Abstract
Process precision index Cp has been widely used in the manufacturing industry for measuring process potential and precision. Estimating and testing process precision based on one single sample have been investigated extensively. In this paper, we consider the problem of estimating and testing process precision based on multiple samples taken from (\(\bar{x}\),R)or (\(\bar{x}\),S)control chart. We first investigate the statistical properties of the natural estimator of Cp and implement the hypothesis testing procedure. We then develop efficient MAPLE programs to calculate the lower confidence bounds, critical values, and p-values based on m samples of size n. Based on the test, we develop a step-by-step procedure for practitioners to use in determining whether their manufacturing processes are capable of reproducing products satisfying the preset precision requirement.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kane, VE (1986) Process capability indices. J Qual Technol 18:41–52
Rado LE (1989) Enhance product development by using capability indexes. Qual Prog 22(4):38–41
Pearn WL, Lin GH, Chen KS (1998) Distributional and inferential properties of the process accuracy and process precision indices. Commun Stat: Theory & Methods 27(4): 985–1000
Montgomery DC (1985) Introduction to statistical quality Control. Wiley, New York
Kirmani SNUA, Kocherlakota K, Kocherlakota S (1991) Estimation of σ and the process capability index based on subsamples. Commun Stat: Theory & Methods 20:275–291
Pearn WL, Yang YS (2003) Distributional and inferential properties of the estimated precision index Cp based on multiple samples. Qual Quant 37:443–453
Pearson ES (1932) The percentage limits for the distribution of range in samples from a normal population. Biometrika 24: 404–417
Patnaik PB (1950) The use of mean range as an estimator of variance in statistical tests. Biometrika 37:78–87
Kocherlakota S (1992) Process capability index: recent developments. Sankhya Indian J Stat 54:352–369
Kotz S, Lovelace, CR (eds)(1998) Process capability indices in theory and practice. Arnold, London
Chou YM, Owen DB, Borrego SA (1990) Lower confidence limits on process capability indices. J Qual Technol 22:223–229
Li H, Owen DB, Borrego SA (1990) Lower confidence limits on process capability indices based on the range. Commun Stat: Simul and Comput 19(1):1–24
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pearn, W., Wu, CW. & Chuang, H. Procedures for testing manufacturing precision Cpbased on (\(\bar{x}\),R) or (\(\bar{x}\),S) control chart samples. Int J Adv Manuf Technol 25, 598–607 (2005). https://doi.org/10.1007/s00170-003-1870-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-003-1870-0