Measurement assurance programs (MAPs) are commonly used in metrology to ensure product performance. The following outlines the steps taken by SeaMetrics to establish a MAP for calibrating its flowmeters. Under the program all measurements performed by the transfer system are traceable to NIST. Uncertainty in flowrate was determined by the Law of Propagation of Error, and the calibration system was validated by a proficiency test.
By Jeff Peery & Jim FrederickThe MAP described herin is a liquid flow calibration system used to calibrate liquid flowmeters. It consists of four elements: 1) calibration of measurement devices; 2) statistical process control of measurement devices; 3) a measurement uncertainty analysis; and 4) a proficiency test. The MAP is responsible for process control, maintaining quality of measurements, and traceability to National Institute of Standards and Technology (NIST, www.nist.org) standards.MAPs are necessary to maintain quality assurance and ties to national standards [1]. They assure quality of all measurement devices and test procedures and assure a state of statistical control of the measurement process. Upon establishing traceability to national standards, a MAP may be implemented to maintain this traceability over time. The MAP described in this article is used to evaluate and manage SeaMetrics’ (www.seametrics.com) liquid flow calibration system. The Law of Propagation of Error is used to predict measurement uncertainty [2]. A proficiency test is used to validate the system’s measurements. Process control is maintained by Shewart’s Statistical Process Control (SPC) [3]. Under the MAP described here, liquid flowrate and K-factor measurements are traced to NIST, thereby maintaining measurement quality.MethodsLiquid flowmeter calibrations are performed by driving liquid water at constant flowrate through a system of closed conduit and referencing a primary flowmeter (meter under test) to a secondary flowmeter (flow standard). The calibration system is composed of a storage tank, flow conditioner, pump, one six-inch secondary flowmeter, and one two-inch secondary flowmeter (Figure 1). All components are connected by epoxy-coated steel pipe. The pump is used to drive fluid from the storage tank to the flow conditioner; maximum flowrate is approximately 1.50×10-1 m3/s and minimum flowrate is approximately 3.16×10-4 m3/s. Exiting the flow conditioner is a section of straight pipe that is sufficient in length to fully develop flow upstream of the primary meter. Downstream of the primary meter the pipe splits into one two-inch line and one six-inch line. Each line leads to a separate secondary meter (six inch and two inch) located at approximately 10 diameters from the bifurcation point to assure fully developed flow. By using two different sizes of secondary meters, a greater operating range is achieved. Two butterfly valves are located at the exit of each bifurcation line and are used to regulate flowrate. Liquid exiting the valves is routed back to the storage tank. Prior to collecting measurements a thermal steady state, hydrodynamic steady state, and test meter output steady state are obtained. After all steady states are found, volume, time, and primary and secondary meter output are measured. K-factor and flowrate measurements are traced to NIST through an unbroken chain of comparisons. Comparisons are created annually by calibrating all measurement devices at an accredited laboratory. Traceability is maintained through statistical process control (SPC). Measurement uncertainty is evaluated by an uncertainty analysis. The entire system is validated by a proficiency test.Statistical Process ControlState of control for the calibration system is assessed using SPC. The system is calibrated monthly against a check standard — currently a new NIST traceable gravimetric liquid flow calibration system is being constructed and will replace the current check standard. Check standard calibrations include four points (four flowrates) and five replicates. Measurements are grouped and plotted using control charts. Upper and lower control limits (Eq. 1-6) for subgroup standard deviation, and subgroup averages are calculated from Shewhart’s control limit factors [3; Table A.5].(3)
(6)Where: • UCL is upper control limit• LCL is lower control limit• CL is control limit• A1 is constant [3; Table A.5]• B3 is constant [3; Table A.5]• B4 is constant [3; Table A.5]• X is control variable• sn is standard deviation of subgroup• Subscripts sn and X refer to control variable and standard deviation of control variable respectively, and bars indicate the average function.Out-of-control subgroups are evaluated using software and condition five is evaluated visually. Given an out-of-control state, assignable cause is identified and system control is established prior to performing further measurements. All instruments are calibrated annually by an NVLAP (National Voluntary Laboratory Accreditation Program).Uncertainty AnalysisLaw of Propagation of Uncertainty [2] was used to determine uncertainty in flowrate and K-factor measurements. The result was second order accurate (Eq. 7).
(12)Where: • t was time s, and Q bar was average volumetric flowrate m3/s.Flowrate uncertainty was determined by taking the appropriate partial derivatives and substituting their result and the dependant variable uncertainty into equation 7 (tables 1 and 2). Uncertainties represented the 67 percent probability interval for a standard normal distribution.ResultsThe greatest uncertainty in flowrate measurement was 0.30 percent (Table 3). Uncertainty of flowrate was most sensitive to uncertainty of test time and uncertainty of secondary meter volume. Test time was maintained at 6.0×101 seconds.Proficiency test results are listed in tables 1 and 3. K-factors measured by Colorado Experimentation and Engineering Station (CEESI, www.ceesi.com) agreed well with those measured by the system described herein. At each flowrate, the 95 percent confidence interval for measurements collected by CEESI was within the 95 percent confidence interval for measurements collected by SeaMetrics.
