Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions

The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

Screening of pharmaceuticals and other pollutants of concern by a combination of chemical and biological methods

This study examined the occurrence of pharmaceuticals and personal care products (PPCP's) in surface waters of Florida and their potential to be use as indicators of wastewater contamination. Previous studies have shown that elimination of pharmaceuticals in municipal sewage treatment plants is often incomplete. Aquatic ecosystems are under increased stress from human activities, particularly in heavily populated areas. The purpose of this study was to find an ideal indicator for wastewater. The applied methods, GC/MS and LC/MS, were suitable for the determination of pharmaceuticals and personal care products in aqueous environmental samples to the lower parts-per-trillion (ng/L) level. As a result of this study a snapshot view of the occurrence of pharmaceuticals and personal care products in south Florida was produced. PPCP's were commonly detected in coastal environments of South Florida at relatively low concentrations. In general, PPCP's were higher inside the canals and contained bodies of water than in open water systems. Caffeine was successfully used to describe impacted versus pristine locations. However, no particular correlation was observed among caffeine and other traditional water quality parameters.