Download the Article (PDF, 129 KB)

**Sang-Gyu Lim, Samsung Economic Research Institute**

This tool will help define the direction you need to take in improving a process.

The fundamental principle of Six Sigma methodology is to solve the right problem the right way. To do this, two important issues need to be addressed. One is to prioritize the selection of target processes for improvement; the other is to choose a proper solution strategy.

The authors of *Managing Six Sigma* emphasize the importance of
looking at the big picture surrounding a process.(1) The big picture is
realized by a so-called 30,000-foot level control chart, which helps quality
practitioners discover whether the variation is due to a common cause
or assignable cause. Because these two distinct causes have different
origins of variation, separate strategies are required to battle against
process variations, and these strategies need to be driven by the processes.

The first step in the Six Sigma approach to business process improvement is to define the critical to quality items (CTQs) that represent business process performance. The CTQ tree has a hierarchical structure, and in manufacturing, final product quality is dependent on many subCTQs.

For example, several subprocesses in a typical manufacturing process merge to form the final assembly or packaging line. It is also not unusual for the same functional manufacturing lines to be operating in multiple locations, including overseas. In these instances it is useful to map the process indicators because it will help you prioritize which processes to select for improvement. To improve the quality of the final product, the subassembly lines should also be investigated and prioritized for improvement.

In solving a specific problem, the define, measure, analyze, improve and control (DMAIC) methodology can be more effective if you visualize and monitor the features of key process output variables in a systematic way. Even in the service industry, you have stratifications, such as region and age group. Process positioning with respect to these stratifications can suggest the direction you need to take to improve the process.

In looking at Six Sigma project implementation using the DMAIC roadmap, the tools should be used strategically. If the main problem is controllability, identifying the assignable noise identification is critical, and using the multi-vari chart is helpful. But if the main problem is process capability, process optimization tools such as design of experiments (DOE) need to be used. You should choose your statistical tools based on the process indicators.

**The Principle of Process Positioning**

Processes can be positioned using two key indicators: process capability
and controllability. Strictly speaking, the capability of a process cannot
be adequately assessed until statistical control has been established,
but a less strict definition of capability is used for the purpose of
process characterization. Process controllability is assessed using control
charts. One criterion is to use control limits driven by the process itself
(natural tolerances), and another is to investigate the existence of any
trend.

Process capability is the ratio of customer requirements to process variation.
In a case in which the result is a binomial distribution, process capability
is defined by the defective rate, provided sufficient data are accumulated.
With the variable data and specifications, the C*p* and C*pk*
represent the process capability in which the statistical distribution
is normal. Sigma level can also be an indicator for process capability.

**Coefficient of Control**

To quantify a process’s controllability, you need to identify a coefficient
of control. This can be defined by the ratio of the standard deviation
of the process to the reference standard deviation,

.

This reference standard deviation can be defined by the distribution of
the process data. For example, for a binomial distribution, the coefficient
of control can be defined by the ratio of the standard deviation of the
process data to the standard deviation of the binomial distribution ,
where

,
is the average defective rate and *ñ* is the average number
of data sampled.

The coefficient of control reflects how process variation is managed within
the control limits. That is, if the data goes out of a control limit,
the coefficient of control gets bigger. If the coefficient of control
gets bigger, it’s more likely the data points exceed the control
limits.

**Applications**

** Process
positioning and project prioritization.** A typical process positioning
map is shown in Figure 1. The x-axis represents
the process capability, and in this case, the defective rate is the indicator
for process capability, so the smaller the better. Controllability is
represented by the y-axis and can be figured out qualitatively in the
control chart. If the time data show any point out of the 3 sigma limit,
then the process may have assignable causes.

In the macroscopic point of view, process positioning can be used to prioritize projects. If there are several processes in an organization and a process positioning chart like Figure 1 is available, then the prioritized target processes can be set. Looking at Figure 1, assume there is no constraint, such as cost, on addressing the problem. The process in cell C is the process that urgently needs to be improved to achieve overall organizational improvement. The process in cell B or D should be improved next.

It’s difficult to achieve a strategic approach for overall improvement without considering the overall distribution of the process characteristics. Even if all your projects are concentrated in cells A and B, your organization will not realize improvement overall.

