Statistical Analysis of the Lifetime of Diamond-Impregnated Tools for Core Drilling of Concrete

Malevich, Nadja; Müller, Christine; Kansteiner, Michael; Biermann, Dirk; Ferreira, Manuel; Tillmann, Wolfgang

doi:10.1007/978-3-030-25147-5_15

Cited by 2 publications

(1 citation statement)

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“…Originally, an inspection took place every minute and this was done over 50 min of drilling. For more details on these experiments and their results see Kansteiner et al (2017a, b) and Malevich et al (2018). It turned out that only very few diamonds broke out within the 50 min for some experimental setups.…”

Section: Introductionmentioning

confidence: 89%

Optimal design of inspection times for interval censoring

Malevich

Müller

2019

Stat Papers

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We treat optimal equidistant and optimal non-equidistant inspection times for interval censoring of exponential distributions. We provide in particular a new approach for determining the optimal non-equidistant inspection times. The resulting recursive formula is related to a formula for optimal spacing of quantiles for asymptotically best linear estimates based on order statistics and to a formula for optimal cutpoints by the discretisation of continuous random variables. Moreover, we show that by the censoring with the optimal non-equidistant inspection times as well as with optimal equidistant inspection times, there is no loss of information if the number of inspections is converging to infinity. Since optimal equidistant inspection times are easier to calculate and easier to handle in practice, we study the efficiency of optimal equidistant inspection times with respect to optimal non-equidistant inspection times. Moreover, since the optimal inspection times are only locally optimal, we also provide some results concerning maximin efficient designs. Keywords Optimal inspection times • Exponential distribution • Optimal spacing of quantiles • Maximin efficient designs • Interval-censored data B Nadja Malevich

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Section: Introductionmentioning

confidence: 89%