Statistical estimation of remaining gamma-percentile lifetime of space hardware based on the results of tests that did not produce any failures and were conducted according to plan with limited time and refurbishment

The problem of estimating the Remaining Lifetime (RL) of space hardware including spacecraft (SC) has been in existence throughout the entire history of space exploration. This is evidenced by numerous publications, which emphasize the importance of this problem. In practice, there are often situations, where a RL estimate needs to be made for a whole group of space hardware, in particular SC. The capability to do this is provided by well-developed methods of mathematical statistics, but only in those cases, where there have been failures in the course of operation, and in those cases the RL estimates that are used are not effective. However, for the group of SC that are in operation in space, in the course of which there have been no failures, conventional methods of mathematical statistics do not apply. The reliability of SC is continuously on the rise, as well as their numbers in space. Therefore, also on the rise is the importance of the problem of RL estimation for a whole group of SC of the same type that are currently in operation, during which there have been no failures. The reliability model is based on the exponential distribution law. The purpose of this paper is to provide an estimate f of the Remaining Gamma-Percentile Lifetime (RGPL) for space hardware - under constraints imposed on the use of life, which will be simple and more efficient as compared with the conventional and slightly inferior to the efficient RGPL estimate, if any such estimate exists, from the standpoint of true RGPL value when using a test plan with limited running hours and refurbishment. To arrive at an efficient estimate, integral numerical characteristics of its accuracy were used, namely, total square of the bias (deviation) of the expected realization of a certain variant of the estimate from all the possible parameters of the binomial test plan. The obtained estimate î of the RGPL f can be used in practice for SC operation, during which no failures occurred.