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 (lowerthe-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.

Six Sigma quality evaluation of life test data based on Weibull distribution

“…This can be evidenced by the availability of a number of research activities in the field of Six Sigma quality and its applications. For example, readers are referred to the works of McFadden (1993), Harry (1998), Lucas (2002), Antony et al (2007), Aboelmaged (2010), Tjahjono (2010), Setijono (2008Setijono ( , 2010, Shruti and Ravi Kant (2017), Ravichandran (2006Ravichandran ( , 2016Ravichandran ( , 2017Ravichandran ( , 2019, Schroeder et al (2008).…”

“…The DisPMO and DePMO represent the cases (customer reactions as dissatisfied or delighted) below the Lower Six Sigma Limit (LSSL) and above the Upper Six Sigma Limit (USSL) respectively. Ravichandran (2016) studied the problem of estimating DPMO and the parts that are extremely good per million opportunities (EGPMO) for quality evaluation from the perspective of higher-the-better and lower-thebetter quality characteristics. In his work, Ravichandran (2006) assumed that the process follows normal distribution and based on that the Sigma Quality Limits (SQLs) are obtained.…”

“…As discussed in the introduction section, Setijono (2008Setijono ( , 2010 considered LSSL and USSL at μ±6σ where μ is the average customer response and σ is the standard deviation of the responses such that the probability that a response will fall outside the limits is 2:00310 −9 for a centered process and 3:4310 −6 for a shifted process with shift in the mean up to ±1:5σ. For more details readers are referred to Lucas (2002), Antony (2004) and Ravichandran (2016). In the work of Setijono (2008Setijono ( , 2010, while DisPMO corresponds to the area < μ − 6σ, the DePMO are considered from the area > μ þ 6σ.…”

“…According to Ravichandran (2016), under normality assumption, for HTB case, while DPMO corresponds to the area < μ − 6σ, the EGPMO corresponds to the area > μ þ 6σ and these areas are > μ þ 6σ and < μ − 6σ for DPMO and EGPMO respectively for LTB case.…”

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

“…Setijono (2010) has considered the case of matching the SSQ limits to specification limits in order to estimate customer dissatisfaction (not meeting specification) and delight (meeting specification) in a survey related study. A similar study was done by Ravichandran (2016) from the perspective of process/product specification to estimate DPMO and extremely good parts per million opportunities (EGPMO) for higher the better and lower the better quality characteristics. A process or product that meets the specification target is always said to be stable.…”