# Six Sigma: Statistical Tools & Analysis

Instructor: James Kuhn

Jim has taught adults for more than 20 years and has a Masters Degree in Christian Leadership.

Six Sigma projects incorporate the use of many tools and techniques to enable continuous improvement. This lesson will focus on the statistical tools that are used in Six Sigma and the accompanying analysis of the results.

## Six Sigma Statistical Tools & Analysis

The Six Sigma methodology provides a powerful toolbox full of various techniques, charts, diagrams, methods, and processes for use in conducting continuous improvement initiatives. Like any toolbox, you must select the right tool for the right job in order to have a successful result. At its core, Six Sigma contains comprehensive statistical tools and statistical analysis to enable quality gains.

We will focus solely on the primary statistical tools and their effective use in a Six Sigma project. Statistical tools and statistical analysis are applied during all the usual project lifecycle phases - define, measure, analyze, improve, and control (DMAIC) - but are most heavily utilized in the measure and analyze phases. As there are over 100 statistical tools and endless variations of those tools, this lesson will highlight the most commonly used Six Sigma statistical tools.

### Define Phase

The define phase of every Six Sigma initiative focuses upon understanding the problem and the desired outcome of the project. Thusly, the majority of the techniques utilized during this phase are non-statistical. One tool, Pareto analysis, can be used to help refine your problem statement. A Pareto chart is a simple graphical representation of the biggest problems that happen most often. Think of the Pareto as the '80/20 rule', in which, 20% of the issues cause 80% of your problem. While the Pareto is most commonly used in the measure and analyze phase, it can really help to hone in on a specific issue in the define phase. In the sample chart, we have the top reasons why callers are put on hold at a customer service center. Almost half of the held calls were due to research and more than 80% were due to three reasons! The Pareto chart often gives early guidance to problem areas and potential solutions in your project.

### Measure Phase

The measure phase quantifies the problem being worked on and gives initial data analysis. The first tool used here is descriptive statistics, which is a summary report of the data surrounding your problem. The descriptive statistics include the average, mean, mode measure about the problem frequency, (known as central tendency), along with the variability of the data (known as dispersion). Analysis of the descriptive statistics will give the Six Sigma team an idea of the scope of the problem (limited or widespread), how often it occurs, and validation that a problem truly exists.

The Pareto chart is used again in the measure phase to further identify and isolate your problem characteristics. Additionally, a histogram is used to summarize the frequency distribution data into a graph. If you were measuring how long it took to answer the phone for a customer service center using 10 second increments, the histogram would show how many callers waited 10 seconds, 20 seconds, 30 seconds and so on. The analysis of the histogram looks at the distribution (normal or abnormal) and how often the results are outside your limits or target answer time. Think of the histogram as the baseline measure which will serve as the foundation to look for improvement.

One of the most important techniques utilized during the measure phase is the measurement system analysis (MSA). By examining the data's accuracy, and how it is collected and measured, The MSA will determine if your data is reliable as a decision-making tool. As Six Sigma is a data-driven process, it is critical that all measurements can be trusted. Repeatability and reliability are the keys to this analysis.

### Analyze Phase

The analyze phase of the Six Sigma DMAIC process is the most statistic-dependent phase. Many critical tools and techniques are utilized in order to fully define the root cause of the issue. These statistical tools center around the stability and/or capability of the process under review. First, we need to know if the process being studied is 'in control,' and performs consistently so that we can depend on the data observations, (the stability of the process). Next, we want to know if the process statistically supports the desired specifications.

In order to assess the stability of your process, the Six Sigma team will want to evaluate the control chart for the target data. Using our running example, let's assume that we are looking to improve the time it takes to answer the phone in our customer service center. Looking at the control chart will tell us if the operation is consistent and in control. Our control chart for this project shows that there is a wide amount of variation, but the operation is in control. All the calls fall between the upper and lower control levels (targets), but frequently miss the bullseye.

Now that we know our data is trustworthy, and that the process is in control, we need to see if the process can support our desired improvements. In our example, we would check to see if our customer support center could answer calls in a 30 second average time, but no more than 60 seconds overall. In order to do so, we would utilize a process capability analysis. The processes capability analysis is a powerful statistical tool that helps us understand our current state of the operation and its subsequent capability.

In our case, about half of the calls are failing to hit their marks by falling outside of the upper service level of 60 seconds. Statistical analysis also shows that, in the current state, the center is not capable of meeting those targets. Unless something changes, it is statistically impossible for them to meet the targets you are shooting for. This is determined by analyzing the process capability values (Cp/Cpk) as shown on the chart. Based on a more advanced calculation, that number must be over 1.33 in order to meet our targets. However, we are here to improve this operation and we've just proven that they need help!

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