STATISTICAL PROCESS CONTROL - THE IMPORTANCE OF USING CALIBRATED MEASUREMENT EQUIPMENT. CASE STUDY

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1 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 PAPER REF: 5376 STATISTICAL PROCESS CONTROL - THE IMPORTANCE OF USING CALIBRATED MEASUREMENT EQUIPMENT. CASE STUDY José Barradas 1(*), Marta Mendes 1 1 CATIM - technological center for metal industry, Porto, Portugal (*) jose.barradas@catim.pt ABSTRACT These days, where competition between companies is great, it is essential that they hold the most optimized processes possible, ensuring the quality of products and services and reducing operational costs. Thus, the use of tools or methodologies to meet the performance of processes and facilitate the detection of problems in order to reduce the variability is essential to ensure their competitiveness. The Statistical Process Control, is one of the seven quality tools used in order to provide information for more effective diagnosis in the prevention and detection of defects and problems in the evaluated processes and, consequently, helping increase productivity and results of the company, avoiding waste, being of greatest importance to guarantee the quality of the company. In this study, we intend to discuss / evaluate the variability introduced into a process capability study, using control charts and having on base the use of uncalibrated measurement equipment vs. calibrated measurement equipment. Keywords: statistical control, quality, control charts, measuring equipment, calibration. INTRODUCTION The study of process capability is a technique of the Statistical Process Control (SPC) that aims to evaluate if the process can reach out the project specifications and/ or the customer specifications (Woodall, 2000). The study consists of collecting a sample of products manufactured under standard conditions to evaluate the stability of the statistical process based on the use of control charts. Control charts are used to follow the evolution of the performance of a process (Kaya and Kahraman, 2011), allowing to make provision of the existence of special or common causes in the process, through unusual variability or normal introduced in it. The control charts are divided in two categories, control charts by variables, used when the characteristic / parameter to be analyzed is the type measurable and control charts by attributes used to record non-conforming units and non-conformities. In this study, was used a control chart by variables, particularly the chart of Averages and Amplitude (X R), which consists of two graphs that illustrate respectively: - Graph of the averages ( ) - the process behavior in relation to the values of the variable under study. - Graph of the amplitudes (R) the process of behavior in relation to dispersion of the variable under study. Through their analysis is possible to determine the need to act in the process, through the elimination of special causes or by reducing the variability introduced by the common causes

2 Symposium_23 Quality Control and Metrology in Engineering The special causes may be related to several factors, such as the manpower, working method, raw material, machines, environment and measuring equipment. The lacks of employee training, failures adjustment or maintenance of machines / equipment, lack of reliability in measurement equipment used are examples of special causes. The determining the ability of a production process to generate a conforming product should only be carried out after verification if the process is statistically controlled. In this study, we intend to discuss / evaluate the variability introduced into a process capability study, using control charts and having on base the use of uncalibrated measurement equipment vs. calibrated measurement equipment. METHODOLOGY In this research work the methodology used was the case study, which involved the collection of 25 samples with the objective of controlling the temperature parameter. Each sample consists of 5 measurements (n = 5) and were always collected under the same conditions and continuously at one hour intervals. For this purpose we used a digital temperature controller (reading unit) and a temperature sensor (thermocouple Type K) which together make up what is known as digital thermometer, which has a resolution of 0,1. The critical point to be controlled in the production process is 46,0, with an tolerance of ±0,5. Was used a control chart of Averages and Amplitude (X R) for registration, monitorization and follow-up the characteristic under study (temperature). To the choice of this type of chart has taken into account the fact that the control characteristic is a variable of continues type (measured) and the size of the sample of the subgroup is five (5 measurements). The control chart of Averages and Amplitude (X R) is the most used at the industrial level and its purpose is to detect as soon as possible any change to the process performance. Based on the sampling were calculated the upper and lower control limits of the graph of the averages X and the graph of the amplitudes R. The control limits are the values that define the maximum variability allowable inside which a particular characteristic / parameter can take values. The control limits were determined according to the following formulas: UCL ( ) = + A 2 * ; LCL ( ) = - A 2 * UCL ( ) = D 4 * ; LCL (R) = D 3 * Where UCL represents the upper control limit, the LCL is the lower control limit, the process average is represented by and is the average of the amplitudes, and A 2, D 3 and D 4 are correction factors (Table 1). Table 1 Constants of correction factors for the control chart ( ), adapted from Down, et al. (2005)

