This research developed a Modified Sequential Probability Ratio Test (MSPRT) for Log Normal and Inverse Exponential Rayleigh Distributions based on truncated life testing. MSPRT is a mechanism designed to minimise the average sample size necessary for conducting statistical hypothesis tests at predetermined significance levels and power (1-β) across various maximum sample sizes (N), indicating that there exists a definitive termination threshold for the minimum number of items required to implement a sampling plan. The study findings compared the maximum sample size necessary for the test at a 5% significance level across various areas. The study concluded that as the duration of test termination increases, the maximum required sample size diminishes, while the values in the graphical representation rise more steeply with improved quality. Consequently, the proposed plan was deemed optimal for selecting the appropriate sample size. In comparison to the two tests, it is evident that the current ASN values at levels 10, 15, and 25 exceed the proposed ASN values of 9, 11, and 18, respectively. This indicates that at a specific ASN level, the proposed plan can be accepted and implemented to reduce inspection time and simultaneously save costs, thereby representing the optimal plan in relation to the existing sequential probability ratio test.

Al-Nasser, A.D.; Al-Omari, A.I. (2013) Acceptance sampling plan based on truncated life tests for exponentiated Fréchet distribution. J. Stat. Manag. Syst. 16, 13–24 doi.org/10.1080/09720510.2013.777571 Al-Omari, A.I.; Al-Nasser, A.D.; Gogah, F.S. (2016) Double acceptance sampling plan for time truncated life tests based on new Weibull-Pareto distribution. Electronic Journal of Applied Statistical Analysis. Vol 9, No 3 . 10.1285/i20705948v9n3p520 Anderson TW (1960). A modification of the sequential probability ratio test to reduce the sample size. The Annals of Mathematical Statistics, 31(1):165–197. Bar S and Tabrikian J (2018). A sequential framework for composite hypothesis testing. IEEE Transactions on Signal Processing, 66(20):5484–5499. Bartroff J, Finkelman M, and Lai TL (2008). Modern sequential analysis and its applications to computerized adaptive testing. Psychometrika, 73(3):473–486. Harsh Tripathi and MahendraSaha (2021), “An application of time truncated single acceptance sampling inspection plan based on transmuted Rayleigh distribution “arXiv:2107.02903 v1 [stat.ME] Lai TL (2001). Sequential analysis: Some classical problems and new challenges.Statistical Sinica, 11(2):303–351 . Lai TL (2004). Likelihood ratio identities and their applications to sequential analysis.SequentialAnalysis, 23(4):467–497 . Lai TL (2008). Sequential Analysis, pages, 1–6. American Cancer Society. Mayssa J. Mohammeda and Ali T. Mohammeda (2021).” Parameter estimation of inverse exponential Rayleigh distribution based on classical methods” Int. J. Nonlinear Anal. Appl. 12(2021) No. 1, 935-944 Sandipan Pramanik; Valen E. Johnson; Anirban Bhattacharya; (2021). A modified sequential probability ratio test. Journal of Mathematical Psychology, (), –. doi:10.1016/j.jmp.2021.102505 Siegmund D (1985). Sequential Analysis: Tests and confidence intervals. Springer-Verlag New York. Wald A (1945). Sequential tests of statistical hypotheses. The Annals of Mathematical Statistics, 16(2):117–186. Wald A and Wolfowitz J (1948). Optimum character of the sequential probability ratio test. The Annals of Mathematical Statistics, 19(3):326–339 Zoramawa and Charanchi (2021) A Study on Sequential Probability Sampling for Monitoring a Resubmitted Lots under Burr-Type XII Distribution Continental J. Applied Sciences 16 (2): 16 - 26 doi: 10.5281/zenodo.5540382 Zoramawa, A. B., Gulumbe S. U, (2021) On sequential probability sampling plan for a truncated life test using inverse Rayleigh distribution 15(1):1-7, 2021; doi: 10.9734/AJPAS/2021/v15il30339