Fisher's transformation of the bivariate-normal correlation coefficient is usually derived as a variance-stabilizing transformation and its normalizing property is then demonstrated by the reduced skewness of the distribution resulting from the transformation. In this note the transformation is derived as a normalizing transformation that incorporates variance stabilization. Some additional remarks are made on the transformation and its uses.

Many SPC software packages determine control chart limits for attribute data using normal approximations. For some sample sizes and/or process parameter values these approximations are far from adequate, mainly due to skewness in the exact distribution. Significant improvements can be made to the probabilistic accuracy of control limits by simple adjustments derived from Cornish and Fisher expansions for percentage points. The adjustments are preferable to normalizing transformations in that the original scale of the data is retained and most SPC packages allow self‐determined control limits to be inserted. The overall objective is to bring operational meaning and practice for attribute charts more into line with charts for variables.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY Asymptotic expansions are used to provide first-and second-order adjustments to large sample approximations for system reliability confidence intervals obtained from component test data. The effectiveness of the adjustments for sample sizes of practical interest is demonstrated by numerical comparisons with results obtained using exact methods and also by a Monte Carlo study for systems with known reliabilities.

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