3 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 In respect to the analysis and interpretation of control charts should be noted, in summary, the signals that can indicate that the process cannot be statistically controlled. Those signs can occur in one or more of the following situations: - The existence of points outside the control limits: this may indicate an incorrect marking of the point, or an error in the calculation of the control limit, or an incident during the sampling, or a machine stop, or end of the production cycle or a change in the measuring system (example might be the use of an inadequate device to process); - Tendencies observation: seven consecutive points on the same side of the average, seven points in ascending or descending line, may indicate instability of a tool, change of operator, start change in the process or a changing tendency of the process with time; - Cyclical movements, up and down: can indicate the existence of effects at a given time and / or rotation of operators and / or maintenance failures. Another important factor in Statistical Process Control is the determination of capability indice, C p and C pk, to check the suitability of the production process to comply with the product specification. The process capability indice (C p ) represents the potential capacity of the process, i.e. the ratio between the specification to the process quality characteristic and the variability of that process. The capability indice (C pk ) is used to evaluate the centrality around the nominal value, corresponding to the product specification. The process capability indices were calculated according to the following formulas: T = USL LSL C p = C pk (USL) = C pk (LSL) = = Where T is the process tolerance, USL and LSL the upper and lower specification limits respectively, the standard deviation is represented by and the correction factor of the standard deviation is defined by d 2 (Table 1). A process to have capability should have the both indices, C p and C pk, with values less than 1,33. The value of C pk to consider should be the lower between the C pk (USL) and the C pk (LSL), (Down, et al., 2005). A C p value very different from C pk value indicates us an opportunity to improve, to center the process around the nominal value, corresponding to the product specification. RESULTS As mentioned in the previous section were collected, always under the same conditions and continuously at one hour intervals, 25 samples and each sample consist in 5 measurements (n = 5), with the objective to control the temperature parameter

4 Symposium_23 Quality Control and Metrology in Engineering We recalled that the process specification is (46,0 ± 0,5). In Table 2 are presented the results from the measurements made. Table 2 Results from the temperature measurements. A control chart of Averages and Amplitude ( - R) was used for registration, monitorization and follow-up the characteristic under study (temperature). Based on the sampling carried were calculated the UCL and LCL of the graph X and the graph R. After were elaborated the respective control charts presented in the following figures. Fig. 1- Graph of the averages ( ) Fig. 2 - Graph of the amplitudes (R)

5 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 From the analysis of the control charts ( - R), we found the existence of points outside the control limits, in particular in the graph of average ( ), thus, we can conclude that the process is not statistically controlled. This unusual variation may be related to the existence of special causes. After the analysis of potential special causes, it was found that one of these was not fully taken into account, particularly the reliability of the measuring equipment used to perform the control of the temperature of the process. This lack of reliability is due to the fact that the measurement equipment is not calibrated. Thus, is unknown the measurement errors of it and its influence in the process. According to the authors, the calibration should be performed in all measurement equipment that have influence on the accuracy or validity of the data or tests carried out, and must be calibrated before being placed (or replaced) in service. But not all measuring devices need to be calibrated, generally must be calibrated those that are used to control the production processes and the quality of products. According to the International Vocabulary of Metrology (JCGM, 2012), calibration is defined as the operation that, under specified conditions, in a first step, establishes a relation between the quantity values with measurement uncertainties provided by measurement standards and corresponding indications with associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining a measurement result from an indication.. The results expressed in calibration certificates of measuring equipment are important because they provide valid and useful information that can help us to making decisions, such as corrections to be made in the measurement process. Without this care, the calibration of the equipments, any results obtained by these, and for more reproducible they are, you may not have the necessary reliability for the control of a process and quality of product. In order to correct or cancel the special cause that may be in the lead to the instability of the process, it was decided to perform the calibration of the measuring equipment (digital thermometer). This calibration was performed by an accredited laboratory in accordance with the standard ISO / IEC The calibration values are presented in Table 3. Standard reading (ºC) Table 3 - Results of the calibration certificate of the digital thermometer. Equipment reading (ºC) Error (ºC) Expanded uncertainty (ºC) 45,03 44,6-0,4 ± 0,051 46,02 45,7-0,3 ± 0,051 47,04 46,7-0,3 ± 0,051 Based on the results of the calibration certificate, the results of the values indicated in the Table 2 were corrected, using only the error of the equipment. After the corrections was created a new table of data (Table 4)

