Optimal truncated sequential test for exponential distribution

Abstract

In order to save on test costs, the optimal truncated sequential test (OTST) for the parameter of the exponential distribution is studied. According to Bayes decision theory, dynamic programming methods and procedures are established to solve the OTST. Through comparison with the test plans provided by international standard IEC 61124 and Russian national standard GOST R 27.402, the results show that the OTSTs solved by our new method can control the error probabilities strictly and save more synthetical expected test time (SETT). The OTSTs are also compared with the near-optimal ones solved by the sample space sorting method (SSSM). The results show that the test plans solved by these two methods are almost consistent. However, our new method is much faster in computation, especially when the maximum sample size (MSS) of a truncated sequential test increases. It can save 74.23% of the computational time compared with SSSM when the MSS equals 15. At last, the MSS of OTST is optimized. By optimizing the MSS, the corresponding OTST can save about 5% of the SETT compared to the one with the minimum MSS.