Summary
Several new criteria are proposed for the determination of suitable sample size for assessing the statistical tolerance limits. The application of the criteria is illustrated on the solution of some problems from the theory of errors and theory of reliability.
Resumen
En este trabajo se proponen algunos nuevos criterios que tratan de fijar el tamaño de la muestra necesario para establecer los límites estadísticos de tolerancia. Como aplicación de estos criterios se resuelven algunos problemas de la teoría de los errores y de la teoría de la confiabilidad.
Similar content being viewed by others
References
Albert, G.E., and Johnson, R.B. (1951). On the estimation of certain intervals which contain assigned proportions of a normal univariate population. Ann. Math. Statist. 22, pp. 596–599.
Birnbaum, Z.W., and Zuckerman, H.S. (1949). Determination of sample-size for Wilks' tolerance limits. Ann. Math. Statist. 20, pp. 313–316.
Epstein, B. (1960). Tolerance limits based on life test data taken from an exponential distribution. Industrial Quality Control 17 No. 2, pp. 10–11.
Faulkenberry, G.D., and Daly, J.C. (1970). Sample size for tolerance limits on a normal distribution. Technometrics 12, pp. 813–821.
Faulkenberry, G.D., and Weeks, D.L. (1968). Sample size determination for tolerance limits. Technometrics 10, pp. 343–348.
Goldberg, H., and Levine, H. (1945). Approximate formulas for the percentage points and normalization oft andX 2. Ann. Math. Statist. 17, pp. 216–225.
Gross, A.J., and Clark, V.A. (1975). Survival Distributions: Reliability Applications in the Biomedical Sciences. John Wiley & Sons, New York-London-Sydney-Toronto.
Guenther, W.C. (1971). On the use of best tests to obtain best β-content tolerance intervals. Statistica Neerlandica 25, pp. 191–202.
Guenther, W.C. (1972). Tolerance intervals for univariate distributions. Naval Res. Logist. Quart. 19, pp. 309–333.
Harman, A.J. (1967). Wilks’ tolerance limit sample sizes. Sankhya Ser. A 29, pp. 215–218.
Harter, H.L. (1964). New Tables of the Incomplete Gamma-Function Ratio and of Percentage Points of the Chi-Square and Beta Distributions. Aerospace Research Laboratories.
Janko, J. (1958). Statistical Tables (in Czech). Academia, Prague.
Jílek, M. (1980). Precision of chemical analyses (in Czech). Chem. Listy 74, 911–921.
Jílek, M. (1981). On errors of measurement. (submitted to Biometr. J.).
Jílek, M., and Burianová, B. (1982). Sample size for tolerance limits in the case of normal distribution (in preparation).
Jílek, M., and Líkař, O. (1960). Table of random sample sizes needed for obtaining non-parametric tolerance regions. Zastosowania Matematyki 5, pp. 155–160.
Kelley, T.L. (1948). The Kelley Statistical Tables. Revised 1948. Harvard University Press, Cambridge, MA.
Likeš, J., and Laga, J. (1978). Basic Statistical Tables (in Czech). SNTL, Prague.
Mann, N.R., Schafer, R.E., and Singpurwalla, N.D. (1974). Methods for Statistical Analysis of Reliability and Life Data. John Wiley & Sons, New York-London-Sydney-Toronto.
Müller, P.H. Neumann, P., and Storm, R. (1973). Tafeln der Mathematischen Statistik. VEB Fachbuchverlag, Leipzig.
Murphy, R.B. (1948). Non-parametric tolerance limits. Ann. Math. Statist., 19, pp. 581–589.
Odeh, R.E. (1978). Tables of two-sided tolerance factors for a normal distribution. Comm. Statist-Simulation Comput. 7, pp. 183–201.
Owen, D.B. (1962). Handbook of Statistical Tables. Addison-Wesley, Reading, MA.
Passi, R.M., and Williams, J.S. (1978). Sample-size requirements for confidence bounds of prescribed precision on multivariate normal quantiles. Comm. Statist. Theory Methods 7, pp. 739–753.
Somerville, P.L. (1958). Table for obtaining non-parametric tolerance limits. Ann. Math. Statist. 29, pp. 599–601.
Tukey, J.W., and Scheffé, H. (1944). A formula for sample sizes for population tolerance limits. Ann. Math. Statist. 15, p. 217.
Weissberg, A., and Beatty, G.H. (1960). Tables of tolerance-limit factors for normal distributions. Technometrics 4, pp. 483–500.
Wilks, S.S. (1941). Determination of sample sizes for setting tolerance limits. Ann. Math. Statist. 12, pp. 91–96.
Zar, J.H. (1978). Approximations for the percentage points of the chi-squared distribution. Appl. Statist. 27, pp. 280–290.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jílek, M. Sample size and tolerance limits. Trabajos de Estadistica Y de Investigacion Operativa 33, 64–78 (1982). https://doi.org/10.1007/BF02888623
Issue Date:
DOI: https://doi.org/10.1007/BF02888623