6 Symposium_23 Quality Control and Metrology in Engineering Table 4 - Results of the corrected temperature measurements. With the corrected results were determined the new control limits and elaborated the new control chart ( - R). The results and the new graphs are show in Figs. 3 and 4. Fig. 3 - Graph of the averages ( ), after values correction. Fig. 4 - Graph of the amplitudes (R), after values correction

7 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 By the analysis of new control charts and the effect of the values correction obtained based on the calibration errors, there was a marked improvement in process stability. With this correction the process has no points outside the control limits, not presents evident trends, so the conditions are fulfilled to assess if the process will be able to comply with the product specifications. Thus, it was determined the capability indice (C p and C pk ) in order to check the suitability of the production process to comply with the product specification: T=46,5 45,5=1,0 σ= 0,4 2,33 =0,17 C = 1,0 6 0,17 =0,98 C USL = 46,5 45,8 3 0,17 =1,37 C LSL = 45,8 45,5 3 0,17 =0,59 Summary the C p and C pk values are C p = 0,98 and C pk = 0,59, which corresponds to the lowest value of C pk (USL) and C pk (LSL). As it was found that the values of the capability indice (C p and C pk ) are less than 1,33, it is concluded that although the process is statistically controlled, cannot comply with the product specifications, probably due the existence of common causes in excess. CONCLUSIONS From the study carried were taken some interesting conclusions. During the investigation, the control charts proved to be an effective tool in the verification of the process stability, being this an important condition for subsequent determination of process capability indices. One of the most relevant conclusions was the importance of calibration of measuring equipment used in the monitoring and control of a production process for the necessary knowledge of the measurement equipment errors. By the analysis of the first results, the production process was out of statistical control, and the reliability of the measurement equipment used for control the temperature parameter, being one of the possible causes for the instability of the process. After the calibration of the measurement equipment used in the monitoring and control of the process and further elaboration and analysis of new control charts (X - R), with the respective correction of the measured values, the production process has passed from the state out of

8 Symposium_23 Quality Control and Metrology in Engineering control to the state under control, reducing the variability introduced by the effect of the measurements errors. It was also found, and after calculation of the process capability indices that the process can not comply with product specifications. Thus we can conclude that the control charts are essential for monitoring and process control. The use of calibrated measuring equipment influences the stability of processes, contributing to a more appropriate control of them. In our study we also can concluded that the compliance with the conditions referred above, by itself, does not mean that the production process is able to comply with the product specifications, since there may be common causes excess that in the future should also be studied and analyzed. In summary and to finish, the main conclusion from this study is that the condition of the equipment, especially in respect to errors, can introduce some influence in the Statistical Process Control studies. However, it will be noted that when we are using calibrated equipment the variation introduced into the process capability studies will be lower. REFERENCES [1]-Kaya I, Kahraman C., Process capability analyses based on fuzzy measurements and fuzzy control charts. Elsevier, 38 (4), pp [2]-Woodall W. H., Controversies and Contradictions in Statistical Process Control. Journal of Quality Technology, 32 (3), pp [3]-Down, M. H. et al., Statistical Process Control (SPC). Second edition. USA: DaimlerChrysler Corporation, Ford Motor Company, and General Motors Corporation. [4]-JCGM, BIPM, International vocabulary of metrology - Basic and general concepts and associated terms (VIM). JCGM