DMAIC—Identifying Rejects is Just the Beginning

Whether a company is defining six-sigma projects or implementing other process control initiatives, enumerating defects is only the beginning. The real challenge is to identify the source of the defects. Some defects may be reduced by training or inspection, but many defects are more difficult to identify and resolve.

Process improvement is an iterative process. One of the common themes being used to describe this cycle is DMAIC – Define, Measure, Analyze, Improve and Control. It is crucial to base decisions on facts and data. Statit offers a variety of tools to maximize the effectiveness of each phase in the cycle.

Define: One of the first tools a company might employ is the identification of the frequency and types of defects. Pareto analysis provides a graphical depiction of the defect spectrum. Options are available to specify a weight to the defect types as appropriate. This is important if factors other than frequency, such as cost, are important components of the defect analysis. The goal of these charts is to help identify the area resulting in the most defects. Ideally, reducing the largest group of defects or the costliest defects first, should result in the most significant improvement in increasing yield. Continuing to monitor the rate and type of defects can help continuing process improvement.

The first example is a Pareto chart of assembly defects. This chart shows the defects in decreasing order of occurrence. There is also a cumulative percent curve plotted against the Y2 axis. The cumulative percent curve indicates the percent of each type of defect as it relates to total defects.

The second example eliminates the cumulate curve and rotates the Pareto bars for a horizontal display. This is a dramatic display of the relative frequency of defect occurrences.

Measure: The identification of what is necessary for process improvement is necessary before decisions can be made regarding what must be measured. Measurements are imperative for consistent comparisons during the process. In some cases, it may not be obvious which factors are important to the process. Conducting experiments may help to ascertain the interaction of salient factors that produce good product or contribute to rejects. Conducting experiments in a rigorous fashion helps to ensure that the results of the experimental trials will lend themselves to rigorous analytical methods with the minimum number of trials. Statit offers tools for the statistical design of experiments. Experiments can be defined for both linear and non-linear models. The models allow multiple factors to be examined within a single experiment. A factorial design is appropriate when each factor is taken at 2 levels. This procedure finds suitable reduced experimental trials involving only a specified number of treatment combinations. Box-Behnken and Central Composite designs allow for each factor to take on more than two levels, so that nonlinearities can also be estimated.

Analyze: Whether data has been gathered from formal experiments or is obtained from existing data sources, analyzing the data produces facts that can be used for process improvement decisions. For example, a t-test can be performed to investigate the significance of change in a process before and after an improvement initiative. Regression analysis can confirm the effect of one or more independent variables on the outcome of an important measure.

This an example of analyzing the vehicle mileage for cars manufactured in the USA compared to cars manufactured in Japan. The t-test can be used to determine if there is a significant difference in the average mileage by country or origin.

Comparison of Means by Country
Means are considered different if the p-value is less than 0.05

Student's t-test for Variables:
	Mileage (Japan) N = 15	Mileage (USA) N = 21
Student's t statistic		Degrees of freedom
1.762		34
One-sided P-value = 0.0435
	Sample Means	Standard Error	Sample Size
Mileage (Japan)	28.6000	1.6756	15
Mileage (USA)	25.6667	0.7475	21

Improve: Many tools are available to measure improvement. An XY plot is a simple way to visualize data trends. The XY does not perform formal analysis. Typically, the X-axis variable is considered the independent variable. The Y-axis variable is the dependent variable, or the variable that is affected by the values of X.

This example plots automobile weight as the independent variable and mileage as the dependent variable. The results suggest that there is an inverse relationship between weight and mileage. An inverse relationship is one where increasing values of one variable, weight in this example, causes decreasing values of the dependent variable or mileage.

Control: Control charts are a well established tool for monitoring how well a process remains in control. Control charts add powerful components to alert users to conditions that may be negatively impacting the process in a timely manner. The following charts monitor the average daily operating temperature for an oven in the fabrication area. The plotted points are the daily averages. The 3-sigma control limits are calculated from the actual data at this process step. For this number of points, the probability that any point that belongs to the normal process variation falls outside of the 3-sigma limits is .3%. The number of sigma limits is controlled by the user. There are many options available for generating control charts that fit given conditions. For example, warning limits may be specified to alert users that a process may be heading out of control prior to a control limit being violated. It is also possible to annotate the chart with assignable causes for points outside the normal process. Assignable causes continue to plot the point on the chart, but the values are removed from the calculations. This ensures that only valid points are used to calculate the control limits. There are additional examples of this in the Statit e-QC Manufacturing demo.

During the process of monitoring control charts, it is important to verify that the within subgroup variability is also in control. There are circumstances where average subgroup values may be in control, but contain unacceptable variation. The variation can be monitored by using range or standard deviation charts, commonly called r or s charts respectively. These charts plot the subgroup ranges or standard deviations and evaluate whether the observed variation is within the limits expected for the observed process variation. The choice of using an r-chart or s-chart is primarily dependent on the subgroup size. Subgroups with less than 10 values are typically evaluated with r-charts. Subgroups of 10 or more are more appropriately evaluated with s-charts. If s-charts are used, the X-bar option to use control limits based on standard deviations needs to be selected. The following is the corresponding r-chart for the oven temperatures.

This discussion has provided examples of some of the basic tools that can be used for each phase of an ongoing cycle for process improvement. While some analyses may require more advanced techniques, many solutions can be identified within the framework described here. It is important to understand the tools employed for any investigation and to trust the results. More complex techniques require additional knowledge. The key to success is to continuously monitor the process. The importance of a single factor on a process may change as the manufacturing process evolves. Continuous monitoring is necessary to quickly identify shifts in the process and minimize the impact.

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