SPC

SPC consists of the following four basic steps
1. Measuring a production process (which we cover in Chapter 8; see Chapter 7 for information on preparing to measure a process)
2. Making the process consistent by eliminating variability (see the later section “Using Control Charts Effectively”
3. Monitoring the process
4. Improving the process to get as close to the target value — what the customer wants — as possible (see the later section “Calculating Process Capability”

If you connect the values in the histogram with a line, you create a curve, shown in Figure 10-2. The curve is called the normal distribution curve, or the normal curve. The normal curve is an important tool because it graphically
shows the variation in a measured process. The wider the curve, the more a process varies, so, naturally, you want to make your curve as skinny as possible. You also want the average, or middle, part of your curve to be as close as

possible to your customers’ desired value for whatever it is you’re measuring. Keep these goals in mind as you discover more detail about the SPC process in this chapter.

Detecting different types of variation

Common-cause variation: The variation inherent in the process. As long as the process doesn’t change, the common-cause variation stays the same.Common-cause variation is part of the production process for
one or more reasons: because of the nature of the system, the way the process is operated, or the way the process is managed.

Special-cause variation: Occurs when a change takes place in the process. It could be an undesirable change, such as a tool wearing out, or it could a desirable change, such as the implementation of a new machine that has less variation than the previous machine.

Population, sample, mean, and range
Population: The entire group of members.
Sample: A subset of the population.
Mean: The arithmetic average of all the values that you measure for a given test.
Range: From the largest to the smallest.

Standard deviation
Standard deviation is a measure of the range of a variation around the average of a group of measurements. In other words, it’s the average distance that each measurement is from the mean of all the measurements. In Statistical Process Control, the Greek letter sigma refers to the standard deviation of an entire population.

You calculate standard deviation by following these steps

1. Take the difference between each recorded measurement and the
mean to get the deviation for each measurement.
Say you have the following five measurements: 6, 8, 7, 9, and 10. Add the measurements for atotal of 40. Then divide 40 by 5 for a mean of 8. Now take the difference of each of these measurements from the mean
6 – 8 = –2
8 – 8 = 0
7 – 8 = –1
9 – 8 = 1
10 – 8 = 2
So, your differences are –2, 0, –1, 1, and 2.

2. Square each of these differences that you calculated in Step 1.
The squared values are the following:
–22 = 4
02 = 0
–12 = 1
12 = 1
22 = 4

3. Add each of the squared values from Step 2 together.
You have 4 + 0 + 1 + 1 + 4 = 10.

4. Divide the added value from Step 3 by the number of samples minus 1
(known as the sample fudge factor).
Subtract 1 from 5 for a total of 4, and then divide 10 by 4 for a total of 2.5.

5. Take the square root of the value from Step 4.
The square root of 2.5 is 1.58, which is your standard deviation.

For variable data, here are the most commonly used control charts
_ X-bar chart: Tracks the mean of a set of samples over some period of time. X-bar (usually written as the letter “X” with a line over the top) is a statistical notation for the mean. This chart is probably the most commonly
used control chart out there, as you normally want your process mean to equal the customer’s specification.

_ R (Range) chart: Used to track the range of a set of samples over time. In most cases, a low range is good; it indicates that yourprocess is consistent.

For attribute data, here are the most commonly used control charts
_ p chart: The “p” stands for the proportion (or percentage) of the sample that’s defective.
_ np chart: The “np” stands for the number (or count) of defective items in the sample.
_ u chart: The “u” stands for the number of defects per unit in the sample.
_ c chart: The “c” stands for the count of the defects from a sample.

Here are some patterns to look for when evaluating your control chart
_ Seven points in a row on the same side of the line. This applies only to X-bar charts (see the section “Checking out different kinds of control charts” earlier in this chapter). This occurrence is statistically improbable
and should be checked out.
_ Six points in a row steadily increasing or decreasing. This is a good indicator that a tool is wearing out.
_ Fourteen points in a row alternating up and down. This can indicate that two alternating factors are causing results to change, such as alternating operators.
_ Any other unusual pattern that you can’t readily explain.

Zooming in on zones
One common evaluation practice is to divide a control chart into three “zones” to look for patterns. You divide the area between the center line and each control limit into three zones, called A, B, and C:
_ Zone Cis the area between the center line and one sigma from the center line (see the earlier section “Standard deviation” to figure out a particular sigma).
_ Zone B is the area between one and two sigma from the center line.
_ Zone A is the area between two and three sigma from the center line. Here are some patterns to look for within the control chart zones

_ Two out of three points in a row in Zone A or beyond. This pattern could mean that your whole process has shifted; that is, your process has changed in one direction so that now your process mean is different.

_ Four out of five points in a row in Zone B or beyond. Again, this pattern could mean that your whole process has shifted.

_ Fifteen points in a row in Zone C. This pattern could indicate that your process variability has changed. Such change isn’t necessarily a bad thing; it could be an opportunity to tighten your control limits (see the
later section “Changing your control limits”).

If all the data points are close to the center line — not out near the upper or lower control limit — you can conclude that the process is very capable.
_ If you see numerous data points close to the control limits, you can conclude that the process is barely capable.
_ If some data points go beyond the control limits, you can conclude thatthe process isn’t very capable.

Table 10-1 Evaluating Process Capability
Amount of CP Evaluation
CP < 1 The variation in the process exceeds customer specifications; you’re making a large number of defective items.
CP = 1 The process is barely meeting customer specifications; you’re making some defective items.
CP > 1 The variation in the process is less than customer specifications; you’re making few, if any, defective items.
Earlier in this chapter, we calculated the standard deviation of a set of measurements (6, 8, 7, 9, and 10) as 1.58. If the customer has specified an upper specification value of 10 and a lower specification value of 5, you calculate
the CP as follows:
CP = (10 – 5) ÷ (6 1.58) CP = 5 ÷ 9.48 = 0.53
Because your CP of 0.53 is less than 1, the variation in your process exceeds customer specifications; you’re making a large number of defective parts.

The capability index works well if your data points in a control chart are pretty evenly spread above and below the center line. However, if your data points appear more on one side of the center line than the other due to the nature of the process, use the following formula to determine process capability:

(Upper customer specified range – mean) ÷ (3 sigma)
(Mean – lower customer specified range) ÷ (3 sigma)