Alumno

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 morea 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 anundesirable 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 thelargest 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 standarddeviation 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 a total 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 thesample 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 theletter “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 your process is consistent.

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