Seven Basic Quality Control Tools HISTOGRAM TOOL

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1 Frequency Frequency Seven Basic Quality Control Tools HISTOGRAM TOOL QUALITY TOOLS Histogram Description of Histogram: The frequency histogram (or distribution) is a statistical tool for presenting numerous data in a form that makes clearer the central tendency and the dispersion along the scale of measurement, as well as the relative frequency of occurrence of the various values. A histogram is a summary of variation in a set of data with its frequency distribution graphically presented in a bar form. They are: (1) Frequency column graphs (fig.1) that displays a static picture of process behavior. Histogram requires a minimum of data points. (2) A histogram is characterized by the number of data points that fall within a given bar or interval. This is commonly referred to as frequency. (3) A stable process is characterized by a histogram exhibiting bell-shaped curves. A stable process is predictable. See fig. 2 below Four concepts related to variation in a set of data underlie the usefulness of the histogram: (1) values in a set of data almost always show variation, (2) variation displays a pattern, (3) patterns of variation are difficult to see in simple numerical tables, and (4) patterns of variation are easier to see when the data are summarized pictorially in a histogram. Analysis consists of identifying and classifying the pattern of variation displayed by the histogram (such as the shape, the location of the center, or the spread of the data from the center) and relating what is known about the characteristic pattern to the physical conditions under which the data were created to explain what might have given rise to the pattern in those conditions. Fig. 3 illustrates some common patterns. Fig. 1 Fig. 2 Column Graph Normal distribution - Bell shaped curve Interval Interval Page 1 of 6 9/10/2012

2 Fig. 3 Pattern/Shapes of histograms Bell shaped curve natural, expected, normal Double-peaked two distinct processes Negatively skewed practical or specification Positively skewed - practical or specification Truncated- forced removal inspection limit Isolated - peaked. Two processes inefficient inspection. Page 2 of 6 9/10/2012

3 Fig. 4 Location of histogram compared to customer requirement: USL CL LSL Process running low Process is centered Process is running high Fig. 5 Histogram spread/variability: USL LSL Variability/Process spread too wide Variability/spread meets customer requirement Variability is well within customer requirement. Page 3 of 6 9/10/2012

4 When to use a Histogram: The Histogram is useful to: Display large amount of data that are difficult to interpret in tabular form Show the relative frequency of occurrence of the various data values Reveal the centering, variation, and shape of the data Illustrates quickly the underlying distribution of the data Provide useful information for predicting future performance of the process Helps answer the question Is the process capable of meeting my customer requirement? How to use a Histogram: Guidelines to creating a histogram includes the following: a) Deciding on the process to measure. b) Gather data. c) Prepare a frequency table from the data. d) Draw a histogram from the frequency table. e) Interpret the histogram Details: 1) Determine applicability of Histogram. 2) Gather a minimum of variable data points of interest 3) Generate frequency table from available data step, n=150; Steps 4 to 8. 4) Calculate the range. R= Max Min = 1.9 5) Calculate the number of interval, k = 150 =12. Or refer to table of reference. 6) Calculate the interval width, H= R/k= 1.9/12= 0.15 or round to nearest convenient number= ) Calculate the class interval beginning from the smallest value X and add the interval width The end of the interval will be x+0.19 not Next interval begins at x+0.20 and so on until the kth interval. 8) Complete a frequency table. 9) Generate histogram from table. Plot your graph of frequency vs. interval. 10) Draw conclusions from your chart. Pay attention to shape location and dispersion previously discussed above. Characteristics of a normally distributed process: Most of the points (data) are near the centerline, or average The centerline divides the curve into two symmetrical halves Some of the points approach the minimum and maximum values The normal histogram exhibits a bell-shaped distribution Very few points are outside the bell-shaped curve Variation inside the bell curve is chance or natural variation. Other variation is due to special or assignable causes. Page 4 of 6 9/10/2012

5 If the base of a histogram is divided into 6 equal lengths, (three on each side of the average), the amount of data in each interval exhibits the following percentages: 68.26% 95.46% 99.73% µ-3σ µ-2σ µ-1σ µ µ+1σ µ+2σ µ+3σ Fig. 6 Normal distribution Tips on use of Histogram: A histogram will provide useful information on how well your distribution is centered compared to your specification/customer requirement. It is a useful tool to help determine variability of a process or product. However, it does not tell if your process is in control. You will need a control chart for that. A number of software are available to quickly and effectively generate a histogram. They include Minitab, QI macro etc. Application of Histogram: Histograms are applied during data analysis, process or product improvement activities. This applies not only to the manufacturing sector, but to other industries where frequency distribution of variable data analysis is required. See below for sample of a completed histogram Page 5 of 6 9/10/2012

6 Fig. 6 Histogram References: Juran Quality Handbook Fifth Edition: Joseph M Juran; A. Blanton Godfrey Juran Quality Handbook Sixth Edition: Joseph M Juran; Joseph A. De Feo The Memory Jogger II First edition Michael Brassard & Diane Ritter CQE Primer Sixth Edition - Quality Council of Indiana Page 6 of 6 9/10/2012