Geodesic
On the two-sided quality control
Applications of Mathematics, Tome 27 (1982) no. 2, pp. 87-95.

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Let the random variable $X$ have the normal distribution $N(\mu,\sigma^2)$. Explicit formulas for maximum likelihood estimator of $\mu,\sigma$ are derived under the hypotheses $\mu+c\sigma\leq m + \delta, \mu-c\sigma\geq m-\delta$, where $c,m,\delta$ are arbitrary fixed numbers. Asymptotic distribution of the likelihood ratio statistic for testing this hypothesis is derived and some of its quantiles are presented.
DOI : 10.21136/AM.1982.103950
Classification : 62E20, 62F03, 62N10, 62P30
Keywords: maximum likelihood statistic; tables of critical values; two-sided hypotheses; normal population 
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Rublík, František. On the two-sided quality control. Applications of Mathematics, Tome 27 (1982) no. 2, pp. 87-95. doi : 10.21136/AM.1982.103950. http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103950/

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