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Six Sigma Material
Measurement System Analysis
Measurement Data
Professional Management calls for taking decisions based on facts, as expressed in terms of dataThe decision to adjust a process or not, is based on the measured values of the output characteristicBenefits of using data based procedures largely depends on the Quality of the measurement dataThe Quality of the measurement data is related to the Statistical properties of multiple measurements from a measurement systemIf all the measurements are close to a master value, the Quality of data is said to be highIf, instead, measurements are away from the master value, the Quality of the data is low.
Measurement System
A measurement system consists of Measuring instrument(s)AccessoriesInspectorEnvironmental conditionsMeasured part
Measurement Process
Measurement can be considered as a process, similar to a manufacturing processMeasurement is the assignment of numbers to material things to represent the relations among them with respect to particular properties.
The parameters of the measurement process are Input:Component to be measuredProcess factors:Equipment, Inspector, etc.Output:Measured value
Thus, we can compare the measurement process to a manufacturing process.
Manufacturing processMeasurement ProcessManufacturing equipment / machineInspection equipmentMachine accessoriesInspection accessoriesOperatorInspectorRaw materialComponent to be measuredProduct outputMeasured value of the characteristic
Statistical Properties of Measurement System
An ideal measurement system will produce only measurements that will always agree with a master value, when repeat measurements are taken in an item.Such a measurement system will have the statistical properties of ZERO variance and ZERO bias.Such systems have Zero probability of mis-classifying the items it measured.Measurement systems with such properties seldom exist.Measurement systems have variations.They do not necessarily provide the same numbers even if repeat measurements on the same part are taken.It is necessary to recognize this variation and to provide systems in such a way that this variation is within the required capability of the measurement system.
Measurement System Requirements
Measurement system must be in a state of Statistical Control.The variation in the measurement system should be due to common causes only.No special causes of variations should be present in a measurement system.Variability of the measurement system must be small compared to manufacturing process variability.Measurement system variability must be small compared to the specification tolerance.
Measurement System Requirements
The increments of measurement must be small relative to the smaller of either the process variability or the specification limits.A common rule of thumb is for the increments to be no greater than one-tenth of the smaller of either the process variability or the specification limits.Statistical properties of the measurement system may change as the items being measured vary.The largest variation of the measurement system must be small relative to the smaller of either the process variability or the specification limits.
The Measurement System Errors
Bias (AIAG: Accuracy)
Repeatability
Reproducibility
Stability
Linearity
Key Measurement Concepts
Bias (Accuracy:AIAG)
The difference between the observed average of measurement sand the reference value.A reference value is the one that is agreed upon for the measured values.A reference value could be determined by averaging several measurements with a higher level measuring equipment.Repeatability
The variation in measurements obtained.With one measuring instrument.When used several times.By one appraiser.While measuring the identical characteristics.On the same part.
ReproducibilityThe variation in the average of measurements made.By different appraisers.Using the same measuring equipment.While measuring the identical characteristics.On the same part.StabilityThe total variation in the measurements obtained with a measurement system.On the same master or parts.When measuring a single characteristic.Over an extended period of time.LinearityThe difference in the bias values.Through the expected operating range of a measuring instrument.
Methods used to determine R & R %1. Average and range method
2. Ford / Chrysler / GM method
3. ANOVA method
Sheet1
Data Sheet
Operator 1Operator 2
Trials/Part1234512345
1217220217214216216216216216220
2216216216212219219216215212220
3216218216212220220220216212220
Average216.3218.0216.3212.7218.3218.3217.3215.7213.3220.0
Range1.04.01.02.04.04.04.01.04.00.0
Sheet2
Sheet3
Repeatability: (Gauge Variation)Fixing all other parameters at some level. Take repeated readings. The variation in the repeat values can be assumed to be due to the gauge.
To ensure that Ris are reliable, we use R-chart, to check the stability of Ris.
Repeatability: (Gauge Variation)Measures of variation
Range (max-min)Standard deviation (s)
d2 is a constant depends on the sample size.
Reproducibility: (Operator Variation)
Part-to-Part Variation: (Due to process chance causes)
1.If
then, the measurement system is satisfactory.
In practice, we want this.
Ideally, we want
2.Use -chart to compare (1) pictorially. If all of the points get plotted inside the control limits, we infer that the gauge variation is much larger than the process variation.
