A table giving approximate values of $E_\theta(r)$ for certain choices of $\theta_0/\theta_1, \alpha,$ and $\beta$ is given for the replacement case. In the replacement case where the number of items on test throughout the experiment is the same, namely $n$, it is shown that $E_\theta(t) = (\theta/n)E_\theta(r)$. (operating characteristic) curve, for the expected number of failures $E_\theta(r)$, and for the expected waiting time $E_\theta(t)$ before a decision is reached. In this paper we obtain likelihood ratio tests and give approximate formulae for the O.C. Similar problems involving a continuous time parameter have recently appeared. Since abnormally long intervals between failures furnish "information" in favor of $H_0$ and abnormally short intervals furnish "information" in favor of $H_1$, these features are not only reasonable but actually desirable. The test can be terminated either at failure times with rejection of $H_0$, or at any time between failures with acceptance of $H_0$. We consider both the replacement case, in which failed items are immediately replaced by new items, and the nonreplacement case. The test is carried out by drawing $n$ items at random from the population and placing them all on a life test. Our primary aim is to test the simple hypothesis $H_0: \theta = \theta_0$ against the simple alternative $H_1: \theta = \theta_1,$ where $\theta_1 < \theta_0,$ with type I and II errors equal to preassigned values $\alpha$ and $\beta,$ respectively. This paper describes sequential life test procedures, considering, as in a recent paper devoted to nonsequential methods, the special case in which the underlying distribution of the length of life is given by the exponential density \begin The unknown parameter $\theta > 0$ can be thought of physically as the mean life. Sevil and Demirhan (2008) developed a group sequential test when response variable has an inverse Gaussian distribution with known parameter. (2000) developed SPRT for testing simple and composite hypothesis regarding the parameters of a class of distributions representing various life-testing models. simple hypothesis concerning the mean of the negative binomial distribution, Epstein and Sobel (1955) dealt the testing of simple hypothesis problem regarding the mean of one parameter exponential distribution through SPRT, Johnson (1966) applied SPRT for testing the hypothesis for the scale parameter of the weibull distribution when the shape parameter is known, Phatarford (1971) dealt the problem of testing the composite hypothesis for the shape parameter of the gamma distribution through SPRT, when the scale parameter is unknown, Bain and Engelhardt (1982) applied SPRT for testing the hypothesis for the shape parameter of a non-homogenous Poisson process and Chaturvedi et al. The SPRT has been applied by various authors, to deal with testing problems, for references, Oakland (1950) developed SPRT for testing the simple vs.
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