A combinatorial estimation approach for storage reliability with initial failures based on periodic testing data

ABSTRACT

Storage reliability that measures the ability of products in a dormant state to keep their required functions is studied in this paper. Unlike the operational reliability, storage reliability for certain types of products may not be always 100% at the beginning of storage since there are existing possible initial failures that are normally neglected in the models of storage reliability. In this paper, a new combinatorial approach, the nonparametric measure for the estimates of the number of failed products and the current reliability at each testing time in storage, and the parametric measure for the estimates of the initial reliability and the failure rate based on the exponential reliability function, is proposed for estimating and predicting the storage reliability with possible initial failures. The proposed method has taken into consideration that the initial failure and the reliability testing data, before and during the storage process, are available for providing more accurate estimates of both initial failure probability and the probability of storage failures. When storage reliability prediction that is the main concern in this field should be made, the nonparametric estimates of failure numbers can be used into the parametric models for the failure process in storage. In the case of exponential models, the assessment and prediction method for storage reliability is provided in this paper. Finally, numerical examples are given to illustrate the method. Furthermore, a detailed comparison between the proposed method and the traditional method, for examining the rationality of assessment and prediction on the storage reliability, is presented. The results should be useful for planning a storage environment, decision-making concerning the maximum length of storage, and identifying the production quality.

KEYWORDS:

• Initial reliability
• Least squares (LS) estimation
• Maximum likelihood (ML) estimation
• Nonparameter (NP) estimation
• Storage reliability

MATHEMATICS SUBJECT CLASSIFICATION:

• 90B25

Acknowledgments

The authors greatly acknowledge the editor and the referees for their constructive comments and suggestions that have led to a substantial improvement of the paper. In addition, the authors also thank the financial supports from the jointly funded project of the National Natural Science Foundation and the Civil Aviation Administration of China under Grant U1333119, and the Defense Industrial Technology Development Program with the Grant number JCKY2013605B002.