1、How is this done?First, we have to know when the parts we make are good. Thats why there are specifications. If the part is within specifications, its good. If it is not, the part is bad. If it is bad, then it is too late. When the specification cannot be met we are back to working hard again.Second
2、, we need a way of telling when our parts are just beginning to get badlong before they become “out of specification” that is when something can be done about it.The first way can be done with inspection. The second way can be done with SPC.WHAT DOES NORMAL MEAN?To know when our parts are getting ba
3、d, we need to know what they look like when they are good. Most of the time our parts are good, otherwise they would never be accepted, and we wouldnt be in business.Of course, they are not all the same. Like the vegetables and bowling scores, and golf scores, they 1_ from part to part. Some may be
4、very large. Some may be very small. But for the most part, they are somewhere in the middle. This is the way things normally are. The things may be cucumbers, tomatoes, watermelons, rivets, mens heights, car speeds, bolts, car doors, voltages, or anything that can be measured.When the farmer grouped
5、 his vegetables by weight, he found the same thing. He found a pattern, a normal pattern. This kind of pattern is called the Normal Curve.THE NORMAL CURVE WHAT IS IT?We have learned that all things vary. There is 2_ in the world. The pattern of variation we usually see is called the 3_ _.The farmer
6、arranged his vegetables by weight. The farmer distributed his vegetables by weight. When he looked at the pattern of weights, he found they were normally distributed. He found they were 4_ according to the 5_ _.This is the way we talk about how things vary. Usually things vary according to a Normal
7、Distribution.Normal Distributions have certain features. Look at the curve. Can you tell what some of them are? We already know one. Most of the things are in the middle. There are fewer and fewer things as you go away from the middle. Way our at the ends there are very few.What else do you see? It
8、looks balanced, doesnt it? The right side of the curve looks like the left, only reversed. Loot at the curve to the left of the triangles. Suppose you cut the paper at the triangles and held it to a mirror. In the mirror it would look like the curve on the right side of the triangle. The right side
9、is the mirror image of the left side. In different words, we say the Normal Distribution is symmetric. The right side of the curve is the 6_ _. The curves kind of looks like a bell. It has a single peak at the middle. The two ends tail out like the bells rim. There are the most number of things at a
10、nd around the peak. And the curve is 7_ about the middle.Lets use all these technical terms to describe the Normal Distribution. It is bell-shaped, symmetric curve. If things vary in the usual way, we can show it by the normal curve. In a normal distribution things vary in a certain way. There will
11、be more thins in the 8_ than at the 9_. The curve will be 10_ about the middle, and the curve will be 11_-shaped.AVERAGESThe normal distribution has an average. It is right in the middle of the curve. The average is defined in a very exact way in statistics. We dont want to be fuzzy or vague when we
12、 talk about our numbers.How doe you get the average? First, look at the things you are interested in. Lets say bolts. Second, you measure them, weigh them, measure the width or length, or even count the number of threads. You may do any number of things. But, up come up with a number. You do this a
13、few time, lets say you measure five bolts. Add up the number of the five measurements. The answer you get is called the sum. Finally, divide the sum by the total number of readings, or five in this example. There isnt much to it.The average is an extremely useful tool in statistics. When most people
14、 think of average, they think of ordinary, normal, usual, everyday, common. You use it every day. You say, “He is of average height,” or “She has an average weight” or “They are average bowlers.”The most important part of the average is that it shows us what things look like in one number. It puts a
15、ll the numbers into one number. Lets look at an example. Lets use the bowling scores we saw at the beginning.Our bowler bowled five games. The number of pins he knocked down were: 129, 141, 135, 148, and 137. What is the average?Step 1: Add up the five scores.129141135148137690The answer 690 is call
16、ed the sum.Step 2: Divide the sum by five.690 I 5 = 138The average tells you what each score would be if all the scores were the same.138To find the average first we 12_ all the numbers. This gives us the 13_. In the second step we 14_ the sum by the number of scores. If we have five scores, we firs
17、t 15_ the five scores together. Second we divide the sum by 16_. Lets try another example.Lets use the golf scores we say in the beginning. Our golfer shot: 98, 91, 96, 89, and 94. What is the average of these scores?9891968994 468The first thing we have to do is add all the numbers. This is called
18、the sum and it equals to 468. The next thing we have to do is divide 468 by 5.Lets do this in a different way this time. Its very easy to divide by 5 if you know a little trick. Here it is. Take the sum and double it: 468 + 468 = 936. To get the average, move the decimal point on place to the left.
19、The answer is 93.6, it is that easy.Much of the work in SPC deals with finding the average of 5 numbers. Most people find this is an easy way to divide by 5.Suppose we fined the average of these numbers: 1, 8, 7, 6, and 2. The first thing we do is find the sum. The sum is 17_. Next we 18_ the sum by
20、 2. The answer is 19_. Now we move the decimal point one place to the 20_. The average is 21_. Use this way of dividing by 5. It will make arithmetic a lot easier.USING THE NORMAL CURVELets go back to the normal curve. It has an average. The average tells you what each measurement would be if all th
21、e measurements were the same. Its where all the measurements are balanced. The average puts all the numbers into one number.A manufacturing company can make a lot of parts. It is impossible to inspect every part. If we cannot inspect them all, how do we know if the parts are good?Using the normal cu
22、rve, we can tell what all the parts look like by looking at only a few parts.A manufacturer makes internally threaded hardware, nuts. An employee by the name of John just made 500,000 of them. Several things had to be controlled. Each nut had to have the right height, width, threads, etc. Every nut
23、is slightly different. Johns boss told him that he wanted to know how many of the nuts had a height of .207 inches. John started to measure the 500,000 nuts. He measured the first 100 and grouped them by size. The varied (were distributed like this:John could measure a part quickly. He could measure
24、 a part in only 15 seconds. To measure 100 parts, he took only 1,500 seconds, or 25 minutes. He thought he was doing a good job. When his boss came by, he asked if John was done yet. John said, “Listen, you havent given me enough time. If I do 100 parts in 25 minutes, I should be done in about a yea
25、r!” Johns boss was none too bright. John was glad his boss only wanted the heights checked. “Well, keep on going, John. Measure 200 bolts this time. We need to know as soon as possible.” So, John measured 200 parts and arranged them by size. The were distributed like this:.206John began to notice so
26、mething. Both groups of nut measurements had patterns that looked the same. The measurements were a little different, but the patterns were alike. They both looked like the normal curve.Now John knew something about the normal curve. He also knew something about averages. He found the averages for t
27、he two groups of nut heights. Give or take .0001 inches, he found each average was .206. When he looked at the two distributions he noticed each average was right in the middle. There were fewer and fewer measurements toward the ends, very few above .208, and very few below .204. The distributions w
28、ere symmetric and they looked bell-shaped. If John was correct in thinking his measurements were normally distributed, where should the average of .206 go one the normal curve?In the middle.As you know there is 22_ in all parts you make. When you arrange the measurements you take, usually they will be distributed according to the 23_ _. The normal curve or normal distribution is symmetric. That means the right side of the curve is the 24_ _ of the left. The curve has the shape of a 25_. More measurements occur in the 26_ than at the ends. The s
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