Kiani, Mehdi and Panaretos, John and Psarakis, Stelios (2008): A new procedure for monitoring the range and standard deviation of a quality characteristic. Forthcoming in: Quality and Quantity

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Abstract
The Shewhart and the Bonferroniadjustment R and S chart are usually applied to monitor the range and the standard deviation of a quality characteristic. These charts are used to recognize the process variability of a quality characteristic. The control limits of these charts are constructed on the assumption that the population follows approximately the normal distribution with the standard deviation parameter known or unknown. In this article, we establish two new charts based approximately on the normal distribution. The constant values needed to construct the new control limits are dependent on the sample group size (k) and the sample subgroup size (n). Additionally, the unknown standard deviation for the proposed approaches is estimated by a uniformly minimum variance unbiased estimator (UMVUE). This estimator has variance less than that of the estimator used in the Shewhart and Bonferroni approach. The proposed approaches in the case of the unknown standard deviation, give outofcontrol average run length slightly less than the Shewhart approach and considerably less than the Bonferroniadjustment approach.
Item Type:  MPRA Paper 

Original Title:  A new procedure for monitoring the range and standard deviation of a quality characteristic 
Language:  English 
Keywords:  Shewhart, Bonferroniadjustment, Average run length, R chart, S chart 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General 
Item ID:  9067 
Depositing User:  J Panaretos 
Date Deposited:  11. Jun 2008 07:29 
Last Modified:  11. Jan 2014 02:49 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/9067 