Efficient Estimation of Mean Time to Failure for a Time-Limited Test Plan with Recoverability.

As an indicator characterizing such a property of reliability of a complex restored product as failure-free operation, the mean time to failure (hereinafter – t) is selected in accordance with. From the organizational and economic points of view, the most suitable for testing restored (replaceable) products, provided that the mean time to failure is subject to the exponential probability distribution law, is the NBτ plan, where N is the number of similar products being tested; τ is the operating time (the same for each product); B is the plan characteristic, meaning that the operability of the product is restored after each failure during the testing period. Traditionally, as an estimate of the mean time to failure (MTTF), the estimate t1 = Nτ/R is chosen, where R > 0 is the number of observed failures that occurred during the time τ. This estimate is biased and, in addition, if a small number of failures (of the order of several units) are observed during the testing period or are not observed, then this estimate can give a significant error due to the bias. Recently, estimates of the SNDO free from the above-mentioned shortcomings have appeared. However, these estimates are not absolutely efficient. Purpose of the work. The purpose of the work is to construct a more efficient estimate   of the SNDO for a time-limited test plan with recovery. Methods. A simple efficiency criterion   of biased estimates is used to compare SNDO estimates for efficiency. Conclusions. 1. An efficient and balanced estimate of the SNDO has been obtained. The search was carried out in the class of linear estimates in accordance with a simple efficiency criterion of biased estimates for a plan with a time-limited test and recovery of failed products. The obtained SNDO estimate is aimed at practical application in testing and operating homogeneous products for various   purposes, during which failures did not occur; 2. Of the estimates with the same efficiency, one should select the estimate with the minimum bias, and then try to balance it. 3. An estimate defined in the class of estimates θ = (Nτ/(R+1)) + Nτf(R) with a minimum bias, starting from a certain bias value down to zero, always corresponds to a large variance. Similarly, an estimate from this class with a large bias always corresponds to a smaller variance, which does not correspond to the principle of minimizing the functional on a biased estimate with a decrease in bias when searching for efficient biased estimates. This allows us to draw a broader conclusion that using variance as a characteristic of the efficiency criterion of biased estimates does not make sense in principle.

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