As a domain expert in Six Sigma methodologies, I'm well-versed with the various tools and concepts used in process improvement and quality management. One such concept is the "Z bench," which is a term that may not be widely recognized in the Six Sigma community but seems to relate to the use of Z-scores in statistical analysis. Z-scores are a statistical measurement that describes a value's relationship to the mean of a group of values. They are used to identify outliers and to determine how many standard deviations an element is from the mean. In the context of Six Sigma, Z-scores are often used to measure the capability of a process. The standard normal distribution, which is what the "Z" in Z.Bench likely refers to, is a normal distribution with a mean (μ) of 0 and a standard deviation (σ) of 1. This distribution is significant because of the Central Limit Theorem, which states that the distribution of sample means will approach a normal distribution as the sample size gets larger, regardless of the shape of the population distribution. In Six Sigma, the long-term capability of a process is often assessed using short-term data. The assumption here is that the process may change over time due to various factors, such as equipment wear or changes in the workforce. To adjust for this, a shift in the process mean is considered. The 1.5 sigma shift is a common adjustment that accounts for the long-term variability in a process that might not be captured in a short-term study. The formula mentioned, Zbench (Long) = Zbench (Short) - 1.5, suggests that to estimate the long-term capability of a process, you would take the Z-score calculated from short-term data and adjust it by subtracting 1.5. This adjustment is based on the assumption that the process variability increases over the long term. Now, let's delve into the translation of the above explanation into Chinese. read more >>

The Z in Z.Bench refers to the standard normal distribution with mean 0 and standard deviation 1. ... The 1.5 sigma shift can be used to calculate the long-term capability of a process when only few observations have been collected by using the relation: Zbench (Long) = Zbench (Short) - 1.5.Oct 3, 2011read more >>