Power law model, correct application in reliability growth do the cumulative times indeed always add up?

Abstract

Reliability growth methodology is a valuable tool to measure product reliability improvement either through planned, dedicated testing or the gradual upgrade and improvement of the fielded product. The methodology is well thought of with appropriate process mathematical assumptions so that when applied, it provides appropriate and justifiable information and tracking of reliability improvement. The usual Homogenous Poisson Process, HPP, with assumed constant failure rates and failure intensities is almost regularly assumed and used in all reliability analysis and especially testing. The Non-Homogenous Poisson Process, NHPP, adequately expresses step changes of failure rates resultant from product design or processes improvement, by fitting them with the continuous Power law curve. All reliability growth modeling done in this manner such as the take-off models Duane and AMSAA/CROW are valid and valuable. This paper proposes some changes in the accounting of the total test times for the cases when the multiple units are observed in test or in the field which may yield more appropriate determination of failure rates and their parameters. This paper points out that the common practice in reliability growth test data analysis with additions of test times of multiple test items at the times of individual failures may be inappropriate in the case where systematic failures - design or manufacturing practices flaws are observed. Therefore, the papr proposes application of the original NHPP power law, which is the model followed in derivations other current reliability growth analytical methods. The proposed analytical method will correct the errors introduced when multiple units are tested or observed, and will also provide uniformity of the data analysis. The errors do not show when a single items' reliability growth is ob served. They become apparent only in the cases of multiple items, and are proportional to the number of observed items and the lack of synchronization of beginning, ending, and upgrades times. To eliminate those errors, which cou ld be rather large when reliability growth of fielded products is followed, this paper proposes following the rules of the original power law model in all of the RG data analysis and calculations of reliability results. It might be also advisable that the additions are done in the published material to provide this guidance.