Reliability Prediction During Development Phase of a System

Abstract

Reliability Growth analysis is a process of collecting, modeling, analyzing and interpreting data from the reliability development test program to achieve reliability goal. Many mathematical models have been developed for reliability growth in the literature. In general, it is not possible to fix a priori the model to be used in a given situation. A physical motivation of the problem, based on failure or defect causes/mechanisms, can help in such a choice. The Power Law Process (PLP) is vastly used for monitoring reliability growth during the development test phase. However, in the reliability growth context, the intensity function of the PLP model has two unrealistic situations, viz., it tends to infinity as t tends to zero and tends to zero as t tends to infinity. In this paper, we have proposed Modified PLP model to overcome the second drawback and Doubly Bounded PLP model to overcome both the drawbacks. For the proposed models, the estimates of the model parameters and other quantities of interest have been obtained using Maximum Likelihood approach, for both failure truncated and time truncated data. Reliability Prediction is done using system reliability measures of intensity function and mean time between failures (MTBF). Further confidence intervals of the relevant parameters have been obtained. The procedures developed have been illustrated using numerical examples.

Key Words:

• Bootstrap confidence intervals
• maximum likelihood estimation
• mean time between failures
• non-Homogeneous Poisson Process
• test-fix-test program

Additional information

Notes on contributors

Srivastava Preeti Wanti

Preeti Wanti Srivastava is Associate Professor in Department of Operational Research, University of Delhi, Delhi-110007, India. She has done B.Sc. (Hons.) in Statistics, M.Sc. (Statistics), M.Phil. (Statistics), Ph.D. (Statistics) in 1987, 1989, 1992, and 2000 respectively from University of Delhi, India. Her research area is Reliability Theory. She has published fourteen papers in journals of international repute.

Jain Nidhi

Nidhi Jain is Research Scholar in Department of Operational Research, University of Delhi, Delhi-110007, India. She has done B.Sc. (Mathematical Sciences), M.Sc. (Operational Research) in 2001 and 2003; respectively from University of Delhi, Delhi, India. Currently, she is pursuing her Ph.D. in the Department of Operational Research, University of Delhi, India under the supervision of Dr. Preeti Wanti Srivastava. Her research area is Reliability Theory.