Design of Experiments for Processes Reliability Management

Transcription

1 10 th International Symposium Topical Problems in the Field of Electrical and Power Engineering Pärnu, Estonia, January 10-15, 2011 Design of Experiments for Processes Reliability Management Marina Pribytkova, Igor Polyantchikov, Tatjana Karaulova Tallinn University of Technology Abstract A lot of assembly lines are made semi-automated where manual work stations are alternate with automated stations which are responsible for control of a product at different stages of assembling process. These automated stations must guarantee that a client will not get a nonconforming product. In order to be sure in reliability of such stations it is necessary to examine their functionality with some periodicity. As usually operators of an assembly line perform inspection of these stations work. The inspection must meet the following requirements like being not time-taking and very laborious. At this point problems occur because such stations as a rule examine not only one parameter but number of parameters and to be sure in reliability of control of all parameters many tests should be done what makes the control prolonged. There is also a problem for engineers to determine how many test models have to be prepared and what mistakes should they reflect. The aim of this research is to be able to find an optimal quantity of station s functionality tests and also frequency of implementation of these tests using design of experiments (DOE) techniques in order to ensure the reliable production and minimize operator s time for this task performance. Keywords: Design of Experiments; Reliability analysis; Reliable production process; Introduction Many companies today still use the old quality techniques of inspection where bad parts are inspected. Although this method is not effective and not the best one though sometimes it is difficult to refuse of this at all and change this method by another one. However it is not meant that nothing can be done in order to improve the inspection process and as far as possible to reduce connected with its costs. One of the biggest minuses of the inspection control is that it requires a lot of time of examiners. As a rule an examiner in production is an operator. Therefore an operator s time that he can spend producing a product is spent on testing. It is pure waste for a firm therefore it is clever to reduce time for testing but at the same time keep the same quality level. An effective way to improve performance is to optimize the engineering designs of products or processes by experimental means [3]. Reliability analysis is commonly thought of as an approach to model failures of existing products or processes [5]. However, reliability analysis can also be used as a powerful tool to design robust products that operate with minimal failures, by adopting the methodology of Design for Reliability (DFR). In DFR, reliability analysis is carried out in conjunction with physics of failure and experiment design techniques. In this article on a concrete example of a traditional quality inspection it will be presented how the process can be optimized without decreasing of quality control s level. Such questions like quantity and frequency of testing will be answered. For the solution of this problem such a method like design of experiments (DOE) and software Minitab will be used. 1 Design of Experiments (DOE) The potential applications of DOE in manufacturing processes include: improved process yield and stability, reduced manufacturing costs, reduced variability and closer conformance to nominal or target requirements and others. Design of Experiments refers to the process of planning, designing and analysing the experiment so that valid and objective conclusions can be drawn effectively and efficiently. In the context of DOE in manufacturing, one may come across two types of process variables or factors: qualitative and quantitative factors. Quantitative factors are represented usually by number characteristics (speed, temperature, pressure and so on). In our research factors are qualitative. The term level refers to a specified value or settings of the factor being examined in the experiment. A trial or run is a certain combination of factor levels whose effect on the output is of interest. The three principles of experimental design such a randomization, replication and blocking can be utilized in industrial experiments to improve the efficiency of experimentation. During our research only randomization and replication principles were used [1]. 203

