Process Variability by Using the Design of Experiment—A Case Study
Process Variability Reduction by Using the Design of
Experiment—A Case Study
Jan Machac* and Frantisek Steiner
Department of Technologies and Measurement
University of West Bohemia
Pilsen, 30614, Czech Republic
ABSTRACT
Low process variability and capability index might be some of customer's requirements. Therefore it is necessary
to fulfil these requirements and guarantee them in the future. Since state-of-art companies that want to keep up
with competitors have to consider all actions which might prevent losses or customer's dissatisfaction. This paper
deals with possibilities how to decrease the process variability and satisfy customers. For process variability
decrease, statistical experiments were carried out. The paper contains a case study devoted to the usage of design
of experiment (DOE) in the production process. The case study reveals ways of dealing with real production
problems and offers an effective treatment.
1. INTRODUCTION
Generally, all manufacturing and measurement processes exhibit variation. The aim of all process and quality
engineers is to decrease this variation. Since, most customers demand a low variability presented by the capability
index. It is not always easy to find out the factor causing the process variability therefore statistical experiments are
necessary to be carried out. One of essential methods for this purpose is the design of experiment (DOE). Design of
experiment is very useful method for identification of critical factors associated with processes and determination of
optimal settings of these process factors due to process capability and performance enhancement. In other words,
design of experiment is a systematic approach that is carried out to identify the input controllable variables in a
process and analyze their effects and interactions in the process output. Design of experiment is commonly used to
discover which set of process variables influences the output, and what level of these variables should be kept to
optimize the process performance. The aim of this study is to show how design of experiment can be successfully
used in production praxis and also prove how critical factors may affect the output and how to use them in order to
decrease the process variability.
2. PROCESS VARIABILITY
When monitoring any process factors, certain variability of these factors is always observed. By the size of this
variability, the standard deviation σ is expressed, respectively its estimate sx. The process variability treatment is the
first presumption for the effective process control and satisfaction of customer's needs. Before analyzing and
consequent variability decreasing, it is necessary to understand how and what variability can be. The monitored
parameters will always vary, but when the process is stable the measured values make a diagram which can be
understood as a distribution of the monitored sign. If only random influences affect the process, it is the normal
distribution. The aim is to stabilize the process and decrease its variability. Causes can be common or assignable.
Common causes are a spectrum of unidentified causes where each cause contributes just slightly, but their sum is a
measurable character of a process. The process is usually stable and predictable. Assignable causes are concerned
when a real process change revealed by a control chart occurs. The cause must be identified, removed and must not
ever happen [1].
*Correspondingauthor: Tel.: (00420) 777-694912; E-mail: jmachac@ket.zcu.cz
Flexible Automation and Intelligent Manufacturing, FAIM 2014
The observed process variability consists of the variability among samples and variability of the measurement
system. Analysis of reproducibility and repeatability (Gage R&R) enables to distinguish between these types of
variability. Measurement system consists of following parts: Measuring devices, Methods and procedures,
Operational definitions and Men. The measurement system variability should not be higher than ten percent. If
higher, a complete check of the measurement system is required. When the measurement system variability is lower
than ten percent, it is necessary to check all samples coming into the production process. Division of the process
variability is seen in Figure 1.
Figure 1. Process variability division.
3. DESIGN OF EXPERIMENT
It is an output or outputs that we check and observe in order to improve a process or customer's satisfaction and
it is important to determine the factors which have the significant influence on the output. In order to obtain required
value of the output, it is necessary to find out the setup of the significant factors and identify their possible
interactions. The aim of experiments is to detect how to set the input factors to guarantee a low variability of the
value of the required output and minimize the influence of uncontrollable factors. In general usage, design of
experiments (DOE) or experimental design is the design of any information-gathering exercises where variation is
present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually
used for controlled experiments. Formal planned experimentation is often used in evaluating physical objects,
chemical formulations, structures, components, and materials. Other types of study, and their design, are discussed
in the articles on opinion polls and statistical surveys (which are types of observational study), natural experiments
and quasi-experiments (for example, quasi-experimental design) [2]. It is not always easy to make up a clear and
acceptable problem description. It is absolutely necessary to develop all thoughts and ideas concerning the problem
and goal of the experiment. When planning the experiment, the help of all interested workers (process engineers,
quality engineers, managers and also operators) is usually required. The factors changing during the process should
be chosen. For the factor selection, a combination of practical skills and theoretical knowledge is recommended. For
designing the experiment, it is needed to use statistical software as Minitab or Statistica. Design of experiments is
thus a discipline that has very broad application across all the natural and social sciences and engineering [3,4].
