Warranty Cost Analysis with an Alternating Geometric Process

In this study we model the warranty claims process and evaluate the warranty servicing costs under non-renewing and renewing free repair warranties. We assume that the repair time for rectifying the claims is non-zero and the repair cost is a function of the length of the repair time. To accommodate the ageing of the product and repair equipment, we use a decreasing geometric process to model the consecutive operational times and an increasing geometric process to model the consecutive repair times. We identify and study the alternating geometric process (AGP), which is an alternating process with cycles consisting of the item's operational time followed by the corresponding repair time. We derive new results for the AGP in finite horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under a non-renewing free repair warranty (NRFRW), a renewing free repair warranty (RFRW) and a restricted renewing free repair warranty (RRFRW(n)). Properties of the model are demonstrated using a simulation study

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

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

Electronic structure, reflectivity and X-ray luminescence of MAPbCl 3 crystal in orthorhombic phase

This study provides a comprehensive analysis of the electronic structure, reflectivity, and luminescent spectra of the organic-inorganic, metal-halide MAPbCl3 perovskite, which has considerable potential for various optoelectronic applications. Using density functional theory (DFT) calculations, we investigated the electronic structure of MAPbCl3 and interpreted the key features of its reflectivity spectra across a wide energy range from 3 to 10 eV. The reflectivity spectra reveal prominent excitonic features at 3.22 eV near the absorption edge and additional optical transitions at higher energies, highlighting the material’s intricate electronic structure. Furthermore, we examined the temperature dependence of radiative decay dynamics under high-energy radiation through X-ray luminescence spectra and decay time measurements. We observe emission from free and bound excitons with an exceptionally short decay time (≤ 1 ns) and significant thermal quenching at low temperatures (100 K) in the 385–430 nm range. These findings underline the importance of continued exploration of optoelectronic properties of the material to enhance its performance in practical applications