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.

Theory and applications of hazard plotting for censored failure data

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.

https://www.jstor.org/stable/pdfplus/2683917.pdf

Use of the Correlation Coefficient with Normal Probability Plots

Modifications of the Weibull distribution: A review

Weibull model selection for reliability modelling

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.

James R. King

Papers

Probability Charts for Decision Making