In the manufacturing process of an aluminium piston, the diameter (measured at a particular height) is a key characteristic. A project is planned to determine the bias and variability associated with each measurement system, that measures the diameter. First step involves measurement of sample piston diameter and comparing it to “true value” determined by a precision laboratory. Graphical and statistical analysis are used to determine variability and bias with measurement system, as well as systems consistency with each other.
We are interested in bias and variability in the measurement systems. The units are a single measurement on a piston. The target process is the act of making a measurement on any piston with a particular gauge. The response variate is the measurement error associated with each unit. The attributes of interest are the average error, variability from “true value”, and the population standard deviation of the errors. Measurement systems consistency with each other can be determined by plotting the data (from each system) on a scattered plot. If the measurement systems are consistent, then the shape of distribution will be similar (interms of spread, and mean).
To determine bias and variability we must measure pistons with known diameter. It was suggested to obtain piston samples over several shifts, in order to expand study population. The advantage of taking measurements from samples collected from different shifts will result in reduced study error if the bias and variability of the measurement system change as other explanatory variates change over time. However, the disadvantage is that it adds time and cost related to the study.
It was also suggested to move OP270 gauges to final gauge environment so that all three gauges would be at the same temperature. This is suggestion ensures that all gauges are working under same conditions, however, there is a measurement error associated with temperature in this study (each change of 1° C increases the size of piston by about 0.75 microns). Hence if temperature at final gauge environment contributes to variability, it will be ignored and will not accounted in the study. One sampling protocol proposed is to measure 1 piston 10 times on each gauge over as short a time period as possible. This is a good protocol, since we are measuring the bias and variability of measuring systems and not that of manufacturing process. Measuring one piston repeatedly eliminates other variates (such as dimensional variations arising from manufacturing processes) and focuses on the accuracy of the measuring system. The advantage of spreading out the study time period is that the results will be accurate and take into account variates such as temperature, gauge callibration (position), surface condition of pistons etc. On the other hand, the disadvantage in spreading out the time period is that it contributes to production delay, and cost (time and money) of study.
In the final plan, three pistons with known values were measured on each gauge twice per shift for 5 shifts. The gauges were calibrated with their normal frequency at the start of each shift.
The data from the study can be summarised as:
The estimate of the bias for each part (from each measurement system are:
Estimated standard deviation of a process is:
sm (OP270A) = 0.74
sm (OP270B) = 0.65
sm (Final) = 0.41
The bias appears to be small on piston 2 in process OP270A, but is high in magnitude on both piston 1 and 3. Where as in process OP270B bias is high on piston 1 and 2, but relatively low on piston 3. In Final process bias is low on piston 1 and 2 but high on piston 3. There is no relation of bias on part size to a measuring system. We use Gaussian model to interpret variability. If we repeatedly measure the same diameter, we would expect the to see the results vary by about ± 2s, i.e. 1.48 (OP270A), 1.3 (OP270B), and 0.82 (Final). Since about 95% of the time, a gaussian random variable will be with in 2 standard deviation of its mean. The graphical results show that overall Final measurement system gave out results that were closest to “true value” on all 3 pistons. System OP270A produced results closer to known value on piston 1 and 2, where as System OP270B produced results closer to known value on piston 2 and 3.
The conclusion of this study may be limited because we have carried out the study on three parts twice per shift for five shifts only. Hence the conclusion may not apply to all future measurements. In addition, the fact that measurements were taken only twice per shift might be misleading if something special was happening at that time.
From the results of this study it is recommended to repeat the study with more than three pistons of known values. It is also recommended to extend the time frame for taking measurements.