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

Authors

Leonid Bekker, Florida International University

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

Jie Mi

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Carlos Brain

Third Advisor's Name

Hassan Zahedi

Fourth Advisor's Name

Zhenmin Chen

Date of Defense

11-15-2002

Abstract

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.

Identifier

FI14050479

Recommended Citation

Bekker, Leonid, "Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions" (2002). FIU Electronic Theses and Dissertations. 1479.
https://digitalcommons.fiu.edu/etd/1479