Regression Estimates Versus Separate Estimation at Individual Test Conditions

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°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.

• Precision Estimates
• Regression Estimates
• Sample Size Determination

Additional information

Notes on contributors

Gerald J. Hahn

Dr. Hahn is manager of the Statistics Program of the Information Technology Branch of the Corporate Research and Development Center of the General Electric Company. He is an adjunct professor of the Institute of Administration and Management of Union College and a Fellow of ASQC.

Josef Schmee

Dr. Schmee is an associate professor in the Institute of Administration and Management of Union College and is associated with the Statistics Program of General Electric Corporate Research and Development. He is a member of ASQC.