2 Another strategy of experimentation that is used extensively in practice is the one-factor-at-a-time approach. This method consists of selecting a starting point for each factor, and then successively varying each factor over its range with the other factors held constant at the baseline level. The major disadvantage of this strategy is that it fails to consider any possible interactions between the factors [2]. One-factor-at-a-time approach is right a thing we desired to eliminate because in our case it was the reason of two problems: first of all we had a lot of test models prepared according this approach. Another thing was an interaction which occurred when we planned to change the method of testing by using test models from current components instead of old test models. Thus our aim was to perform test controlling several factors at a time. The correct approach to dealing with several factors is to conduct a factorial experiment. This is an experimental strategy in which factors are varied together, instead of one at time [2]. A factorial design can be either full or fractional factorial. A full factorial designed experiment consists of all possible combinations of levels for all factors. The total number of experiments for studying k factors at 2-levels is 2 k. Very often experimenters do not have adequate time, resources and budget to carry out full factorial experiments. If the experimenters can reasonably assume that certain higher-order interactions (thirdorder and higher) are not important, then information on the main effects and two-order interactions can be obtained by running only a fraction of the full factorial experiment. We can assess the impact of the identified factors by implementing a Design of Experiments approach and then analyzing the collected data. Often, however, the number of factors analysed, which determine the number of test runs to implement, may make an experiment extremely costly or time consuming. We need to reduce the number of runs, in order to make it feasible. We can achieve this by implementing "Fractional" versions of Experimental Factorial Designs. 1.1 Strategy of experimentations In general, experiments are used to study the performance of processes and systems. The process or system can be represented by the model shown in Figure 1.1. We can usually visualize the process as a combination of operations, machines, methods, people, and other resources that transforms some input (often a material) into an output that has one or more observable response variables. Some of the process variables and material properties x 1, x 2,..., x p are controllable, whereas other variables z 1, z 2,.., z q are uncontrollable (although they may be controllable for purposes of a test). The objectives of the experiment may include the following: 1. Determining which variables are most influential on the response y 2. Determining where to set the influential x so that y is almost always near the desired nominal value 3. Determining where to set the influential x so that variability in y is small 4. Determining where to set the influential x so that the effects of the uncontrollable variables z 1, z 2,..., z q are minimized. Fig.1.1. General model system or process [6] 1.2 Number of experiments calculation The goal of any experimental activity is to get the maximum information about a system with the minimum number of well designed experiments. An experimental program recognizes the major factors that affect the outcome of the experiment. The factors may be identified by looking at all the quantities that may affect the outcome of the experiment. The total number of experiments (n) that need to be performed is: n= k n i i= 1 (1) Where, k- number of factors; n i - number of levels for the i th factor. 1.3 Fractional factorial design A factorial design can be either full or fractional factorial. A full factorial designed experiment consists of all possible combinations of levels for all factors. The total number of experiments for studying k factors at 2-levels is 2 k. Each of the k factors is assigned only two levels. The levels are usually High = 1 and Low = -1. Such a scheme is useful as a preliminary experimental program before a more ambitious study is undertaken. The outcome of the 2 k factorial experiment will help identify the relative importance of factors and also will offer some knowledge about the interaction effects. 204

3 2 Formulation of the Problem The objective of the research was to optimize the process of inspection s control of the vision camera (figure 2.1) at the production line. wanted to use the current components for the test we could not obtain the same effect, all the time the interaction between the components occurred. 3. The quantity of the tests model was quite big and tests took a lot of operator s time to be performed. 4. And finally what kind of test to prepare and how often to perform the tests, previously engineers detected these questions by intuition, only from own experience. How exactly it was detected was difficult to determine. As all problems were analyzed it was decided to use the Design of Experiments method as it was considered like the most suitable in the current case. 2.2 Equipment noise Fig.2.1. A Cognex vision camera The object of this camera is to inspect every part for the purpose of presence and right position of specified components. Like any other equipment the camera has to be controlled from time to time just to be sure that it performs its mission correctly. For this purpose initially wrong assembled test models are used. The operators of the lines perform the test with some periodicity. The common scheme of analysis implementation is introduced in figure 2.2 Product noise Noise factor Equipment noise Control factor Test object Fig.2.2. Layout of control station inspection Quality characteristics Quality Characteristic (QC) generally refers to the measured results of the experiment. The QC can be single criterion or a combination of several criteria together into a single index. The QC-tools are a set of simple, effective, statistical and graphical tools for analyzing data. Equipment noise factors are defined, in general, as anything that causes an FR to deviate from its target value. There are following noise factors [7]: Manufacturing variability is a result of the inability to manufacture two parts exactly alike. Manufacturing processes and machines are two major sources Customer usage noise. Customer exhibits different patterns of using a given product and hence different duty cycles are generated. Deterioration (internal) noise which represents product aging. Environment (external) noise, which are sources of variability that comes outside of the product such as temperature, lightening and humidity. Coupling noise. This is a system noise that happens because of the physical mapping decisions. The causes of variation in the functional requirements (FRs) of the process are called noise factors. 2.1 Product noise The following problems were connected with this control: 1. One and the same specially prepared test models were always used for the tests. This was the cause of a problem that even if the test model passes the test in the camera the real products which are made of the current components does not pass the camera due to variability in quality of the components. The camera was adjusted according the test models and not according the current products. 2. The old test models were made by using glue in order to keep only one mistake at the time. If we Fig 2.3 The effect of noise factors during the system life cycle [8] The noise factors affect the FRs in the life cycle (see Figure 2.3). As a result, they can cause dramatic reduction in product reliability. Early life failures can be attributed to manufacturing variability. The unit to unit noise causes failure in the field when the product is subjected to external noise. The random failure rate that characterizes most of the product life is attributed to external noise. Deterioration noise is active at the end of life. Therefore, a product is said to be robust (and reliable) when it is insensitive to the effect of noise factors, even though the sources themselves have not been eliminated. 205

