Abstract
When screening a production process for nonconforming items the objective is to improve the average outgoing quality level. Due to measurement errors specification limits cannot be checked directly and hence test limits are required, which meet some given requirement, here given by a prescribed bound on the consumer loss. Classical test limits are based on normality, both for the product characteristic and for the measurement error. In practice, often nonnormality occurs for the product characteristic as well as for the measurement error. Recently, nonnormality of the product characteristic has been investigated. In this paper attention is focussed on the measurement error.
Firstly, it is shown that nonnormality can lead to serious failure of the test limit. New test limits are therefore derived, which have the desired robustness property: a small loss under normality and a large gain in case of nonnormality when compared to the normal test limit.
Monte Carlo results illustrate that the asymptotic theory is in agreement with moderate sample behaviour.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albers W, Kallenberg WCM, Otten GD (1997) Robust test limits. Mathematical Methods of Statistics, to appear
Albers W, Kallenberg WCM, Otten GD (1994a) Accurate test limits with estimated parameters. Technometrics 36:92–101
Albers W, Kallenberg WCM, Otten GD (1994b) Setting test limits under prescribed consumer loss. Metrika 41:163–181
Bai DS, Kim SB, Riew MC (1990) Economic screening procedures based on correlated variables. Metrika 37:263–280
Bai DS, Kwon HM (1995) Economic design of a two-stage screening procedure with a prescribed outgoing quality. Metrika 42:1–18
Bai DS, Lee MK (1993) Economic designs of single and double screening procedures. Metrika 40:95–113
Bhattacharya RN, Rao RR (1976) Normal approximation and asymptotic expansions. Wiley, New York
Easterling RG, Johnson ME, Bement TR, Nachtsheim CJ (1991) Statistical tolerancing based on consumer's risk considerations. Journal of Quality Technology 23:1–11
Grubbs FE, Coon HJ (1954) On setting test limits relative to specification limits. Industrial Quality Control 10:15–20
Kim SB, Bai DS (1992) Economic design of one-sided screening procedures based on a correlated variable with all parameters unknown. Metrika 39:85–93
Mason DM, Shorack GR, Wellner JA (1983) Strong limit theorems for oscillation moduli of the uniform empirical process. Z. Wahrsch. Verw. Gebiete 65:83–97
Mullenix P (1990) The capability of capability indices with an application to guardbanding in a test environment. 1990 International Test Conference IEEE:907–915
Otten GD (1995) Statistical test limits in quality control. Ph.D. dissertation, University of Twente, The Netherlands
Owen DB, Boddie JW (1976) A screening method for increasing acceptable product with some parameters unknown. Technometrics 18:195–199
Owen DB, Su YH (1977) Screening based on normal variables. Technometrics 19:65–68
Owen DB, Li L, Chou YM (1981) Prediction intervals for screening using a measured correlated variate. Technometrics 23:165–170
Tang K (1987) Economic design of a one-sided screening procedure using a correlated variable. Technometrics 28:477–485
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Albers, W., Kallenberg, W.C.M. & Otten, G.D. Accurate test limits under nonnormal measurement error. Metrika 47, 1–33 (1998). https://doi.org/10.1007/BF02742862
Issue Date:
DOI: https://doi.org/10.1007/BF02742862