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Case Study 1: Vane Pump Cylinder Block Process Parameter Study
(This case study is intended only to demonstrate general steps involved in experiment DESIGN and ANALYSIS tasks.Qualitek-4(Windows) software was used for all design and analysis output which are best viewed by Netscape browser)

Project Description
A Manufacturer of large industrial pumps was experiencing manufacturing related performance problems with one of their established line of products. Subsequent investigations revealed that, over the years, a number of process parameter specifications were modified, and, in the recent past, suppliers for a few key components were also changed. Concerned about customer satisfaction and future sales, the company initiated a study of the process parameter with a view to determine the best process condition.

The objectives were to minimize or eliminate the observed performance deficiencies in the areas: (1) Cylinder Size Change, (2) Debris Accumulated, (3) Change of End-Play, and (4) Vibration Observed

Criteria and Scheme of Evaluations
When there are multiple objectives evaluated by different measuring units, special analysis strategy must be followed. A common practice is to analyze the DOE results separately for each of the criteria of evaluations. A more effective strategy is to combine the evaluations into a single index called an Overall Evaluation Criteria (OEC). The OEC requires a special combination scheme as the criteria of evaluations have different units, quality characteristics (QC), and relative weightings. The detailed formulation of the scheme of OEC is too involved to discuss in this report and is left for readers to study on their own.

Note that the results shown below represent the combined effect of the four criteria of evaluations which have the ranges and QC's as indicated. A sample evaluation, for Trial#1, and the OEC(39) is also shown. (Quality Characteristic for the OEC = Smaller is Better)

Factors and Levels
Based on a brainstorming session for planning an experiment, the following process factors and their levels were among the many identified.

FACTORS                         LEVEL - I	LEVEL - II	LEVEL - III
A: Shaft Straightness            In Spec.        Out of Spec.
B: Piston Bore Cylinder        	Minimum      	Maximum        
C: Piston Processing  		Tumble        	Ground
D: Cyl. Block Finish       	31 Micron      	60 Micron
E: Shoe Hold-down 		Tight       	Loose
F: Shoe Steam Treatment   	On           	off
G: Cyl. Block Steam Treat   	In-house  	Other Supplier
H: Process Contamination 	Present      	Absent
I: Magnetism       		Present     	Removed
K: Cylinder Bore			Brush-Sc	Brush-AO   	Unbrushed
L: Piston S.T.M.	 	        Cold TSW	Bar TSW	        Bar On&Off

A number of interactions were suspected, but because there were a large number of candidate factors for the experiment, and with limited time to complete the project, no interaction was included in this initial study.

Noise Factors
Several noise factors were identified, but none included in the study.

Orthogonal Array and Column Assignment
An L-16 orthogonal array with two modified columns was used to design the experiment. The two 3-level columns necessary for the two 3-level factors were obtained by first upgrading columns 1 2 3 and 4 8 12, then downgrading (Dummy Treatment) to 3-level. The modified array is as shown below.

To accomplish the design, the two 3-level factors (K & L) were assigned to the modified columns 1 and 4 and the columns 2, 3, 8, and 12 are zeroed out. The remaining 9 factors are assigned to the 9 unused columns as shown below.


The sixteen samples were fabricated as per the specifications called for by the trial conditions described by the orthogonal array above, and one sample in each trial condition was tested. The performance of the test samples were evaluated by the four criteria of evaluations indicated above. The evaluations for each sample were then combined into a single number (OEC) which is considered as the result (performance measure) as listed below.

Strategy for Analysis of Results
Five separate analyses, one for each of the criteria of evaluations and one with the OEC, were carried out. This report only demonstrates the analysis performed using the combined effect (OEC) of all evaluations.
Since there was only one sample tested in each of the trial conditions, the standard method of analysis (S/N not being applicable) was followed.

Factor and Interaction Effects

The factor average effects indicate the trend of influence of the factor to the result. The graphical display conveys the relative magnitude of influence by the slopes of the lines as shown below. In case of factor levels beyond two levels, a least square curve fit predicts more realistic/expected behavior.

Examining many factor effects together is convenient way to evaluate the trends. Because the QC = Smaller is Better, the levels indicating the lowest values, are the desirable factor levels for the Optimum Condition.

Test of Presence of Interactions
Although interaction was not included in this study, it is indeed possible to establish whether or not interaction is PRESENT between any two factors. The information about the PRESENCE of interaction, however, does not tell us anything about their SIGNIFICANCE, which can only be found when special columns are reserved to study the interaction. So, what is so good about learning the presence of interaction?

The benefits are many. First, it does not cost any additional time and money. Second, calculating all possible interactions and ranking them in order of their relative strength (Severity Index, S.I.., 0- 100%), may serve as a list of contender interactions for the repeat experiments. With 11 factors included in the experiment, there can be 11 x (11 - 1)/2 possible two-factor interactions. A list of the top interactions as shown below, are noted for future studies. (Qualitek-4, Automatic Interaction option).

Interaction between any two factors can be displayed graphically as shown below. The strength of PRESENCE of interaction is indicated by the angle (IS = 0 for 0 degree, IS =100 for 90 degrees) between the lines (level 1 - 2).

Relative Influences of Factor and Interaction (ANOVA)
ANOVA calculations are carried out to determine the relative influences of the factor to the variation of results. It also provides a means for examining the level of significance of the factor influence. All factors which are found to have confidence level(1 - % level of significance) below 90%, have been pooled (considered insignificant).

Significant Factors
The five most significant factors and their relative influence to the variation of results are generally shown by paretoized bar graph and by pie diagram.

Optimum Condition and Improved Performance
Among the 11 factors studied, only six factors are found to be significant. It is customary to include only the significant factors in estimating the performance at the optimum condition. The optimum condition and the expected performance (in terms of OEC) thus calculated are shown below. The Confidence Interval (C.I.) on the optimum performance is calculated to be +/- 10.3. This means that, when the process is set at the optimum condition, the average performance of a set of samples tested, is expected to be within (22.198 - 10.3) and (22.198 + 10.3).

Confirmation Test Results
As part of the confirmation tests, five samples were fabricated at the optimum condition. The samples were evaluated following the same criteria used for the original experiments and the OEC values were calculated for all samples. The average of the sample OEC's were found to be 18.5 which is within the Confidence Interval.


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