Analyze Phase

# 1 of 8Attribute Sequence - Transform Data

• Variables data offers a richness not offered by attribute data. Thus, it is often advantageous to transform attribute data to variables data.
• If the average count is large (> 20), treat the count as variables (continuous) data.
• Perform transformation on either c or p to convert to variables data.
• Test normality to verify a valid transformation. Must also have 5+ values in the distribution.
• If not valid, continue attribute assessment. If valid, treat the data as variables data. In the Analyze phase, it is important to use tools and methods in the proper sequence. For example, graphical tools should always be used before statistical tools. Likewise, testing for normality and stability should always be done before hypothesis testing. This guide provides a general sequence in terms of tool usage during the analysis of data.

Analyze Phase

# 2 of 8Attribute Sequence - Descriptive Statistics

• Compute statistics related to the process such as p-bar, np-bar if counting nonconforming units, and c-bar and u-bar if counting nonconformities.
• Compute confidence intervals around descriptive statistics to quantify the uncertainty in them. Smaller samples have larger uncertainty.
Analyze Phase

# 3 of 8Attribute Sequence - Stability

• Use control charts to determine if the process is stable over time.
• Use c and u charts for nonconformities and p and np charts for nonconforming units.
• Can determine whether improvement opportunity rests with special and/or common cause variation. If special cause variation is the primary issue, work with the process owners. If common cause variation is the primary issue, work with management.
Analyze Phase

# 4 of 8Attribute Sequence - Capability

• Capability is p, the proportion of nonconforming units.
• The confidence interval around p may also be computed to better understand uncertainty in the sample statistic.
Analyze Phase

# 5 of 8Attribute Sequence - Hypothesis Testing

• Use the Z test to compare the proportion of nonconforming units from two different processes.
Analyze Phase

# 6 of 8Attribute Sequence - Correlation

• Use correlation to determine the strength of relationship between variables and learn which inputs are the key drivers of the process output.
• Correlation can be seen graphically by creating scatter plots of each input variable vs. the output variable.
• Determine strength of relationship statistically by computing the correlation coefficient (R) and the coefficient of determination (R2).
Analyze Phase

# 7 of 8Attribute Sequence - Model The Process 

• Use regression to develop a mathematical model of the process so that it can be optimized.
• Use the appropriate form of logistic regression (binary, ordinal, or nominal).
• If the model is not sufficiently robust, consider a designed experiment.
Analyze Phase

# 8 of 8Attribute Sequence - Model The Process 

• Use Design of Experiments to develop a mathematical model of the process so that it can be optimized.
• Generally, DOE is used only when regression does not sufficiently address optimization and/or the cost of DOE is relatively low. DOE, when properly run, has less noise in the data, resulting in more robust and accurate models relative to regression.
• Use sequential design for maximum efficiency.