Parameter Estimates of General Failure Rate Model: A Bayesian Approach

The failure rate function plays an important role in studying the lifetime distributions in reliability theory and life testing models. A study of the general failure rate model $r(t)=a+bt^{\theta-1}$, under squared error loss function taking $a$ and $b$ independent exponential random variables has been analyzed in the literature. In this article, we consider $a$ and $b$ not necessarily independent. The estimates of the parameters $a$ and $b$ under squared error loss, linex loss and entropy loss functions are obtained here

Flame Retardant Treatments of Nylon Textiles: A Shift towards Eco-Friendly Approaches

Among the synthetic polymeric textiles, Nylon (Polyamide) textiles (Nylon66/Nylon 6) are one of the most widely used materials, especially as apparel and industrial uses for their excellent properties, namely higher strength and good wear resistance. Unfortunately, due to their organic structures, they show the relative ease of burning, which poses a great risk to fire. For the flame retardant (FR) treatment of nylon textiles, several strategies have been developed throughout the years and the earlier studies show the enormous uses of petroleum-based flame retardant compounds via energy intensive application methods. However, the rapid improvement in living standards as well as the recent call for a reduction of environmental impacts during manufacturing and use have been pushed researchers to come up with environmentally benign chemistries and processes. Therefore, the challenges in search of the most sustainable, efficient and durable flame retardant treatments for nylon textiles still remain as a hot topic to be addressed. This chapter discusses the eco-friendly approaches that have been taken in escalating the fire performance of these novel nylon textiles, especially focusing on the applied compounds and the application techniques along with the durability issues of such applications

Characterizations based on length-biased weighted measure of inaccuracy for truncated random variables

summary:In survival studies and life testing, the data are generally truncated. Recently, authors have studied a weighted version of Kerridge inaccuracy measure for truncated distributions. In the present paper we consider weighted residual and weighted past inaccuracy measure and study various aspects of their bounds. Characterizations of several important continuous distributions are provided based on weighted residual (past) inaccuracy measure

On generalized conditional cumulative past inaccuracy measure

summary:The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order $\alpha$ and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI are discussed. Furthermore, we characterize some bivariate distributions under the assumption of conditional proportional reversed hazard rate model. Finally, the role of GCCPI in reliability modeling has also been investigated for a real-life problem