Solutions as good as gold

Paul Boughton

Eston Martz reports on how statistical analysis software is helping a supplier of precious metals optimise its processes.

Swiss-based Metalor Technologies, an international leader in precious metals and advanced materials, is a supplier to companies around the world that produce electronics and to manufacturers of medical and electrical equipment.

Metalor's skill in creating innovative and reliable technology has earned the company a preferred-vendor status and a global reputation for excellence. In fact, well beyond the benefits to its own interests, Metalor's expertise has fostered the creation of new market segments for many of its partners. In its quest for innovative solutions, Metalor relies on Minitab Statistical Software for help in achieving its process engineering goals.

The company, which was founded in 1852, is headquartered in Switzerland with subsidiaries in 15 countries. It includes refining, advanced coatings, and electrotechnics divisions. Metalor employs more than 1600 people worldwide, and has annual revenues over $330 million.

Among Metalor's products is a high-purity silver powder used in the fabrication of a variety of microelectronic products, ranging from solar cell metallization on silicon wafers to membrane touch switches on flexible plastic. Two properties of the powder - density and surface area - are critical to its quality and performance in their customer's processes. However, these two properties are very difficult to predict or control in production.

Silver is expensive so developing an effective experiment to control costs was necessary. Using the Design of Experiment (DOE) tools in Minitab, as well as some DOE best practices of its own, Metalor set out to determine how density and surface area were affected by three key process inputs: reaction temperature, ammonium level, and stir rate. Their ultimate goal: to improve the quality of their silver powder.

Once Metalor identified the three key factors in its process, it analysed them to determine their effect on its silver powder products. A full factorial experiment in Minitab - using only one high and one low setting for each input - let Metalor simultaneously evaluate the effect of each input, as well as the interaction effects between these inputs, on the two output variables of interest.

One result of analysing a designed experiment in Minitab is a main effects plot, which examines differences among level means for one or more factors. A main effect is present when the low and high levels of an individual factor have a different effect on the response. A main effects plot graphs the response mean for each factor level connected by a line. There are general patterns to look for:

- When the line is horizontal (parallel to the x-axis), then there is no main effect present. Each level of the factor affects the response in the same way, and the response mean is the same across both factor levels.

- When the line is not horizontal, then a main effect is present. The two levels of the factor affect the response differently. The steeper the slope of the line, the greater the magnitude of the main effect. Provided p-values can then be used to assess the significance of each main effect.

This main effects plot for density clearly shows that two of the three factors Metalor tested had a stronger effect on the powder's density.

To easily view interactions between factors, experimenters can use Minitab's Interactions Plot. When an interaction between two factors is present, experimenters must evaluate the settings for both factors when optimizing responses, rather than evaluating each factor individually when only main effects are present.

Their Minitab analysis resulted in two equations that were used to generate an overlaid contour plot showing both responses as a function of the process conditions. Contour plots are used to explore the potential relationship between three variables. A contour plot is like a topographical map in which x-, y-, and z-values are plotted instead of longitude, latitude, and elevation. These plots show a three-dimensional relationship in two dimensions, with x- and y-factors (predictors) plotted on the x- and y-scales, and response values represented by contours.

Overlaid contour plots are used to visually identify the feasible inputs for multiple responses for a designed experiment. Feasible input variable settings for one response may be far from feasible for another response. You can use overlaid contour plots to consider the responses simultaneously.

When you create an overlaid contour plot, you specify a lower and upper bound for each response. The overlaid contour plot displays contours for these bounds versus two continuous factors on the axes. The rest of the variables in the model are held at user-specified settings. The plot highlights the region (if any) where all responses are within their bounds.

This plot makes it easy to find the ranges of the factors that will give the desired results. Using the overlaid contour plot, Metalor found the feasible settings for ammonium and stir rate, holding temperature at 40 degrees, to optimise both the density and surface area of the silver powder. The white region on the plot is the feasible region, or the area that satisfies the criteria for all responses. When your factors are set at any of the levels shown in the white area of an overlaid contour plot, the predicted responses should fall within the specified ranges.

The overlaid contour plot created in Minitab helped Metalor adjust their process to meet customer specifications for both the density and the surface area of their powder.

Once the new process settings were implemented, Minitab's control charts clearly showed the sustained benefits of the improved process. A control chart plots your process data in time-ordered sequence to help identify common cause versus special cause variation. By identifying the different causes of variation, you can take action on your process without overreacting to it and making unnecessary adjustments. In any process, some variability is expected. This variability, which is naturally inherent in the process, is called common cause variation. Other times, the variability is different than what is expected due to some influence that is not part of the normal process. That is special cause variation, and indicates that something may be introducing unexpected - and potentially problematic - variability in the process.

In Metalor's case, Minitab control charts demonstrate the effect of implementing the optimal process conditions determined by the designed experiment. Minitab's solution decreased variation in their process by 50 per cent and improved the quality of their silver powder. Minitab control charts illustrated the decrease in process variation that led to a higher quality powder. These improvements also reduced rejected batches by 75 per cent.

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Eston Martz is with Minitab Inc, State College, PA, USA.

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