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Regression Estimates Versus Separate Estimation at Individual Test Conditions

 

作者: HahnGerald J.,   SchmeeJosef,  

 

期刊: Journal of Quality Technology  (Taylor Available online 1980)
卷期: Volume 12, issue 1  

页码: 25-35

 

ISSN:0022-4065

 

年代: 1980

 

DOI:10.1080/00224065.1980.11980927

 

出版商: Taylor&Francis

 

关键词: Precision Estimates;Regression Estimates;Sample Size Determination

 

数据来源: Taylor

 

摘要:

The quality control engineer is often faced with the following problem. An estimate of mean product performance is required at some specified operating condition, e.g., 100°C. Data are available both at 100°C and at other temperatures. In estimating the mean at 100°C, the engineer must decide between (1) using the data at the condition of interest only, i.e., using only the 100°C data, or (2) using a regression line fitted to the entire data to obtain the desired estimate, i.e., obtaining a smoothed estimate. The gain in precision due to smoothing the data by simple linear regression analysis is considered in this article. For three equally spaced and equally replicated test conditions, gains of 42.3 percent and of 8.7 percent are achieved in estimating the mean response at the center condition and at the outside conditions, respectively. These gains are equivalent to increasing the sample size three-fold at the center condition, but only by 23.5 percent at the outside conditions. Curves quantify the results for different sample sizes, replication schemes, spacing of test conditions, and number of conditions. An expression which can be used to assess the gain in a specific situation is given and its use illustrated. The gain from using linear regression analysis in predicting a single future observation is also considered.

 

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