This posting describes a grinding process case study to illustrate the use of design and analysis of experiments to study cause and effect and reduce common-cause variation. We continue the case study reported by Gijo (2005) in the 2/28/2005 posting. That posting describes the construction of a cause-and-effect diagram by a team in an engineering organization identify potential causes of low grinding machine capability. The team selected four factors for further analysis based on designed experiments. These factors were Feed Rate, Wheel Speed, Work Speed, and Wheel Grade. The team chose to perform experiments using two levels for each factor. The following table shows the levels and factors selected for experimentation. The levels with an * were existing operating levels.
| Factor | Code | Low Level (-1) | High Level (+1) | Unit |
Feed rate | A | .0008* | .0010 | Mm/Rev |
Wheel speed | B | 2200 | 2450* | RPM |
Work speed | C | 250* | 360 | RPM |
Wheel grade | D | A54 | A60* | - |
Experimental design terminology defines the effect of a factor as the change in the response produced by a change in the level of the factor. Assume that the response in this experiment is the variance of the outer diameter measurements. For example, if increasing the feed rate from .0008 to .0010 mm/revolution increases the variance of the outer diameter by .003 mm2 then the feed-rate (factor A) effect is .003 mm2. When the difference in response to a factor level change is not the same at all levels of another factor, an interaction effect exists between the factors. The factor A effect might be .003 mm2 when the wheel speed is 2200 rpm and .005 mm2 when the wheel speed (factor B) is 2400 rpm, then an interaction effect exists between factors A and B. The magnitude of the interaction effect is the average difference between the two A effects. Thus the AxB interaction effect is (.005-.003)/2 = .001 mm2.
The team selected an experimental design the enables them to estimate the effects of the four factors in the above table. They also wanted to estimate two interaction effects: 1. (AxB) between Feed Rate and Wheel Speed (AxB) and 2. (AxC) between Feed Rate and Work Speed. The linear graph shown below depicts the effects the experimental design must be capable of estimating. That is, the A, B, C and D effects, the AxB and AxC interaction effects and the error variance.
The next posting will describe the experimental design.
References
- Gijo, E. V. (2005). "Improving Process Capability of Manufacturing Process by Application of Statistical Techniques." Quality Engineering 17(2): 309-315.