Three-phase optimal design of sensitivity experiments

Wu, C. F. J.; Tian, Yubin

doi:10.1016/j.jspi.2013.10.007

Cited by 31 publications

(15 citation statements)

References 10 publications

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“…This results in samples where the Fisher information for the threshold value is near its maximum. The test algorithm uses the three-phase design of Wu [27] to obtain a meaningful estimate of the scale parameter more quickly. In the final stage, samples are taken near the threshold (plus or minus a small fraction of the Full Paper scale parameter).…”

Section: Detonator Testingmentioning

confidence: 99%

The Role of Pentaerythritol Tetranitrate (PETN) Aging in Determining Detonator Firing Characteristics

Lease

Burnside

Brown

et al. 2020

Propellants Explo Pyrotec

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Pentaerythritol tetranitrate (PETN) is one of the most commonly used explosives for both military and mining applications. PETN is used in EBW (exploding bridge wire) and EFI (exploding foil initiator) detonator devices. Due the widespread usage of PETN, studies focusing on how the explosive changes with age, primarily its function in detonators has received particular interest. Aging studies have identified several factors that affect PETN detonator function over time, most notably the specific surface area of the explosive powder. Though small-scale studies have been performed on specific detonator systems with isolated batches of material, what is missing is a large statistically-significant study focusing on PETN aging characteristics-such as powder coarsening-and their influence on detonator performance. Herein we report the first large statistically viable PETN aging study focusing on four batches of PETN powder from the same stock of PETN using two stabilizers, polysaccharide and TriPEON. PETN was aged both as a free-flowing powder as well as in modified EBW RP-2 detonators, for one month at 75°C. The PETN powder has been analyzed chemically using Fisher specific surface area analysis, SEM imaging and light scattering particle size analysis. Additionally the detonators were tested for performance through voltage-sweep threshold testing and function time measurements. Findings from the study indicate that aging at 75°C for one month significantly changes the specific surface area and particle size of unstabilized PETN, leading to increases in detonator function time, but not detonator threshold values. Powders stabilized with TriPEON displayed less significant increases in function time, while powder stabilized with polysaccharide exhibited no aging effects, despite the high temperature aging.

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Section: Detonator Testingmentioning

confidence: 99%

The Role of Pentaerythritol Tetranitrate (PETN) Aging in Determining Detonator Firing Characteristics

Lease

Burnside

Brown

et al. 2020

Propellants Explo Pyrotec

View full text Add to dashboard Cite

show abstract

“…This finding about signs was put forth as a conjecture in a discussion (Ray et al, 2013) of the paper by Wu and Tian (2013) on sensitivity experiments. These sensitivity experiments are sequential experimental designs to estimate quantities such as a dose with 50% lethality (LD50) in toxicology.…”

Section: Introductionmentioning

confidence: 84%

The Sign of the Logistic Regression Coefficient

Owen¹,

Roediger²

2014

The American Statistician

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Let Y be a binary random variable and X a scalar. Letβ be the maximum likelihood estimate of the slope in a logistic regression of Y on X with intercept. Further letx 0 andx 1 be the average of sample x values for cases with y = 0 and y = 1, respectively. Then under a condition that rules out separable predictors, we show that sign(β) = sign(x 1 −x 0 ). More generally, if the x i are vector valued, then we show thatβ = 0 if and only ifx 1 =x 0 . This holds for logistic regression and also for more general binary regressions with inverse link functions satisfying a log-concavity condition. Finally, whenx 1 =x 0 then the angle betweenβ andx 1 −x 0 is less than 90 • in binary regressions satisfying the log-concavity condition and the separation condition, when the design matrix has full rank.

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“…Several authors have explored sequential design strategies to prevent separation in sensitivity tests, where the goal is to estimate the threshold level of a single design factor that will generate a success (1) versus a failure (0). Novel three‐part testing strategies are proposed by Neyer and Wu and Tian, where the second part of the tests is focused on generating overlapped response data to find unique ML estimates. However, these strategies are not directly applicable to this work.…”

Section: The Problem Of Separationmentioning

confidence: 99%

Separation in D‐optimal experimental designs for the logistic regression model

Park

Mancenido

Montgomery

2018

Quality & Reliability Eng

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The D‐optimality criterion is often used in computer‐generated experimental designs when the response of interest is binary, such as when the attribute of interest can be categorized as pass or fail. The majority of methods in the generation of D‐optimal designs focus on logistic regression as the base model for relating a set of experimental factors with the binary response. Despite the advances in computational algorithms for calculating D‐optimal designs for the logistic regression model, very few have acknowledged the problem of separation, a phenomenon where the responses are perfectly separable by a hyperplane in the design space. Separation causes one or more parameters of the logistic regression model to be inestimable via maximum likelihood estimation. The objective of this paper is to investigate the tendency of computer‐generated, nonsequential D‐optimal designs to yield separation in small‐sample experimental data. Sets of local D‐optimal and Bayesian D‐optimal designs with different run (sample) sizes are generated for several “ground truth” logistic regression models. A Monte Carlo simulation methodology is then used to estimate the probability of separation for each design. Results of the simulation study confirm that separation occurs frequently in small‐sample data and that separation is more likely to occur when the ground truth model has interaction and quadratic terms. Finally, the paper illustrates that different designs with identical run sizes created from the same model can have significantly different chances of encountering separation.

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Three-phase optimal design of sensitivity experiments

Cited by 31 publications

References 10 publications

The Role of Pentaerythritol Tetranitrate (PETN) Aging in Determining Detonator Firing Characteristics

The Role of Pentaerythritol Tetranitrate (PETN) Aging in Determining Detonator Firing Characteristics

The Sign of the Logistic Regression Coefficient

Separation in D‐optimal experimental designs for the logistic regression model

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