Companies typically plan for warranty costs through creation of a reserve fund. Most researchers assume that the warranty reserve is set based on the expected total warranty costs. However, companies rarely keep reserves to cover their liabilities for the whole life of their products, since...

We provide a sufficient condition for a mixture of Beta distributions to have log-concave density. This is true whenever the Beta distributions to be mixed together have constant parameter sum and the mixing weights are themselves log-concave. The result has applications in economics and...

Modular decomposition is a thoroughly investigated topic in many areas such as switching theory, reliability theory, game theory and graph theory. Most appli- cations can be formulated in the framework of Boolean functions. In this paper we give a uni_ed treatment of modular decomposition of...

In this paper we study convolution residuals, that is, if <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$X_1,X_2,\ldots ,X_n$$</EquationSource> </InlineEquation> are independent random variables, we study the distributions, and the properties, of the sums <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\sum _{i=1}^lX_i-t$$</EquationSource> </InlineEquation> given that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\sum _{i=1}^kX_it$$</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$t\in \mathbb R $$</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$1\le k\le l\le n$$</EquationSource> </InlineEquation>....</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

A crucial problem of evaluating, discovering, and creating the value of resources remains at the center of the subject of business strategy. The present article draws on reliability theory to advance an analytical platform that can address part of this problem, the evaluation of resource value....

Earlier researchers have studied some aspects of the classes of distribution functions with decreasing ?-percentile residual life (DPRL(?)), 0 ? 1. The purpose of this paper is to note some further properties of these classes, and to initiate a theory of nonparametric statistical estimation of...

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are...

Modular decomposition is a thoroughly investigated topic in many areas such as switching theory, reliability theory, game theory and graph theory. Most appli- cations can be formulated in the framework of Boolean functions. In this paper we give a uni_ed treatment of modular decomposition of...