4 3 DOE Method Application for the Control Station A case study was carried out in a real production process for a Vision camera working as a control station. The process involved in conducting a successful design of experiments can be broken down into five steps: Define the problem. Plan the experiment. Run the experiment. Analyze the data by statistical methods. Report the results [4]. 1. First of all we defined our problem. The objective of the experiment was to identify the most significant parameters which have to be controlled by test models among all parameters that are controlled by the camera. 2. Then we planned the experiment. The response of interest for the experiment was the result (Passed/ Failed) for each test from the camera. For the experiment it was agreed that factor Passed would be designated by -1 and Failed by 1. Five main factors were identified during brainstorming. These factors are: Spring loop (A), Spring position Right (B), Spring position Left (C), Left LB position (D) and Right LB position (E). Each factor was studied at 2-levels. The ranges of parameters are represented in Table 1. Table 1. Factors and their uncoded levels Factor Name Low level High level A Spring loop -1 1 B Spring position Right -1 1 C Spring position Left -1 1 D Left LB position -1 1 E Right LB position -1 1 Before starting the experiment it was agreed about cofficient k. It was decided to use this coefficient to calculate a frequency of future tests on the basis of results from the experiment. If the result of any trial for one type of the test model during the experiment will be negative (will pass instead of being failed) the coefficient will be multiplied by the quantity of negative trials and thus we will determine a frequency of tests for the operators. The following ranges of the coefficient was accepted: k = once a week k = once a day k 4 - at the beggining of each shift 3. Running the experiment. The part of uncoded design matrix of the experiment is represented in Figure 3.1. The shown matrix is not full because of its big volume. Fig.3.1. The uncoded matrix with responses 4. Analysing the data. As our aim was to determine the main factors and possible interactions between them it was decided to use a Normal plot of effects (figure 3.2) and a Pareto plot (figure 3.3). As a number of studied factors were more than 4, it was decided to use for the experiment a fractional design. If we use a full factorial design the number of runs for our experiment will be 2 5, or 32 runs. In addition it was decided to replicate each run 5 times. To sum up it is 160 runs. In the conditions of real production it is hardly possible due to lack of resources and time. The number of degrees of freedom in our case is 5 and the closest number of experiment runs is 8. This means that it is a 2 (5-2) fractional factorial design. The experiment was carried out by using Minitab software. All initial data was recorded to the Minitab. Fig.3.2. Normal plot of factors It is clear from the Normal plot that significant factors are Left LB position, Right LB position and also one interaction between spring left and right positions. 206

5 It is seen from the Pareto plot that factors D and E have the greatest influence on the final result and really there is an interaction between factors and these are B and C factors. In order to see how this interaction influences our experiment an Interaction plot was created (figure 3.4). Table 2. Test models and frequency of testing Test model Model with wrong position of left LB Model with wrong position of right LB Wrong position of the spring at both edges Frequency At the beginning of each shift Once a day Once a week 3.1 Summarising of analysis results Introduced application of the DOE method shows that experiment was carried out successfully. All objectives that were raised were achieved. The result of the experiment was created schedule of the testing and also the set of the test models. Fig.3.3. Pareto plot of factors 1. As it was planned the quantity of the test models was reduced by half. At the same time quality level remained the same. 2. Time an operator spends to perform test also was reduced by half. Approximately it was cut down from 8 minutes to 4 minutes what helped to increase performance rate. 3. Using of test models produced from current components was introduced that allowed to increase stability of camera s performance and decrease quantity of false signals Fig.3.4. Interaction plot of B and C factors Figure 7 indicates that interaction is strong and the worst result is obtained when both edges of the spring are in wrong position. 5. Reporting the results. As the result of the experiment the decision on quantity and frequency of testing was finally done. It was decided that in order to test the camera on the required level 3 test models are needed: Model with wrong position of left LB Model with wrong position of right LB And model combining 2 mistakes wrong position of the spring at both edges As for the frequency of the test it was calculated using the coefficient k which was mentioned above and results of each trial from the experiment. All results of the experiment are not reflected in the article, however the result was: 4 negative results for the first test model 3 negative result for the second test model 1 negative result for the third model Final decision about quantity and frequency of the test is shown in Table For engineers it became easier to plan quantity and frequency of the test. The decision became not intuition based, but was exactly calculated using scientific method. In the future the engineers would continue using the method for planning the tests what would significant reduce there time for this task. 4 Conclusions Problem solutions in design and productions environments often require experiments to find a solution. Design of experiments are collection of statistical methods properly used maximize the probability of finding the best solution at the lowest cost. Design of experiments is used to identify important factors, to optimize production systems and to create robust products and processes. Acknowledgements Hereby we would like to thank the Doctoral school of energy and geotechnology II that enabled us to carry out this work. References 1. Jiju Antony, Design of experiments for engineers and scientists, Butterworth-Heinemann, ISBN , Douglas C. Montgomery, Design and analysis of experiments, John Wiley and Sons,

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