## Introduction: Statistical Process Control for Capacitors, Part 1

Statistical Process Control (SPC) was first used in Japan in the 1970's as a way to measure quality.

I became interested in seeing how well electronic components held the advertised tolerances. In my first instructable about SPC I looked to see if the internal clock on the Atmel Attiny85 microcontroller held the +/- 10% tolerance specified in their datasheet. Next I wrote instructables looking at gold and silver band resistors. This is my fourth instructable where I use SPC to see if electronic components met their specifications. This time I will be looking at capacitors, first 0.1 uF (100nF) ceramic capacitors. Soon I will be doing another study looking at 10 uF electrolytics.

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/753

These capacitors are made by Vishay and the specified tolerance is -20%/+80%. I have no way of knowing if all the parts came from the same lot number or not.

## Step 1:

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.

## Step 5: Capability Study Data

The following is the data.

The files are:

- ceramics.ods - The data for this study.
- SPC.ods - An empty template you can use for a capability study of your own.

.

The high numbers for CP and CPK indicate that the parts are well within tolerance. I was surprised to see the parts were all on the low side. I suspected that the manufacturing process would aim for the center of the tolerance range, at 130 nf. If all the capacitors they make are this good they could change the tolerance to +/-20% and still have a CPK of 1.6,

It appears that my meter reads consistantly, but another possibility is that my meter reads low. I know my meter is accurate for checking resistance, voltage, and frequency, but I am not sure about capacitance.

Statistical Process Control Capability Study Worksheet Company: Vishay Order #: 100nf (.1uf) ceramic capacitors USL 180 LSL 80 Sample 1 91.7 2 93 3 94 4 90.2 5 90.9 6 96.9 7 87.5 8 92.9 9 90.2 10 92.5 11 92.1 12 93.6 13 88.3 14 94 15 91.8 16 92.9 17 91 18 94.7 19 91.3 20 92.3 21 88.6 22 91.2 23 90.2 24 89.8 25 98.3 26 94.3 27 91.7 28 89.6 29 89.4 30 91 Nominal 100.0000 Mean 91.8633 Median 91.7000 Mode 90.2000 CP 6.9580 CPK 5.8257 LSL 80.0000 LCL 84.6774 UCL 99.0493 USL 180.0000

.