Regression Estimates Versus Separate Estimation at Individual Test Conditions

Journal of Quality Technology vol. 12 issue 1 - January 1980

Abstract: 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 degrees C. Data are available both at 100 degrees C and at other temperatures. In estimating the mean at 100 degrees C, the engineer must decide between (1) using the data at the condition of interest only, i.e., using only the 100 degree 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.

Keywords: Statistics - Estimation - Regression analysis - Sample size

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