** Process positioning and solution strategy.** In Figure
1, the most desired cell for a process to be in is cell A because
it indicates both the process capability and controllability are good.
In this case, the process is running without any problems, and you can
use statistical process control to monitor the process. The process is
running under continuous improvement, adjusting the assignable causes.(2)

A process that lands in cell C has poor controllability and capability. To reach cell A, the process should follow one of the structured solution paths shown by the arrows in Figure 1: CBA (process capability is increased first and then controllability is stabilized) or CDA (controllability is stabilized and then process capability is increased).

In general, when you have poor process controllability, it’s not easy to increase process capability. To do this, the process factors need to be optimized using DOE. But if the process is uncontrollable, the data response is unstable, and the optimizing process is unreliable. It’s more feasible to take the CDA path and improve controllability first by eliminating assignable causes. This way, the process positioning helps set the solution strategy in using Six Sigma methodology right away.

If a process lands in cell B, your improvement efforts should focus on how to obtain stable controllability. A control chart should be used to figure out the assignable causes and process noise analysis tools such as multi-vari charts to discover whether a significant stratification factor is causing the large variations. At the same time, you need to investigate the adequacy of specification because the process capability is good in spite of poor controllability.

For processes that end up in cell D, improvement efforts should focus on increasing process capability. The common causes are dominant because the process is under control. In this case, you should use process optimization techniques such as DOE. Processes that settle in this cell generally make perfect Six Sigma projects.

**Case Study**

Let’s say a service company decided to improve its customer claim
rate. The company provides the same service at six different locations,
and the daily number of service transactions and claims are gathered at
each location and sent to the company’s headquarters.

Figure 2 shows the control chart (p-chart) depicting the data gathered over one month. It shows the average claim rate to be 0.01121; the controllability looks poor. Now the company needs to quantify the controllability for each region so it can draw a process positioning map.

The p-charts for each of the six different locations are shown in Figures 3a – 3f. Each control chart shows the average claim rate for each region. Qualitatively, region six has the worst controllability and region two has relatively good controllability.

The results of the process positioning are illustrated in Figure 4, where the control factors are obtained using the relation, reference = binomial. The control factor is expected to be near 1 for good controllability in the process. The range of the control factors for the six different locations is between 3.5 and 5.5, and the claim rate is between 0.0095 and 0.0135.

The defective rate (claim rate) is on the x-axis and the coefficients of control are on the y-axis. The data points indicate the six different service locations, and the point in the middle is the average of the six locations. The average point represents the average customer claim rate of the total system, but the arithmetic average of the coefficient of control does not represent the coefficient of the total system. As can be seen in Figure 2, a far bigger coefficient of control can be imagined. The purpose of using the average point is to set the criterion for the four quadrants.

After laying out the points in Figure 4, the company realized the controllability of its system is poor. And if the company is pursuing six sigma level capability, its process capability is far from satisfactory. As was shown in Figure 2, the total system has poor controllability and is quantified in Figure 4 in terms of the coefficients of control for the different service locations.

Since the Six Sigma process improvement should focus on overall performance improvement, the company should start with regions six and four, where the controllability is poor and the claim rates are high. The next area to target could be region three or five; however, region three needs to be investigated before region five because process capability is based on the assumption of processes being under control.

In implementing selected Six Sigma projects, the company’s first effort should be to resolve the assignable causes using control charts and process noise analysis with multi-vari charts. That is, its first priority should be to recover the process’s controllability. In the next phase of Six Sigma project implementation, the company can focus on reducing the overall claim rate (increasing process capability) by using Six Sigma methodology to redesign the processes.

After the company successfully completes the Six Sigma project, Figure 4 will evolve into a different shape, and the position and magnitude of the axes will change. Accordingly, the company can set new process targets to further improve the process, while its Six Sigma application strategy may vary considering the process position. This position map should be updated regularly so it can be used as a baseline for the processes.

It can be challenging for a company to visualize the big picture surrounding a process, including the voice of the customer. The process positioning method can act as a link between a company’s management strategy and its Six Sigma implementation.

*References*

- Forrest Breyfogle III, James Cupello and Becki Meadows,
*Managing Six Sigma*, John Wiley & Sons, 1999. - Douglas Montgomery,
*Introduction to Statistical Quality Control*, John Wiley & Sons, 1996.

*Acknowledgment*

Part of this article was written while I was working at Samsung Electro-Mechanics
in Korea, and I would like to thank Dongyoung Yu for the valuable discussions
he and I had.