SPCChapter 7.docx

1、SPCChapter 7Statistics at WorkHARD WORK AND BAD PARTSWe all work hard. We work harder when things are going badly. When things are going well, our work seems a lot easier. We all want things easier.The same is true for the parts our company makes. When parts are bad, we get in trouble, the company l

2、oses money, we get paid less, our family complains, life becomes difficult. Bad parts make hard work.SPC on the other hand make good parts easy.MAKING GOOD PARTS BETTERHow 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 s

3、pecifications, 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, we need a way of telling when our parts are just beginning to get badlong before they become “out of specification” that is when s

4、omething 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 bad, 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 accept

5、ed, 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 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. Th

6、e 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 his vegetables by weight, he found the same thing. He found a pattern, a normal pattern. This kind of pattern is called the Normal

7、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 arranged his vegetables by weight. The farmer distributed his vegetables by weight. When he looked at the pattern of weights, he fou

8、nd 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 Distribution.Normal Distributions have certain features. Look at the curve. Can you tell what some of them are? We already know one.

9、 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 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 tria

10、ngles. 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 is the mirror image of the left side. In different words, we say the Normal Distribution is symmetric. The right side of the curve i

11、s the 6_ _.What else do you see? 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 and around the peak. And the curve is 7_ about the middle.Lets use all these technical terms to describe the Nor

12、mal 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 be more thins in the 8_ than at the 9_. The curve will be 10_ about the middle, and the curve will be 11_-shape

13、d.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 talk about our numbers.How doe you get the average? First, look at the things you are interested in. Lets say

14、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 few time, lets say you measure five bolts. Add up the number of the five measurements. The answer you get is ca

15、lled 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 think of average, they think of ordinary, normal, usual, everyday, common. You use it every day. You say, “He

16、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 all the numbers into one number. Lets look at an example. Lets use the bowling scores we saw at the beginning.Ou

17、r 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 called the sum.Step 2: Divide the sum by five.690 I 5 = 138The average tells you what each score would be if all th

18、e scores were the same.138138138138138690To 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 first 15_ the five scores together. Second we divide the sum by 16_. Lets try another example.Lets u

19、se 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 the sum and it equals to 468. The next thing we have to do is divide 468 by 5.Lets do this in a

20、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. The answer is 93.6, it is that easy.Much of the work in SPC deals with finding the average of 5

21、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 2. The answer is 19_. Now we move the decimal point one place to the 20_. The average is 21_. U

22、se 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 the measurements were the same. Its where all the measurements are balanced. The average puts all

23、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 curve, we can tell what all the parts look like by looking at only a few parts.A manufacturer make

24、s 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 is slightly different. Johns boss told him that he wanted to know how many of the nuts had a hei

25、ght 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 a part in only 15 seconds. To measure 100 parts, he took only 1,500 seconds, or 25 minutes. He

26、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 year!” Johns boss was none too bright. John was glad his boss only wanted the heights checked. “Wel

27、l, 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 something. Both groups of nut measurements had patterns that looked the same. The measurements wer

28、e 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 the two groups of nut heights. Give or take .0001 inches, he found each average was .206. When he

29、 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 were symmetric and they looked bell-shaped. If John was correct in thinking his measurements were

30、 normally distributed, where should the average of .206 go one the normal curve?In the middle.206As 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