Evaluating The Ufulness Of Data By Gage Repeatability
凶狠的意思
And Reproducibility
By Keith M. Bower and Michelle E. Touchton
硕士简历Abstract
The u of Gage Repeatability and Reproducibility (Gage R&R) studies is widespread in industry. Such analys allow one to estimate the contribution of variation attributable to the measurement system itlf. If the estimates indicate that the recorded measurements may be unreliable, this may impact all subquent analys, e.g. control charts, capability analys, etc. It is the aim of this paper to address such issues by the u of discussion and an example, and to provide some uful guidelines and insights when using MINITAB .
Gage R&R
We shall consider a measurement process whereby veral operators u a particular gage. As such, we may consider the following:
1. An effect due to the operator (Operator)
2. An effect due to the particular part being measured (Part)
3. An operator by part interaction effect (Op*Part)
4. The precision of the gage (Replication)
The elements that contribute to the reproducibility piece of “R&R” are the Operator and Op*Part effects. The two-way random effects ANOVA model that will be considered for the purpos of such an analysis may take the form:洗礼的意思
Y ijk = µ + Operator i + Part j + (Op*Part) ij + Replication k(ij), i = 1,2,…,a; j = 1,2,…,b; k = 1,2,…,n
and the variance components may be reprented by the identity:
σ2y = σ2Operator+ σ2Part + σ2Op*Part + σ2
The operators and parts are considered to be random factors. Certain practitioners choo some parts for the study that fall in the extremes of recorded measurements, possibly including some outside of the specification limits, in order to obtain a better reprentation of the overall performance of the measuring system.
Example
Consider a manufacturer of fuel injector nozzles who is required to asss a measurement system with an allowable tolerance of 8 microns. It is decided upon to obtain nine nozzles, measured twice by two operators. It is important to randomize the order in
抄股which the operators measure the parts each time. As is discusd by Montgomery and Runger1 (1993), one would be advid in practice to perform fewer replications on more parts than vice-versa. In the ca of destructive testing, one would u the Nested Gage R&R functionality in MINITAB Relea 13.
女生外貌描写As is shown in Figure 1, u is made of the Gage R&R Study (Crosd) since each operator measures each part. With the ANOVA output corresponding to the full model, we are unable to reject the null hypothesis that the operator by part interaction effect is equal to zero, even at the α = 0.1 level. By default, if the p-value for this effect is greater than 0.25, MINITAB will include this term into the error, and repeat the ANOVA computations.
Figure 1
狗肉炖什么好吃1 Montgomery, D.C., Runger, G.C. (July 1993). “Gauge Capability and Designed Experiments: Part I: Basic Methods,” Quality Engineering, Vol. 6, No. 1.
踏莎行秦观Figure 2
In Figure 1 we also find that with the reduced model, the part component is statistically significant, as one would desire, and we are unable to reject the null hypothesis that the operator effect is equal to zero at the 5% level. The variance component computations in Figure 2 indicate that less than 1% of the total variation is due to Gage R&R.
Frequently, practitioners investigate the relationship between allowable tolerances, and/or the Study Variation with the Total Gage R&R computations. As is shown in Figure 2, the process variation ud is defined as 5.15 times σtotal , where σtotal = gage 2product 2σσ+, hence the estimate of this is ud in comparison with 5.15 times the Total Gage R&R (0.55626/6.20424) = 8.97% and with the Tolerance (0.55626/8) = 6.95%. The number of distinct categories indicates how many parate groups of parts the measurement system may be able to distinguish. For example, if the number of distinct categories is two, the process may only distinguish parts by placing into high and low groupings. With 16 distinct categories, the system may be considered very capable of distinguishing between parts. The AIAG 2 states that the “number of categories must be five, and preferably more, for the measurement system to be acceptable…” Under AIAG guidelines, this measurement system would be deemed acceptable.
The graphical output in Figure 3 illustrates how most of the variation is due to the part-to-part component, as one would desire. The R-chart shows that the operators recorded the values for each part with a similar amount of variability, with the Xbar chart indicating an 2 Automotive Industry Action Group (June 1998). Measurement Systems Analysis
out-of-control situation, as one would hope, emphasizing the discriminating power of the instrument.
研学课程The average values on all parts measured (twice) by the two operators are reprented in the “by operator” graph, and indicates that the overall means recorded by both operators are similar. The operator by nozzle interaction effect exhibits parallelism, reflected in the statistically insignificant term being removed from the model.
Figure 3
Conclusion
Obtaining data of high quality is imperative for correct analysis. The u of Gage R&R is a uful component in a measurement system analysis program. Through the u of the ANOVA methodology, along with uful graphs, such insights may be obtained.
Keith M. Bower, M.S. is a Technical Training Specialist with Minitab Inc. His main interests are in continuous quality improvement techniques, especially control charting, as well as business and healthcare statistical methodologies. Keith is a member of the American Society for Quality, the American Statistical Association and the International Society of Six Sigma Professionals.
Michelle E. Touchton, B.S. is a Customer Support Specialist with Minitab Inc. Her interests include statistical quality control methodologies.
