Introduction: Statistical Process Control for Capacitors, Part 2
Welcome to my second capability study to see if capacitors meet their specified tolerance. This time I am looking at 10 uf electrolytic capacitors.
You will need a digital multimeter that can measure capacitance and a bunch of capacitors.
I used thirty of these capacitors from Adafruit: https://www.adafruit.com/products/2195
I could not determine who made these capacitors, the datasheet is in Japanese. Adafruit says the tolerance is +/-20%.
For more information on statistical process control and capability studies on more electronic components please check out my SPC collection:
Step 1: Statistical Process Control
To understand SPC it is necessary to understand the following terms:
Nominal is the exact measurement you are trying to achieve. But in reality nothing is ever perfect. There is variation in all processes, the Tolerance sets the limits of how much variation is acceptable. The Lower Specification Limit (LSL) and Upper Specification Limit (USL) are the limits of the tolerance.
The Mean is the arithmetic average of a set of values, or distribution. The Median is the point where half of the values are less and half are more. The Mode is the most common value. In an ideal situation the Nominal, Mean, Median, and the Mode will all be the same.You can get a rough estimate of how consistent your process is running by comparing them.
Process Capability (CP) is the measurement to determine if the process is capable of holding the tolerance allowed. To find the CP first you find the Standard Deviation. The Mean + ( Standard Deviation * 3) gives you the Upper Control Limit (UCL). Next find the Lower Control Limit (LCL), Mean - ( Standard Deviation * 3). The capability is the ratio of the specification limits over the control limits, (CP = (USL - LSL) / (UCL - LCL). If the CP equals one the control limits fit exactly within the specification limits.
You want it to be larger than one to give you some room for error. The reason for using +/- three standard deviations is because in a normal distribution 68.2% of the values will fall within 1 standard deviation. 95.5% will fall within 2 standard deviations, and 99.7% will fall within three. These figures are mathematical constants known as the Empirical Rule. As the amount of variation increases the standard deviation will also increase.
CPK is the measurement of how well centered the Mean is to the Nominal, if they are identical the CPK will equal the CP. More variation between the two in either direction will result in a lower CPK.
The standard of acceptability most widely used in industry is a CPK of 1.3.
The math mentioned here gets complicated, but it is easy to estimate. With a normal distribution over the center half of the tolerance with the mean centered on the nominal your CPK will be approximately 1.3. An even distribution over the center half of the tolerance with the mean centered on the nominal will give you a CPK of approximately 1.1. If the CP and CPK both equal exactly one 99.7% of the parts will be within the tolerance. The other .3% will be bad.
Step 2: Capable and in Control
In this illustration both of the control limits (LCL and UCL, plus and minus three times the standard deviation) are within the specification limits (LSL and USL) meaning the process is capable.
The vertical line represents the nominal specification and the top of the curve represents the process mean.
The mean is well centered on the nominal so the process is said to be in control. CP and CPK are equal.
Step 3: In Control But Not Capable
In this illustration the control limits fall outside the specification limits. The mean is centered on the nominal, but there is too much variation in the process. The process is in control but not capable.
Make an adjustment to decrease the variation it the process.
In this instance the CPK and the CP are equal, and they are both too low.
Step 4: Capable But Out of Control
In this illustration the control limits would fall within the specification limits if the mean was centered on the nominal. The process is capable but out of control.
Make an adjustment to bring the mean in line with the nominal.
Here the CPK is lower than the CP.
The following is the data.
The files are:
- Electrolytics.ods - The data for this study.
- SPC.ods - An empty template you can use for a capability study of your own.
In this study the mean deviated from the nominal more than I expected. But the parts were very consistant so I got a CP of 4.2761, very good. With the CP that good the mean can vary more from the mean and still hold a good CPK. In the case the CPK was 1.4189.
Company: Adafruit Order #: 10 uf electrolytic capacitors USL 12 LSL 8 Sample 1 11.35 2 11.52 3 11.44 4 11.23 5 11.48 6 11.22 7 11.59 8 11.42 9 11.39 10 11.25 11 10.95 12 11.53 13 11.21 14 11.3 15 11.29 16 11.35 17 11.43 18 11.57 19 11.47 20 11.11 21 11.41 22 11.45 23 11.24 24 11.46 25 11.47 26 11.32 27 11.24 28 11.14 29 11.12 30 11.14 Nominal 10.0000 Mean 11.3363 Median 11.3500 Mode 11.1400 CP 4.2761 CPK 1.4189 LSL 8.0000 LCL 10.8686 UCL 11.8041 USL 12.0000 High Sample 11.5900 Low Sample 10.9500