How is Taguchi's quality loss function related to the process capability ratio and the process capability index? Which process performance measure is it closest to?

What will be an ideal response?

The quality loss function is zero when the quality characteristic is exactly on the target value and otherwise is computed as a quadratic function as the process deviates from the target. The higher the process standard deviation is in relation to the width of the specification limits, the greater the average loss will be as computed by the quality loss function. The process capability ratio is the ratio of the width of the specification limits to the natural spread of the process. As the process standard deviation increases, the process capability ratio falls. The loss function and the capability ratio move in opposite directions as the standard deviation varies. The process capability index is the minimum of two ratios; the upper spec limit less the process mean to three standard deviations and the process mean less the lower spec limit to three standard deviations. As the process standard deviation increases, the process capability index falls. The process capability index does not assume that the process is perfectly centered, thus the need to take the minimum of the two ratios. It can be argued that the process capability index is more similar to the Taguchi loss function for this reason; both take the process mean into consideration but the process capability ratio does not.