# Statistical Power Analysis in Reliability Demonstration Testing: The Probability of Test Success
## 6 Discussion and Conclusions  
The estimation of the success rate of a reliability test is established and defined herein as the Probability of Test Success. This enables consideration of the type II error in reliability test planning and represents the statistical power held by a reliability test. Therefore, it is an indispensable metric and tool for the planning of efficient reliability demonstration tests. In addition to the general calculation method, which uses a bootstrap approach and allows all reliability tests to be assessed, an approximate method is introduced. It enables a fast and easy to implement calculation of most reliability demonstration tests, such as uncensored and censored EoL, tests without the need for a Monte Carlo simulation. The exact method for calculating the \(P_{\rm{ts}}\) of an SR test is the best method in all SR test planning scenarios. In addition, a method for calculating \(P_{\rm{bs}}\) by test simulation is shown. The comparison shows very good performance for both the general and approximate methods. However, the performance of the test simulation method is subject to the flaws of the estimation methods being used, and often does not agree with the general and the approximate methods for small sample sizes. A case study demonstrates the use and benefits for the planning process as well as the possibilities in terms of monetary decision making in reliability demonstration test planning. The approximate method enables the identification of the feasible test design region, while the general method allows precise calculation and assessment in terms of the cost of the tests to be performed. It has been shown that an objective assessment of reliability tests using the \(P_{\rm{bs}}\) is required for balanced decision-making in reliability test planning. In principle, the approach can be applied to all technical products. For example, in the case of structural mechanical failure of brake calipers, chassis structures, and electronic components such as inverters as well as vehicles, aircraft, ships, cable cars, elevators, rail vehicles, combustion engines, and much more. Additional research could enable the concept for accelerated tests as well as test planning for systems with multiple failure modes. The approach of using the MLE for the approximate calculation as well as for the general calculation can be easily adapted to incorporate additional parameters of a lifetime model for accelerated tests. Furthermore, the uncertainty of the prior knowledge can be implemented into the concept in order to account for uncertain prior knowledge, thereby ensuring more accurate estimates of the \(P_{\rm{bs}}\).  
Conceptualization, A.G. and M.D.; methodology, A.G.; software, A.G.; validation, A.G., T.H. and M.D.; formal analysis, A.G. and M.D.; investigation, A.G.; resources, A.G.; data curation, A.G.; writing--original draft preparation, A.G.; writing--review and editing, A.G. and M.D.; visualization, A.G.; supervision, A.G. and M.D.; project administration, A.G. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.