Frequency Plots

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

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. 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. 10 9 8 7 6 5 4 3 2 1 0 4:00 4:05 4:10 4:15 4:20 4:25 4:30 4:35 4:40 4:45 4:50 4:55 5:00 5:05 Frequency Plot Features 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. How to construct a frequency plot • Decide on the process measure • Gather data (at least 50 data points) • Prepare a frequency table of the data • Count the number of data points • Calculate the range • Determine the number of class intervals • Determine the class width • Construct the frequency table • Draw a frequency plot (histogram) of the table • Interpret the graph

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. Bell shaped. Symmetric. 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).

8. Two humps. Bimodal. 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

9. Long tail. Not symmetric. 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. • 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. Basicallyflat. 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.

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. 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 Five or fewer distinct values. 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.

13. Large pile-up around a minimum or maximum value 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.

14. One value is extremely common 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.

15. Saw-tooth pattern 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.

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