1. Frequency Plots Sector Enterprise Quality Northrop Grumman Corporation Integrated Systems CA/PA-RCA : Basic Tool

2. 2 Why use frequency plots  Summarizes data from a process and graphically presents the frequency distribution in bar form  Helps to answer the question whether the process is capable of meeting customer requirements

3. 3 When to use the frequency plots  To display large amounts of data that are difficult to interpret in tabular form  To show the relative frequency of occurrence of the various data values  To reveal the centering, spread and variation of the data  To illustrate quickly the underlying distribution of the data

4. 4 Frequency Plot Features 0 3 2 1 6 5 4 7 8 9 10 4:00 4:054:204:104:154:404:354:304:255:055:004:554:504:45 Height of column indicates how often that data value occurred Target time Label target and/or specifications Overall shape shows how the data is distributed

5. 5 How to construct a frequency plot 1.Decide on the process measure 2.Gather data (at least 50 data points) 3.Prepare a frequency table of the data a.Count the number of data points b.Calculate the range c.Determine the number of class intervals d.Determine the class width e.Construct the frequency table 4.Draw a frequency plot (histogram) of the table 5.Interpret the graph

6. 6 What to look for on a frequency plot  Center of the data  Range of the data  Shape of the distribution  Comparison with target and specification  Any irregularities

7. 7 Common Shapes of Frequency Plots If a frequency plot shows a bell-shaped, symmetric distribution:  Conclude – No special causes indicated but the distribution; data may come from a stable process (Caution: special causes may appear on a time plot or control chart).  Action – Make fundamental changes to improve a stable process (common cause strategy). Bell shaped. Symmetric.

8. 8 Common Shapes of Frequency Plots ( cont’d )  If a frequency plot shows a two- humped, bimodal distribution:  Conclude – What we thought was one process operates like two processes (two sets of operating conditions with two sets of output)  Action – Use stratification or other analysis techniques to seek out causes for two humps; be wary of reacting to a time plot or control chart for data with this distribution Two humps. Bimodal.

9. 9 Common Shapes of Frequency Plots ( cont’d )  If a frequency plot shows a long-tailed distribution (is not symmetric):  Conclude – Data may come from a process that is not easily explained with simple mathematical assumptions (like normality). A long-tailed pattern is very common when measuring time or counting problems.  Action – You’ll need to use most data analysis techniques with caution when data has a long-tailed distribution. Some will lead to false conclusions. Long tail. Not symmetric.  For example, the control limit calculations are based on the assumption that the data have a bell-shaped curve. Calculating control limits for data with a long-tailed distribution will likely make you overreact to common cause variation and miss some special causes. Other tests that rely on normality include hypotheses tests, ANOVA, and regression.  To deal with data with this kind of distribution, you may need to transform it.

10. 10 Common Shapes of Frequency Plots ( cont’d )  If a frequency plot shows a basically flat distribution:  Conclude – Process may be “drifting” over time or process may be a mix of many operating conditions.  Action – Use time plots to track over time; look for possible stratifying factors; standardize the process. Basically flat.

11. 11 Common Shapes of Frequency Plots ( cont’d )  If a frequency plot shows one or more outliers:  Conclude – Outlier data points are likely the result of clerical error or something unusual happening in the process.  Action – Confirm outliers are not clerical error; treat like a special cause. One or more outliers.

12. 12 Common Shapes of Frequency Plots ( cont’d )  If a frequency plot shows five or fewer distinct values:  Conclude – Measuring device not sensitive enough or the measurement scale is not fine enough.  Action – Fine tune measurements by recording additional decimal points. Five or fewer distinct values. 4.05.04.56.05.56.57.08.07.5

13. 13 Common Shapes of Frequency Plots ( cont’d )  If a frequency plot shows a large pile-up of data points:  Conclude – A sharp cut-off point occurs if the measurement instrument is incapable of reading across the complete range of data, or when people ignore data that goes beyond a certain limit.  Action – Improve measurement devices. Eliminate fear of reprisals for recording “unacceptable” data. Large pile-up around a minimum or maximum value

14. 14 Common Shapes of Frequency Plots ( cont’d )  If a frequency plot has one value that is extremely common:  Conclude – When one value appears far more commonly than any other value, the measuring instrument may be damaged or hard to read, or the person recording the data may have a subconscious bias.  Action – Check measurement instruments. Check data collection procedures. One value is extremely common

15. 15 Common Shapes of Frequency Plots ( cont’d )  If a frequency plot shows a saw- tooth pattern:  Conclude – When data appear in alternating heights, the recorder may have a subconscious bias for even (or odd) numbers, the measuring instrument may be easier to read at odd or even numbers, or the data values may be rounded incorrectly.  Action – Check measuring instrument and procedures. Saw-tooth pattern

16. 16 Frequency Plots Questions? Call or e-mail: Bob Ollerton 310-332-1972/310-350-9121 robert.ollerton@ngc.com