| An important aspect of total quality is the identification | | | | class. Continue in this way until you have drawn in all |
| and control of all the sources of variation so that | | | | the classes. |
| processes produce essentially the same result again | | | | 10. Draw a vertical dotted line through your histogram |
| and again. A histogram is a tool that allows you to | | | | to represent the mean value of all your data points. |
| understand at a glance the variation that exists in a | | | | 11. If there are specification limits for the characteristic |
| process. Although the histogram is essentially a bar | | | | you are studying, indicate them as vertical lines as well. |
| chart, it creates a "lumpy distribution curve" that can be | | | | 12. Title and label your histogram. |
| used to help identify and eliminate the causes of | | | | Now what? |
| process variation. Histograms are especially useful in | | | | The shape that your histogram takes tells a lot about |
| the measure, analyze and control phases of the Lean | | | | your process. Often, it will tell you to dig deeper for |
| Six Sigma methodology. | | | | otherwise unseen causes of variation. |
| What can it do for you? | | | | The symmetrical or bell-shaped type of histogram: The |
| A histogram will show you the central value of a | | | | mean value is in the middle of the range of data. The |
| characteristic produced by your process, and the | | | | frequency is high in the middle of the range and falls |
| shape and size of the dispersion on either side of this | | | | off fairly evenly to the right and left. This shape occurs |
| central value. The shape and size of the dispersion will | | | | most often. |
| help identify otherwise hidden sources of variation. The | | | | The "comb" or multi-modal type of histogram: Adjacent |
| data used to produce a histogram can ultimately be | | | | classes alternate higher and lower in frequency. This |
| used to determine the capability of a process to | | | | usually indicates a data collection problem. The problem |
| produce output that consistently falls within | | | | may lie in how a characteristic was measured or how |
| specification limits. | | | | values were rounded. It could also indicate an error in |
| How do you do it? | | | | the calculation of class boundaries. |
| 1. Decide which Critical-To-Quality characteristic you | | | | If the distribution of frequencies is shifted noticeably to |
| wish to examine. This CTQ must be measurable on a | | | | either side of the center of the range, the distribution is |
| linear scale. That is, the incremental value between | | | | said to be skewed. When the histogram is positively |
| units of measurement must be the same. For example, | | | | skewed. The mean value is to the left of the center of |
| a micrometer or a thermometer or a stopwatch can | | | | the range, and the frequency decreases abruptly to |
| produce linear data. Asking your customers to rate | | | | the left but gently to the right. This shape normally |
| your performance from "poor" to "excellent" on a | | | | occurs when the lower limit, the one on the Left, is |
| five-point scale probably will not. | | | | controlled either by specification or because values |
| 2. Measure the characteristic and record the results. If | | | | lower than a certain value do not occur for some |
| the characteristic is continually being produced-such as | | | | other reason. |
| voltage in a line or temperature in an oven, or if there | | | | If the skewness of the distribution is even more |
| are too many items being produced to measure all of | | | | extreme, a clearly asymmetrical, precipice-type |
| them, you will have to sample. Take care to ensure | | | | histogram is the result. This shape frequently occurs |
| that your sampling is random. | | | | when a 100% screening is being done for one |
| 3. Count the number of individual data points. Add the | | | | specification limit. |
| values for each of the data points and divide by the | | | | If the classes in the center of the distribution have |
| number of points. This is the mean (or average) value. | | | | more or less the same frequency, the resulting |
| 4. Determine the highest data value and the lowest | | | | histogram looks like a plateau. This shape occurs when |
| data value. Subtract the lower number from the higher. | | | | there is a mixture of two distributions with different |
| This is the range. | | | | mean values blended together. Look for ways to |
| 5. The next step is determining how many "classes" or | | | | stratify the data to separate the two distributions. You |
| bars your histogram should have. | | | | can then produce two separate histograms to more |
| To make an initial determination, you can use this table: | | | | accurately depict what is going on in the process. |
| Number of data points Number of classesunder 50 5 | | | | If two distributions with widely different means are |
| to 7 | | | | combined in one data set, the plateau splits to become |
| 50 to 100 6 to 10 | | | | twin peaks. The two separate distributions become |
| 100 to 250 7 to 12over 250 10 to 20 | | | | much more evident than with the plateau. Examining |
| 6. Divide the range by the trial number of classes you | | | | the data to identify the two different distributions will |
| selected. The resulting number will be your trial class | | | | help you understand how variation is entering the |
| interval (the horizontal graduation or width) for each | | | | process. |
| bar on your chart. You may round or simplify this | | | | If there is a small, essentially disconnected peak along |
| number to make it easier to work with, but the total | | | | with a normal, symmetrical peak, this is called an |
| number of classes should be within those shown | | | | isolated-peak histogram. It occurs when there is a small |
| above. In determining the number of classes and the | | | | amount of data from a different distribution included in |
| class interval, consider how you are measuring data. | | | | the data set. This could also represent a short-term |
| Increase or decrease the number of classes or modify | | | | process abnormality, a measurement error or a data |
| the class interval until there is essentially the same | | | | collection problem. |
| number of measurement possibilities in each class. | | | | If specification limits are involved in your process, the |
| 7. Determine the class boundaries. You can do this by | | | | histogram is an especially valuable indicator for |
| starting at the center of the range. If you have an odd | | | | corrective action. The histogram shows that the |
| number of classes, center the middle class | | | | process is centered between the limits with a good |
| approximately at the mid-point of the range, then | | | | margin on either side. Maintaining the process is all that |
| alternately add or subtract the class interval to define | | | | is needed. |
| the other class boundaries. If you have an even | | | | When the process is centered but with no margin, It is |
| number of classes, begin the process of adding or | | | | a good idea to work at reducing the variation in the |
| subtracting the class interval at approximately the | | | | process since even a slight shift in the process center |
| center of the range. | | | | will produce defective material. |
| 8. Tally the number of data points that fall in each of | | | | A process that would have produced material within |
| the classes. Add the frequency totals for each class. | | | | specification limits if it were centered is shifted to the |
| This number should equal the total number of data | | | | left. Action must be taken to bring the mean closer to |
| points. Divide the number of data points in each class | | | | the center of the specification limits. A histogram that |
| by the total number of data points. This will give you | | | | shows a process that has too much variation to meet |
| the percentage of points falling in each class. Add the | | | | specifications no matter how it is centered. Action |
| percentages of all the classes. The result should be | | | | must be taken to reduce variation in this process. |
| approximately 100. | | | | A process that is both shifted, in this case to the right, |
| 9. Graph the results by beginning with the lowest | | | | and has too much variation. Action is necessary to |
| measurement-value class. Make the bar height | | | | both center the process and reduce variation. This is a |
| correspond to the percentage of data points that fall in | | | | picture of the statistical variation in your process. Not |
| that class. Draw the bar for the second class to the | | | | only can histograms help you know which processes |
| right and touching the first bar. Again, make the height | | | | need improvement, they can also help you track that |
| correspond to the percentage of data points in that | | | | improvement. |