Sample size determination strategies for normal tolerance intervals using historical data

Young, Derek S.; Gordon, Christopher P.; Zhu, Shihong; Olin, Bryan

doi:10.1080/08982112.2015.1124279

Cited by 17 publications

(15 citation statements)

References 31 publications

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“…Both of these strategies assume there is some historical data and specification limits for the process at-hand. We briefly illustrate these strategies below and refer the reader to Young et al (2016) for further details.…”

Section: Sample Size Determination Strategiesmentioning

confidence: 99%

“…for one-sided upper tolerance limits, one-sided lower tolerance limits, or equal-tailed tolerance intervals, respectively. As emphasized in Young et al (2016), this approach is intended simply for planning purposes and it does not guarantee any specific bounds relative to the nominal coverage probability. Note that (29) is for an equal-tailed tolerance interval since we posit values for µ and σ and, thus, the resulting tolerance interval would be built around a (hypothetically) true center of the normal population.…”

Section: Sample Size Determination Strategiesmentioning

confidence: 99%

“…The second alternative strategy presented in Young et al (2016) is a method for providing datadependent values of the precision quantities P and δ in the approach due to Faulkenberry and Weeks (1968). The approach assumes there is information on historical data, a set of current data, and specification limits that can be used for calculating values of P and δ.…”

Section: Sample Size Determination Strategiesmentioning

confidence: 99%

See 2 more Smart Citations

Normal Tolerance Interval Procedures in the tolerance Package

Young¹

2016

The R Journal

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Statistical tolerance intervals are used for a broad range of applications, such as quality control, engineering design tests, environmental monitoring, and bioequivalence testing. tolerance is the only R package devoted to procedures for tolerance intervals and regions. Perhaps the most commonly-employed functions of the package involve normal tolerance intervals. A number of new procedures for this setting have been included in recent versions of tolerance. In this paper, we discuss and illustrate the functions that implement these normal tolerance interval procedures, one of which is a new, novel type of operating characteristic curve.

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Section: Sample Size Determination Strategiesmentioning

confidence: 99%

Section: Sample Size Determination Strategiesmentioning

confidence: 99%

Section: Sample Size Determination Strategiesmentioning

confidence: 99%

See 1 more Smart Citation

Normal Tolerance Interval Procedures in the tolerance Package

Young¹

2016

The R Journal

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“…Specifically, their work was aimed at assessing results from an MRI‐guided prostate biopsy research trial. Young et al addressed the conformance to specifications during the design verification stage of a medical device that aids in the treatment of refractory epilepsy and treatment‐resistant depression. Lizotte and Tahmasebi assessed the variability in individual outcomes under a dynamic treatment regime to provide patient‐centered data‐driven sequential decisions.…”

Section: Introductionmentioning

confidence: 99%

Improving coverage probabilities for parametric tolerance intervals via bootstrap calibration

Zou

Young

2020

Statistics in Medicine

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Statistical tolerance intervals are commonly employed in biomedical and pharmaceutical research, such as in lifetime analysis, the assessment of biosimilarity of branded and generic versions of biopharmaceutical drugs, and in quality control of drug products to ensure that a specified proportion of the products are covered within established acceptance limits. Exact two-sided parametric tolerance intervals are only available for the normal distribution, while exact one-sided parametric tolerance limits are available for a limited number of distributions.Approximations to two-sided parametric tolerance intervals often use the Bonferroni correction on the one-sided tolerance interval calculation; however, this often incurs a higher coverage probability than the nominal level. Recently, the usage of a bootstrap calibration has been demonstrated as a way to improve coverage probabilities of tolerance intervals for very specific and complex distributional settings. We present a focused treatment on using a single-layer bootstrap calibration to improve the coverage probabilities of two-sided parametric tolerance intervals. Simulation results clearly demonstrate the improved coverage probabilities towards the nominal level over the uncalibrated setting.Applications to medical data for various parametric distributions also highlight the utility of constructing these calibrated tolerance intervals.

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“…For example, researchers have proposed TIs for a normal distribution. [12][13][14][15][16] Simultaneously, many studies on the TI for an exponential distribution also emerged. [17][18][19][20] Besides, TIs have also been studied for the Pareto distribution, 21 hypergeometric distribution or negative hypergeometric distribution, 22 and binomial distribution.…”

Section: Introductionmentioning

confidence: 99%

Constructing exact tolerance intervals for the exponential distribution based on record values

Guo

Zhu

Wang

et al. 2020

Quality & Reliability Eng

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Recently, with the wide application of tolerance intervals (TIs), especially in quality management, the construction of TIs has attracted increasing attention. However, TIs applied to record data have not been well established as they have been for complete data. In many industrial stress tests, only record data are stored instead of complete data, which leads to the fact that the developments of methods based on record data are as important as those based on complete data. In this paper, we propose the exact two-sided TIs for the exponential distribution based on record values from the frequentist and Bayesian perspectives. The accuracy of each type of TIs is quantified. The results show that the Bayesian approach is superior to the frequentist approach in terms of the accuracy. A real data example is used to illustrate the constructions and implementations of the proposed TIs.

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Sample size determination strategies for normal tolerance intervals using historical data

Cited by 17 publications

References 31 publications

Normal Tolerance Interval Procedures in the tolerance Package

Normal Tolerance Interval Procedures in the tolerance Package

Improving coverage probabilities for parametric tolerance intervals via bootstrap calibration

Constructing exact tolerance intervals for the exponential distribution based on record values

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