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Probability Charts for Decision Making
01 Dec 1981-
About: The article was published on 1981-12-01 and is currently open access. It has received 107 citations till now.
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TL;DR: Applications of the hazard plotting method are given for multiply censored data on service life of equipment, for strength data on an item with different failure modes, and for biological data multiply censored on both sides from paired comparisons.
Abstract: This paper presents theory and applications of a simple graphical method, called hazard plotting, for the analysis of multiply censored life data consisting of failure times of failed units intermixed with running times on unfailed units. Applications of the method are given for multiply censored data on service life of equipment, for strength data on an item with different failure modes, and for biological data multiply censored on both sides from paired comparisons. Theory for the hazard plotting method, which is based on the hazard function of a distribution, is developed from the properties of order statistics from Type II multiply censored samples.
578 citations
Cites background or methods from "Probability Charts for Decision Mak..."
...These data appear in [12] and are used here with the kind permission of Mr....
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...Further discussion and practical details on how to use and interpret hazard and probability plots are given in [12, 14, 15]....
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...Additional applications are given in those references and in [12]....
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TL;DR: Goodness-of-fit tests were constructed using this technique for several commonly used plotting positions for the normal distribution as discussed by the authors, which were then compared on the basis of power against certain nonnormal alternatives.
Abstract: The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position pi = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.
181 citations
TL;DR: An extensive review of some discrete and continuous versions of the modifications of the Weibull distribution to allow for non-monotonic hazard functions.
156 citations
TL;DR: The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these Weibull models are suitable for modelling a given data set.
119 citations
TL;DR: In this paper, the authors estimate the tree and shrub diameters at which avalanches could cause breakage using both the mechanics of large deflec- tions in tapered beams and the resulting stem bending stress.
Abstract: Snow avalanche return intervals on two avalanche paths in the southern Canadian Rockies were estimated from scarred trees and shrubs. The interval between avalanches increased exponentially down each path. The tree and shrub diameters at which avalanches could cause breakage were predicted using both the mechanics of large deflec- tions in tapered beams and the resulting stem bending stress, and these predictions were confirmed by comparison to actual diameters at breakage on avalanche paths. Lodgepole pine (Pinus contorta) and Engelmann spruce (Picea engelmannii) bend when small, but were broken by avalanches when larger than ~6 cm in diameter at the base. Glandular birch (Betula glandulosa) and willow (Salix glauca) never grew large enough to break. Breakage was influenced by size rather than wood elasticity or strength. Information on thinning mortality was reconstructed from live and dead stems in two Engelmann spruce populations and one lodgepole pine population. Dead trees were cross-dated, using ring widths, to determine time of death. Avalanche mortality of trees was more important than thinning mortality when the average interval between avalanches was < 150 yr. The shift from shrub- to tree-dominated growth habit down the avalanche path occurred when the average interval between avalanches was less than 15 to 20 yr.
110 citations