Higher National Certificate in Engineering Unit 36 – LO4.2 Recording Information on Variation

Learning Outcome 4.2 Record information on variation from a process.

Summary of Recording Methods Name Purpose Application Interpretation Ease of Use Tally Provides a quick tally of total quantity and by class interval. Provides visual idea of the distribution shape Used to count defect quantity by type, class and / or category Tally mark concentration and spread roughly indicate distribution shape. Tally mark of five are crossed out as a group for easy counting. Isolated groups of tally marks indicate uneven distribution Very easy to create and interpret

Summary of Recording Methods Name Purpose Application Interpretation Ease of Use Frequency distribution Provides a view of numerical data about location and spread Especially if tally column cells have a large number of marks Concentration of data is seen as a peak and spread of the data is demonstrated by the width of the curve. Thinner distribution indicates less variation. Distribution can be uni-modal (with one peak) bimodal (two peaks) or multimodal (multiple peaks) indicating a mixture of populations. Distribution with no peak and flat curve indicates rectangular distribution Not easy to create but easier to interpret

Summary of Recording Methods Name Purpose Application Interpretation Ease of Use Stem-and leaf plot Provides numerical data information about the contents of the cells in a frequency distribution Useful to quickly identify any repetitive data within the class interval If data values within cells are not fairly evenly distributed, measurement errors or other anomalous conditions may be present Easy to create but difficult to interpret

Summary of Recording Methods Name Purpose Application Interpretation Ease of Use Box-and whisker plot Provides a pictorial view of minimum, maximum, median and interquartile range in one graph Provides more information than distribution plot but easier to interpret. Outliners are easily identified on the graph If the location of the centre line of the box is right in the middle, the data may be normally distributed. If moved to one of the sides, may be skewed. The data points outside the whiskers indicate outliners. Unequal whiskers indicate skewness of the distribution. Easy to create and interpret

Summary of Recording Methods Name Purpose Application Interpretation Ease of Use Scatter diagrams Detects possible correlation or association between two variables or cause and effect Used for root cause analysis, estimation of correlation coefficient, making prediction using a regression line fitted to the data To estimate correlation the relationship has to be linear. Nonlinear relationship may also exist between variables. If plotted data flow upwards left to right, the relationship is positively correlated. If the plotted data flow downward from left to right the relationship is negatively correlated. If data are spread about the centre with no inclination to right or left, there may not be any correlation Easy to create and intepret

Summary of Recording Methods Name Purpose Application Interpretation Ease of Use Run chart Provides a visual indicator of any non-random patterns Used when real-time feedback is required for variables data Patterns like cluster, mixture, trend and oscillation are spotted based on the number of runs above and below mean or median. P value identifies the statistical variance of a non-random pattern. P value less than 0.05 identifies a stronger significance. Easy to create and interpret

Stem-and-leaf plot A stem-and-leaf plot is constructed much like a tally column except that the last digit of the data is recorded instead of the tally mark. This plot is often used when data are grouped. Consider the following…milliwatt power is recorded from a transmission at periodic time intervals…. 10.3, 11.4, 10.9, 9.7, 10.4, 10.6, 10.0, 10.8, 11.1, 11.9, 10.9, 10.8, 11.7, 12.3, 10.6, 12.2, 11.6, 11.2, 10.7, 11.4

Stem-and-leaf plot A histogram for this data would be something like…

Stem-and-leaf plot N = 20 Leaf unit 0.1 Freq Stem Leaf 1 9 7 4 10 034 (7) 6678899 11 1244 5 679 2 12 23

Box plot The box plot (also called box-and-whisker plot) was developed by Professor John Tukey of Princeton University, used high and low values of the data as well as quartiles.

Box plot Outliner – an unusually large or small observation. Values beyond the whiskers are outliners * The upper whisker extends to the highest value within the upper limit. Upper limit = Q3 + 1.5(Q3-Q1) The top of the box is the third quartile (Q3). 75% of the data vales are less than or equal to this value The median (middle) value of the data. Half of the observations are less than or equal to it The bottom of the box is the third quartile (Q1). 25% of the data vales are less than or equal to this value The lower whisker extends to the lowest value within the lower limit.

Box plot Consider the following data collected from tests undertaken on the strength of adhesive bonds… 8.250, 8.085, 8.795, 9.565, 11.880, 9.180, 9.950, 9.630, 8.150 Arranging in ascending order… 8.085, 8.150, 8.250, 8.795, 9.180, 9.565, 9.630, 9.950, 11.880 median = 9.180, Q1 = 8.20 Q3 = 9.97

Box plot 12 11 10 . 9 8

Box plot Approximately symmetric Increased Variability Left Skewed

Period Box plot * 10.0 9.5 * * 9.0 2 3 1 Period