Demonstrating reliability growth requirements with confidence

Abstract

Reliability growth testing is used to find reliability problems in the system design through testing so that effective corrective actions can be taken to improve the reliability. In addition, many systems are subjected to a follow-on reliability demonstration test and the results are typically compared to a reliability requirement. The expectation is that by conducting the reliability growth test the probability of passing the demonstration test is improved. While this is generally true for the original requirement, in many cases the criteria for passing the demonstration test is to demonstrate the requirement with confidence as a lower bound, for example 80%. This criteria, in effect, changes the original requirement and design goals, and if the lower confidence bound is based strictly on de monstration test data, this may dramatically lower the probability of passing the demonstration test. In order to pass the demonstration test with a high probability, say 80%, then the true design reliability needs to be much higher than the requirement. The higher the true design reliability needs to be the higher the associated engineering costs and the higher the risk of not passing the demonstration test. This paper develops a methodology that utilizes both the reliability growth test data and the demonstration test data in order to (1) demonstrate the requirement with confidence and (2) with sufficient reliability growth lower the true design reliability that is necessary to pass the demonstration test with a high probability. The focus is to reduce risks and costs. This paper is limited to a system with a continuous time to failure, and it is assumed that the Crow (AMSAA) model applies to the reliability growth results. The specific problem addressed is a recognized important issue, particularly in the Department of Defense. The objective of this paper is to provide a practical solution to this problem.