On Revelation Transforms that Characterize Probability Distributions

A characterization of exponential, geometric and of distributions with almost-lack-of-memory property, based on the revelation transform of probability distributions and relevation of random variables is discussed. Known characterizations of the exponential distribution on the base of relevation transforms given by Grosswald et al. [4], and Lau and Rao [7] are obtained under weakened conditions and the proofs are simplified. A characterization the class of almost-lack-of-memory distributions through the relevation is specified

Study of effects of rare earth impurities on structure of matrix emission of the lead tungstate crystals

The paper reports study of complex structure of matrix emission of undoped and RE-doped PbWO4 crystals. Decomposition of the spectra shows contributions of five components at 410, 485, 520, 565, 635 nm in emission of all the investigated samples. Their relative contributions depend on RE doping. Observed effects of RE doping are the same for the crystals with different RE impurities. Structures of luminescent centres are discussed taking into account studied effects of the impurity RE ions on spectral characteristics of the matrix emission

Two-dimensional Warranty Cost Analysis for Second-hand Products

In spite of the recent steady increase of the volume of the second-hand markets, often customers remain in doubt regarding the quality and durability of the secondhand products. Aiming to reduce and share this uncertainty, dealers offer warranty on their products. Offering warranty for second-hand products is a relatively new marketing strategy employed by dealers of used electronic equipment, furniture, automobiles, etc. Usually, for used products, the dealer’s expected warranty cost is a function of product reliability, past age and usage, servicing strategy and conditions and terms of the warranty policy/contract. Sometimes the offered policy is limited by two parameters, typically the product age and usage after the sale. This type of policies is referred to as two-dimensional warranty policies. In this article, we develop statistical models for estimating the dealer’s expected warranty cost for second-hand products sold with two-dimensional free repair/replacement warranty

Luminescence properties of KAlP₂O₇ crystals doped with chromium ions

Luminescence properties of the KAlP₂O₇ crystals doped with the chromium ions were investigated. Luminescence spectra consist of two main bands: one of them lies in the blue-green spectral region and the other lies in the red spectral region. The maximum positions of the bands depend on the crystal composition and temperature of the samples. The blue-green band consists at least of three components. Complex structure of the blue-green broad band results from a superposition of matrix intrinsic radiation and emission of the distorted CrO₄²⁻ groups, where chromium ions have 6+ ion charge. The red luminescence band and the narrow spectral lines observed for the chromium-doped KAlP₂O₇ crystals were assigned to electron transitions in the Cr³⁺ ions in octahedral oxygen surround. Structure peculiarities of the various types of the chromium luminescence centers formed in the investigated matrix are discussed

Warranty Data Analysis: A Review

Warranty claims and supplementary data contain useful information about product quality and reliability. Analysing such data can therefore be of benefit to manufacturers in identifying early warnings of abnormalities in their products, providing useful information about failure modes to aid design modification, estimating product reliability for deciding on warranty policy and forecasting future warranty claims needed for preparing fiscal plans. In the last two decades, considerable research has been conducted in warranty data analysis (WDA) from several different perspectives. This article attempts to summarise and review the research and developments in WDA with emphasis on models, methods and applications. It concludes with a brief discussion on current practices and possible future trends in WDA