A note on determination of sample size from the perspective of Six Sigma quality

Abstract

In most empirical studies (clinical, network modeling, and survey-based and aeronautical studies, etc.), sample observations are drawn from population to analyze and draw inferences about the population. Such analysis is done with reference to a measurable quality characteristic of a product or process of interest. However, fixing a sample size is an important task that has to be decided by the experimenter. One of the means in deciding an appropriate sample size is the fixation of error limit and the associated confidence level. This implies that the analysis based on the sample used must guarantee the prefixed error and confidence level. Although there are methods to determine the sample size, the most commonly used method requires the known population standard deviation, the preset error and the confidence level. Nevertheless, such methods cannot be used when the population standard deviation is unknown. Because the sample size is to be determined, the experimenter has no clue to obtain an estimate of the unknown population standard deviation. A new approach is proposed to determine sample size using the population standard deviation estimated from the product or process specification from the perspective of Six Sigma quality with a goal of 3.4 defects per million opportunities (DPMO). The aspects of quality improvement through variance reduction are also presented. The method is effectively described for its use and is illustrated with examples.