4. CASE STUDY
In this study, the subject for the process variability improvement is a production of fuel valves for the automotive
industry. The valve is based on its simplicity. A company operating in the automotive industry, specializing in the
development and manufacture of valves for fuel tanks was dealing with a difficulty. During the serial production
process of high voluminous filter, high scrap rate, high process variability occurred and capability indexes were not
satisfying as well. The customer requests the flow through the filter to be 140 liters per a minute (l/min) with the
standard deviation of ± 10 liters / min which is the quantity monitored by a testing machine.
First of all, it was necessary to find out how the current process looked like in time. For this display, around 100
accidentally measured values were taken and the control chart was made for them in Minitab, as seen in Figure 2.
Here, it is possible to see that some values are out of required tolerance boundaries. Thus, the process is statistically
Process Variability by Using the Design of Experiment—A Case Study
uncontrollable. It is also necessary to determine whether it is normal data or not. For this test, the normality test in
Minitab was used. In Figure 3, the normality test of the process is seen. P-value is higher than 0.05 so it is possible
to say with probability of 95 percent that this is the normal distribution.
Figure 2. Control chart of the production process.
Figure 3. Normality test.
It was feasible to carry out the capability analysis of the process for the normal distribution and determine
present values of Cp (Process Capability) and Cpk (Process Capability Index). In Figure 4, it is seen that the indices
are not sufficient (Cp = 0.69 and Cpk = 0.53) and it is needful to initiate counter-measures in order to reduce the high
process variability and increase the capability indices. The goal was set to approach the approximate value of Cp and
Cpk indices to be 1,33 as it is required in automotive industry [5].
Figure 4. Capability analysis.
Flexible Automation and Intelligent Manufacturing, FAIM 2014
4.1. GAGE R&R
Then,it was necessary to determine what causes the variability. Whether product individual parts or the
measurement system. Human factor was not taken into consideration due to a large number of operators working
there with the same constant scrap rate. When having a wrong testing machine setting, all scrap parts might just be
pseudo-scrap. Therefore, Gage R & R study was conducted to verify the measurement system. In order to verify the
measurement of the test machine, the selected sample is measured for twenty five times in a row and recorded.
Consequent evaluation was made in Minitab. From the results in Figure5,it shows that the measurement system is
fine as it only brings the variability to the process of 3.77% (allowed value is 10%). It was considered that the
process variability was affected by components of the product. Thus, design of experiment was required to be
carried out in order to find out the components causing scrap. Then, selection of proper components and their
parameters (called factors all together) which are the input for design of experiment needed to be performed.
Figure 5. Gage R&R study.
4.2. DESIGN OF EXPERIMENT - PROPOSAL
Selection of proper input factors affecting the output is not always an easy procedure. Random selection is not
the optimal way of design of experiment preparation. There are methods that are able to ease the selection. One of
those methods is called Analytic Hierarchy Process. The method is based on the process where it is necessary to
accomplish three steps. First, state the objective, it is to select right factors in this case. Then, criteria (components in
this case) must be defined (spring, pin and float). Finally, picking of alternatives is required (force, height, weight,
concentricity and diameter). From this information, a hierarchical tree can be arranged as shown in Figure 6.
Figure 6. Hierarchical Tree.
Process Variability by Using the Design of Experiment—A Case Study
In the next step, using judgments to determine the ranking of criteria was carried out. This step needs to be
performed by designers or product specialist. The Delphi method might be also used. Further, the relative
importance of one criterion over another was expressed by using pairwise comparisons according to the rate line as
shown below.
1 equal - 2 moderate - 3 strong - 4 very strong - 5 extreme
According to [6], eigenvector solution is the best approach. The procedure is shown in Figure 7. The first step
was the matrix squaring. The row sums are then calculated and normalized. The normalization was carried out by
dividing the row sum by the row of totals (i.e. 10,5 divided by 36,75 equals 0,29). The result is the eigenvector.
