improvement, especially when the amount of reference data is small. Finally, a real application is used to illustrate the construction and implementation of the proposed TIs.

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σ^{2}

can be calculated using Equation . The variance of each shot and the estimator

S_{p}^{2}

are given in Table .…”

Section: Illustrationmentioning

confidence: 98%

Section: Adjusted Control‐both‐tails Tismentioning

confidence: 99%

Section: Adjusted Control‐both‐tails Tismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact two‐sided tolerance interval controlling tail proportions for sample variances

Guo

Zhu

Wang

et al. 2020

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…The performances of the two proposed approximate tolerance intervals are examined by means of the assessment of the accuracy of the corresponding approximate tolerance factors and an illustration of a dataset from a real application. For more details on the exact method and the second approximate method, see Sarmiento et al (2018) and Yao et al (2019), respectively, which are two resulting articles of the present thesis.…”

Section: Derivation Of the Two-sided Tolerance Limits For Sample Varimentioning

confidence: 99%

Tolerance Intervals for Sample Variances Applied to the Study of the Phase Ii Performance and Design of S(2) Charts With Estimated Parameters

SARMIENTO¹

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Exact tolerance interval with specified tail probabilities and a control chart for the sample variance

Alqurashi

Chakraborti

Holcombe

2022

Quality & Reliability Eng

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A 𝛽-content tolerance interval (TI) is a statistical interval which contains at least some fraction (proportion) 𝛽 of the population with a given confidence level. When we are interested in the precision of a quality characteristic, a TI for the sample variance is useful. In this paper, we consider an exact two-sided 𝛽-content TI for the sample variance from a normal distribution with a specified ratio of the tail probabilities. The proposed tolerance interval allows the practitioner more control over how the probabilities in the tails are distributed, which may be useful in certain applications. A comparison with an existing two-sided 𝛽-content TI shows that the proposed TI is better on the basis of expected coverage and standard deviation of the coverage. In addition, the proposed TI is shown to require fewer subgroups to achieve a specific accuracy level. Moreover, a phase II control chart with guaranteed performance is obtained from the proposed TI. Finally, a real and a simulated data are used for illustration.

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Approximate two-sided tolerance interval for sample variances

Cited by 5 publications

References 35 publications

Exact two‐sided tolerance interval controlling tail proportions for sample variances

Exact two‐sided tolerance interval controlling tail proportions for sample variances

Tolerance Intervals for Sample Variances Applied to the Study of the Phase Ii Performance and Design of S(2) Charts With Estimated Parameters

Exact tolerance interval with specified tail probabilities and a control chart for the sample variance

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