Estimation of DPMO and EGPMO for higher-the-better and lower-the-better quality characteristics for quality evaluation

Abstract

Whenever specification is provided for a measureable quality characteristic, under normality assumption, the defects per million opportunities (DPMO) can be computed by taking into account both the tail probabilities. This implies that a unit of a product is declared defective if a measurement on quality characteristic falls either below the specified lower limit or above the upper limit. However, there are practical situations, where a unit is said to be defective if the measurement either falls below the lower limit (higher-the-better) or falls above the upper limit (lower-the-better). Under this circumstance, the DPMO needs to be computed taking into account the appropriate tail probabilities (left or right). In this paper, the aspects of Six Sigma are used to decide the upper and lower sigma quality limits for these two cases. Followed by this, the DPMO is estimated accordingly. Probabilities of far good units, that is, extremely good parts per million opportunities (EGPMO), of the quality characteristic are also determined. It is discussed about how DPMO and EGPMO help in evaluating the overall quality level of the process/product of interest. The procedure is illustrated with numerical examples.