According to this, the most important criterion seems to be the spring.
Figure 7. Eigenvector procedure for criterions.
The same procedure as was performed for criterions (components) must be done for alternatives as shown in Figure
8. The most important alternatives for all criterions are marked in Figure 9.
Figure 8. Eigenvector procedure for alternatives.
Flexible Automation and Intelligent Manufacturing, FAIM 2014
Figure 9. The most important alternativesmarked in red.
Criterions and alternatives that could affect the flow through the valve were selected from Figure 9. For each
criterion (component), the most probable alternative (parameter) was selected. It was the weight of the float inside
the valve and its weight range, labeled in the Design of Experiment as float weight. Next chosen factor was the
spring force holding the float inside the valve. The spring is also moving in a certain tolerance field, labeled as
Spring for the Design of Experiment. The last factor possibly influencing the flow is the concentricity of the float
pin, in Design of Experiment identified as Concentricity.
Consequently, the Design of Experiment model for three critical factors that may affect the flow through the
valve was created. For each factor, it was necessary to find parts in their upper and lower limits of the tolerance
field. The upper boundary is marked as 1in the DoE model, the lower limit as -1. For each possible combination,
there were performed four repetitions in a random order. Then, there were produced thirty two products and the
same number of measurements carried out exactly according to the specified model, as shown in Figure 10.
Figure 10. The Design of Experiment (DoE) model.
Process Variability by Using the Design of Experiment—A Case Study
Subsequent measurement data was recorded and completed in the model. The actual evaluation of the model was
again performed in the Minitab statistical software. The evaluation consists of several optional graphs. In Figure 11,
it can be seen the Pareto Chart of these factors and all sorts of combinations. The results clearly show that the most
significant factor was the B factor, or spring, and its force. Results of Main Effect Plot uniquely determined the
weight of the float and the concentricity of pin had no effect on the flow. Furthermore, it also shows the clear
influence of the spring, and its force. Thus, as shown in Figure12, the bigger spring force, the lower the flow rate is.
In order to verify this theory, it was necessary to perform several tests.
Figure 11. Pareto Chart. Figure 12. Main Effect Plot.
4.3. VERIFICATION
In order to verify the result of Design of Experiment, a test with adjusted springs was carried out. For the test,
approximately one hundred springs with force on the upper boundary of the tolerance were selected. Further,
products from selected springs were assembled and tested in the test machine. The resulting values were recorded as
shown in Figure 13. Optically, the control chart looks much better than at the beginning of the process, no value
coming outside of the limits. Therefore, it was not necessary to find out whether the process is capable and how
indices Cp and Cpk look like. For this purpose, the statistical software Minitab was used again. The results of the
capability test can be seen in Figure 14. Cp and Cpk indices were 1.41 and 1.31 which wasa great improvement
compared to the original 0.69 and 0.53.The goal for Cp was successfully accomplished. The value for Cpk missed the
goal only of 0,02 but it can be also recognized as a success. Recommendation for the company was to start
negotiating with suppliers in order to receive springs that are on the upper tolerance level.
Figure 13. Control Chart of the improved process.
Flexible Automation and Intelligent Manufacturing, FAIM 2014
Figure 14. The capability test of the improved process.
5. SUMMARY
Decreasing the variability of production processes is the issue for many production companies. The index values
of Cp and Cpk may be specified by the customer to a specific value. Therefore, it is necessary to monitor these values
and strive for the greatest numbers. There are many techniques to achieve high Cp and Cpk indices. This case study
describes a real case, the found solution was to improve the process by means of statistical experiments, namely by
Design of Experiment with usage of Minitab. When, both indices were nearly increased by the value of 1. Such an
improvement will certainly bring significant savings for the company. However, the method cannot be used in all
cases and it is not always easy to make a Design of Experiment model. In this case, it was a real situation and a real
example of usage of Design of Experiment methodology.
ACKNOWLEDGEMENTS
This research has been supported by the European Regional Development Fund and the Ministry of Education,
Youth and Sports of the Czech Republic under the Regional Innovation Centre for Electrical Engineering (RICE),
project No. CZ.1.05/2.1.00/03.0094.
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