Performance evaluation of exponential distribution using Six Sigma-based tail probabilities

Abstract

While it is customary and simple to deal with normality assumption of the data on hand, such assumption may lead to inaccurate outcomes if the underlying distribution is non-normal. Six Sigma analysis of any process is, in general, based on normality assumption irrespective of the nature of the original data. There are studies where non-normal data is transformed into normal data before performing Six Sigma analysis. In this paper, we have proposed to study the Six Sigma metrics for life test data that follow exponential distribution by matching the Six Sigma-based tail probabilities. Both centered and shifted cases of the exponential data are considered. Further, we considered higher-the-better and lower-the-better type product specifications to determine defects per million opportunities (DPMO) and extremely good units per million opportunities (EGPMO) based on the exponential distribution. Extensive numerical computations are done in addition to simulations to illustrate how DPMO and EGPMO are determined for centered or shifted exponential distribution. Some comparisons are also done with the existing approaches.

Keywords:

• DPMO
• EGPMO
• exponential distribution
• non-normal process
• Six Sigma metrics
• tail-probabilities

Acknowledgment

The authors would like to express their sincere thanks to the Editor and anonymous reviewers for their comments on the original version of the manuscript that helped to improve the paper to a great extent.