Sheet1
Table 1. Data Sheet
Operator 1Operator 2
Trials/Part1234512345
1217220217214216216216216216220
2216216216212219219216215212220
3216218216212220220220216212220
Average216.3218.0216.3212.7218.3218.3217.3215.7213.3220.0
Range1.04.01.02.04.04.04.01.04.00.0
Sheet2
m
23456789101112131415
g11.411.912.242.482.672.832.963.083.183.273.353.423.493.55
21.281.812.152.402.602.772.913.023.133.223.303.383.453.51
31.231.772.122.382.582.752.893.013.113.213.293.373.433.50
41.211.752.112.372.572.742.883.003.103.203.283.363.433.49
51.191.742.102.362.562.732.872.993.103.193.283.353.423.49
61.181.732.092.352.562.732.872.993.103.193.273.353.423.49
71.171.732.092.352.552.722.872.993.103.193.273.353.423.48
81.171.722.082.352.552.722.872.983.093.193.273.353.423.48
91.161.722.082.342.552.722.862.983.093.183.273.353.423.48
101.161.722.082.342.552.722.862.983.093.183.273.343.423.48
111.161.712.082.342.552.722.862.983.093.183.273.343.413.48
121.151.712.072.342.552.722.852.983.093.183.273.343.413.48
131.151.712.072.342.552.712.852.983.093.183.273.343.413.48
141.151.712.072.342.542.712.852.983.083.183.273.343.413.48
151.151.712.072.342.542.712.852.983.083.183.263.343.413.48
>151.1282.0592.5342.8473.0783.2583.407
1.6932.3262.7042.9703.1733.3363.472
Sheet3
Gage Repeatability & Reproducibility Study (Gage R&R Study)
For variable measuring equipment
Initial considerations
Use the engineering judgement to assess the variation factorsCritical dimensions require more parts and/or trials (repeat measurements)Bulky/heavy parts may dictate fewer samples and more trialsAppraisers should be selected from those who normally operate the instrument
Gage Repeatability & Reproducibility StudyGage R&R Study)
For variable measuring equipment
Initial considerations (Contd)
Sample parts must be selected from the process and they should represent its entire operating rangeInstrument must have a discrimination (resolution) that allows at least one-tenth of the expected process variation of the characteristicThe measurement method is well definedMeasurements should be made in a random order.
Conducting the R&R Study
Select ten parts from the process at random, preferably one part from every days production
Identify them with a serial number, than cannot be observed by the appraisers
Select two or three appraisers, who normally operate the measuring system
Measure the parts randomly so that all the parts are measured by all the appraisers for two or three times (trials)
Record the observations
Conducting the R&R Study
Calculate the variations due to different factors, according to the formulae given
A measurement system with a R&R% of 10% or less is considered good
A measurement system with R&R% more than 30% requires review and is considered not acceptable
A measurement system with R&R% between 10% to 30% may have to be evaluated for acceptance, considering the criticality of the part.
Table for recording R&R study observations
Formulae
Xa-bar, Xb-bar, Xc-bar = Average of all the measurements made by A, B & C, respectivelyRa-bar, Rb-bar, Rc-bar = Average of the range of the trials made on 10 parts by A, B & C, respectivelyRp = Maximum part average Minimum part averageR-bar = (Ra-bar + Rb-bar + Rc-bar) / No. of operatorsX-bar Diff = Max X-bar Min X-barUCLR = R-bar * D4D4 = 3.27 for 2 trials; 2.58 for 3 trialsLCLR = R-bar * D3D3 = 0 for both 2 & 3 trialsHomogenize the data for RangeCalculate R-bar, X-bar Diff and Rp only after homogenizing.
Formulae
Equipment Variation (EV) = R-bar * K1(K1 = 4.56 for 2 trials; 3.05 for 3 trials)Appraiser Variation (AV) = Sqrt{(X-bar Diff * K2)2 [EV2/(nr)]}(K2 = 3.65 for 2 operators; 2.70 for 3 operators)(n : No. of parts; r : No. of trials)Repeatability & Reproducibility (R&R) = Sqrt{EV2 + AV2}
Formulae
Part Variation (PV) = Rp * K3Total Variation (TV) = SQRT{R&R2 + PV2}
nK3NK3NK323.6552.0881.7432.7061.9391.6742.3071.82101.62
Formulae
% EV= (EV / TV) * 100% AV=(AV / TV) * 100% R&R= (R&R / TV) * 100% PV= (PV / TV) * 100
This material was complied at Indian Statistical Institute, Chennai. MSA manual of AIAG was used as a source.