This paper attempts to identify how much testing time is cost effective in determining the number of redundant units needed to achieve high reliability with high confidence. This requires a two-phase test program, an initial period of testing for reliability growth followed by life testing to more accurately determine the final failure rate achieved by reliability growth. Newly designed systems often have high initial failure rates which can be reduced by finding failure modes and removing them by redesign until the system achieves an acceptable failure rate. This failure rate will be constant if there are no further redesigns or wear out. To plan for high reliability with high confidence using redundancy, the test time must be long enough to accurately determine the failure rate. The measured failure rate decreases throughout the reliability growth period as failure modes are removed. The first few failures during life testing provide an estimate of the final failure rate, but since here are few failures, the failure estimate has a wide variance. There is a 50% chance that the actual final failure rate is higher, and it could be much higher. If a too low estimated failure rate is used to compute the redundancy needed to achieve the required reliability, the number of spare units provided will be too low. Using the estimated failure rate gives only a 50% confidence that the failure rate and number of spares are not too low. Given the failure rate and the desired reliability using redundancy, the number of spares can be determined and the confidence in the reliability computed. A lower reliability requirement would be met with higher confidence. Here a different approach is used, where both the redundant reliability and the confidence level are independently set requirements. The confidence that the redundant reliability is not too low can be increased by increasing the failure rate and the corresponding number of spares. When there are only a few failures, the variance of the failure rate is high and the failure rate and number of spares must be increased greatly to reach high expected reliability with high confidence. The high number of spares creates a high cost for redundancy. Longer test time reduces the variance in the failure rate and reduces the proportional increase in the failure rate and number of spares that is needed to increase confidence. Longer testing produces more failures. More failures narrow the spread of the possible true failure rates that could have produced the measured number of failures. The narrower the spread of the possible true failure rates, the less the needed increase in the test failure rate increase confidence that the estimated failure rate is not too low. The less the failure rate is increased to increase confidence, the fewer spares are needed. As the test time is increased, the test cost increases linearly but the number of needed spares drops, at first exponentially. The total cost is the sum of the cost of the redundant units and of the test time. There is often an optimum test time that produces the minimum total cost for the system failure rate, mission length, reliability, and confidence level. If the total cost must be reduced, either reliability, confidence level, or both must be reduced. The required reliability and confidence identify and justify a minimum total cost for redundant units and testing. Extended testing has a cost-based justification that can help prevent insufficient testing.
