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H OW TO S ELECT THE A PPROPRIATE T YPE OF C ONTROL C HART IN M ETROLOGY 2014 NCSL International Workshop and Symposium Author: Chen-Yun Hung, Gwo-Sheng Peng and Paul Kam-Wa Lui Center for Measurement Standards (CMS) / Industrial Technology Research Institute (ITRI) Abstract According to Section 5.9 of ISO/IEC 17025:2005 [1], laboratories shall have quality control procedures for monitoring the validity of tests and calibrations undertaken. The resulting data shall be recorded in such a way that trends are detectable and, where practicable, statistical techniques shall be applied to the review of the results. In order to meet the requirements given above, control charts are commonly used to monitor the stability of the measurement systems. However, the inappropriate selection of process parameters or control charts may result in a failure to detect changes in the stability of measurement systems. For this reason, this paper focuses on how to select the appropriate types of control charts in metrology, such as for process parameters characterized by trend or lower resolution. The accuracy of the measurement results could be continuously ensured through the correct use of control charts. Principle of Control Chart The principle of a control chart was proposed by Dr. Walter A. Shewhart in 1924 [2], which is based on the upper and lower control limits established by the confidence interval with a set of data. Thus, the control charts derived from this principle are called Shewhart control charts. Assuming that the process parameter is x i, the mean is μ x, and the standard deviation is σ x, a general model can be expressed as Equation (1) to (3): Upper Control Limit (UCL):UCL = μ x + kσ x (1) Centerline (CL):CL = μ x (2) Lower Control Limit (LCL):LCL = μ x – kσ x (3) When k = 3, a typical control limit established at three times the standard deviation, the probability of the measured value falling within the upper and lower control limits is 99.73 %. Determination of Process Parameters The determination of process parameter is critical to the effectiveness of a control chart in monitoring whether the state of measurement system is in- control or out-of-control. In general, the process parameters should be stable and sensitive enough to detect the signals of measurement systems. They are usually related to measurement procedures and measurement equations. From the statistical point of view, if the process parameter data are subject to a normal distribution, the interpretation of the control chart will be reasonable. In practice, the determination of process parameters commonly includes utilizing check standards and reference standards to obtain a single measured value, the difference between two measured values, or a ratio, etc. For example, in the caliper calibration system of length, the process parameter is defined as the measured value of the check standard (caliper) which measures the reference standard (caliper checker or gauge block); in the accelerometer calibration system of vibration, the process parameter is defined as the ratio of output voltages from the check standard and the reference standard. Many more types of process parameters are described in [3]. It is recommended that as much time as possible is spent in collecting sufficient data when first determining process parameters. This will ensure that the data are stable and subject to a normal distribution. Moreover, it is better for the process parameters having high sensitivity to be able to detect the signals of measurement systems. Process Parameter with Lower Resolution When the process parameter is defined as the measured value of the meter having lower resolution, on condition that the standard is extremely stable, it will likely result in zero standard deviation and be unable to establish the upper and lower control limits of the control chart with a general model. Otherwise, it is also possible that the control limits are smaller than the resolution due to low standard deviation, and the signals of measurement system are detected by shifting only one resolution even though the measurement system is actually in control. If the above situation occurs, it is suggested that technical staff with expertise appropriately adjust the upper and lower control limits. For example, if the measurement system is regarded as normal by shifting one resolution from practical experience, the upper and lower limits can be set up by 1.5 times the resolution, as shown in Figure 3. Conclusions In order to construct a control chart monitoring the stability of the measurement system effectively, the determination of process parameter is the primary factor. The second factor is the selection of the appropriate type of control chart. This paper only provides several appropriate types of control charts summarized by practical experience of the author. However, as the wide scope of metrology, the types of control charts mentioned herein may not be able to meet the needs by each laboratory. Laboratories should still cautiously consider the characteristics of measurement systems or process parameters to select the appropriate types of control charts. If there are international standards available, they should be followed first. References [1]ISO/IEC, “General requirements for the competence of testing and calibration laboratories,” ISO/IEC 17025, 2005. [2]R. DeVor, T. Chang, and J. Sutherland, Statistical Quality Design and Control, Prentice-Hall, 1992. [3]C. Croarkin,, “Measurement Assurance Programs Part II: Development and Implementation, ” National Bureau of Standards Special Publication 676-II, April 1985. Table 1. Measured value c i once per three months. Figure 1. Method (A) control chart with c i.Figure 2. Method (B) control chart with x i. Figure 3. Lower-resolution control chart. (resolution = 0.1 mm)

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