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Keywords:
two-sided quality control; normal distribution; small sample sizes; hypothesis testing; tolerance limits
two-sided quality control; normal distribution; small sample sizes; hypothesis testing; tolerance limits
Summary:
Critical constants for a test of the hypothesis that the mean $\mu$ and the standard deviation $\sigma$ of the normal $N(\mu,\sigma^2)$ population satisfy the constrains $\mu + c\sigma \leq M$, $\mu - c\sigma \geq m$, are presented. In this setup $m < M$ are prescribed tolerance limits and $c > 0$ in a chosen constant.
References:
[1] N. Johnson, F. Leone: Statistics and Experimental Design. Wiley, New York, 1977. Zbl 0397.62001
[2] J. Likeš, J. Laga: Fundamental Statistical Tables. SNTL, Prague, 1978. (In Czech.)
[3] F. Rublík: On the two-sided quality control. Aplikace matematiky 27 (1982), 87-95. MR 0651047
[4] F. Rublík: Correction to the paper "On the two-sided quality control". Aplikace matematiky 34 (1989), 425-427. MR 1026506
[5] F. Rublík: On testing hypotheses approximable by cones. Math. Slovaca 39 (1989), 199-213. MR 1018261
[6] F. Rublík: Testing a tolerance hypothesis by means of an information distance. Aplikace matematiky 35 (1990), 458-470. MR 1089926
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