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- 2. 6. Graphs & Histograms Graphs, either presentational or mathematical are used to allow understanding and analysis of collected data sets. Tools for prioritizing and communicating
- 3. Graphs BAR CHARTS • This is the data set totalled up and shown graphically. • It immediately identifies the major defects for all to see. Defects 0 2 4 6 8 10 12 14 16 Power up Boot up Sink test Case damage Keyboard damage Monitor damaged Bundled s/w included Type Quantity
- 4. Graphs • The below graph shows a factory output for February. This time it shows specific dates which could be analysed. 0 10 20 30 40 50 60 70 80 90 100 01/02/03 02/02/03 03/02/03 04/02/03 05/02/03 06/02/03 07/02/03 08/02/03 09/02/03 10/02/03 11/02/03 12/02/03 13/02/03 14/02/03 15/02/03 16/02/03 17/02/03 18/02/03 19/02/03 20/02/03 21/02/03 22/02/03 23/02/03 24/02/03 25/02/03 26/02/03 27/02/03 28/02/03 Output % Average Feb production output
- 5. Graphs • The graph below shows the major cause for customer complaint, the use of the pie chart and the colours enforce the message. Customer complaints 2007 by qty 20 60 5 15 Product quality Shipped Late Shipped early Shipped wrong goods
- 6. Rules for Graphing • Use Clear titles an indicate when the data was collected • Ensure the scales are clear, understandable and represent the data accurately. • When possible use symbols for extra data. • Always keep in mind the reason why the graph is being used.
- 7. Exercise Graphs • You are the marketing director of XZY automotive, a new Scottish company. You have organised a local survey to rate your car against other small cars. • 30 people were polled and the results are shown below. • Xzy, ka, Clio, Clio, ka, fiesta, xzy, ka, 206, xzy, fiesta, fiesta, xzy, polo, fiesta, 206, 206, polo, 206, fiesta, fiesta, fiesta, polo, xzy, polo, fiesta, xzy, xzy, ka, xzy. • You recognise the power that graphs produce. And you have decided to Graph the results as part of you marketing drive. Explain your choice of graph.
- 8. What is a Histogram? • The Histogram is a graphical representation of data that is a dimensional measurement of one feature.
- 9. What is a Histogram? • This is the computer defect data set totalled up and shown graphically, but is it a histogram? Defects 0 2 4 6 8 10 12 14 16 Power up Sink test Keyboard damage Bundled s/w included Type Quantity Checks/only record failures Total Power up 4 Boot up 15 Sink test 5 Case damage 4 Keyboard damage 0 Monitor damaged 3 Bundled s/w included 7
- 10. What is a Histogram? • The answer to the previous question is NO • The Histogram is a graphical representation of data that, is a dimensional measurement of one feature.
- 11. When is a Histogram Used? • To look at one particular set of results • To check for patterns in a process • To examine large amounts of data
- 12. Histograms • The following data was collected when measuring the bow (warp) of a plastic component. The specification is 0 to 8 x10-3 mm. • At a glance this tells you very little, but it can be plotted as a histogram because we have quantities data with target limits. Bow measurements 2 5 8 8 2 4 6 6 6 4 4 7 6 6 4 8 7 7 5 9
- 13. 0 1 2 3 4 5 6 Thou Frequency Histograms Bin Frequency 0 0 1 0 2 2 3 0 4 4 5 2 6 5 7 3 8 3 9 1 More 0
- 14. What is a Histogram? Exercise • Sort the following data into appropriate sets, then plot them. • The limits are 3 volts ± 0.1 • What can you deduce from this?
- 15. What is a Histogram? Exercise 3.00 2.80 2.85 2.80 2.85 3.00 2.80 2.75 2.65 2.90 2.80 2.85 2.90 2.95 2.85 2.85 2.90 2.85 3.00 2.90 2.85 3.05 2.95 3.05 2.95 2.85 2.95 3.00 2.80 2.85 2.90 2.70 2.85 2.85 2.90 2.90 2.90 2.80 2.85 2.85 2.85 3.00 2.85 2.85 2.75 2.80 2.90 3.05 2.85 2.85
- 16. 7. Pareto Analysis Arranging data acc to its defects and causes 80% of defects from 20% of causes – vital few Remaining % of defects from various causes – trivial many/useful many
- 17. Pareto What is Pareto Analysis? • Pareto analysis is a method for prioritising data. • It consists of a Bar Chart displayed either in order of frequency or relative cost.
- 18. Pareto Example: The information to be represented on a Pareto diagram should already have been collected in some sort of record. Houshold repairs over the last 10 years Problem frequency Cost £ per occurance Total cost £ Light bulb fails 100 0.6 60 Broken central heating pump 1 190 190 Broken window 2 50 100 Leaking taps 16 2.5 40 Faulty central heating boiler 1 3000 3000 Leaking radiators 3 15 45
- 19. Pareto Pareto Chart The data are then displayed graphically. Firstly in terms of frequency..... House repairs 1998-2008 0 20 40 60 80 100 120 Light bulb fails Leaking taps Leakiung radiators Broken window Broken central heating Faulty central heating Fault Occurance frequency Cum %
- 20. Pareto ... and then by cost. House repairs 1998-2008 Total cost £ 0 500 1000 1500 2000 2500 3000 3500 Faulty central heating boiler Broken central heating pump Broken window Light bulb fails Leakiung radiators Leaking taps Total cost £
Notas del editor
- The Histogram is a tool for looking at data in groups rather than representing individual measurements. Units of measurement would be minutes, kilograms, millimetres.
- Although histograms show continuous data values, they can also be used in the same way for discreet values i.e. number of defective parts, absenteeism, defectiveness etc. Although, you may often see asymmetrical shapes (skewed distributions). Also look for Bi-model (two peaks) distributions and check stratification.
- The purpose of a Histogram is to take the data that is collected from a process and graph it to show how the data is distributed. The histogram will show: The centre of the data. The spread of the data. The skew of the data (slant, bias or run at an angle). The occurrence of out of range conditions. The presence of peaks within the data.
- The table shows the data sorted and tallied up. The graph is a Histogram, showing that the components are not all within the limits and they are not centred correctly.
- If the symptoms or causes of a defect or some other “effect” are identified and recorded, it will be possible to determine what percentage can be attributed to any cause, and the probable results will be that the bulk (typically 80%) of the errors, waste or “effects”, derive from a few of the causes (typically 20%). Without an analysis of this sort it is all too easy to devote resources to addressing one symptom only because its cause seems immediately apparent. As someone once said “If the only tool you have is a hammer it is surprising how everything starts looking like a nail.” It is based on the assumption that a “vital few” sub-problems are the main contributors to an overall problem and that the “trivial many” sub-problems make only a minor contribution. Pareto Analysis is used to ensure that the” vital few” are tackled first and the “trivial many” are left for future examination.
- Check sheets are a logical point to start in most process control or common problem solving efforts. It is particularly useful for recording direct observations and helping to gather in facts rather than opinions about the process. (The word faulty does not accurately describe the mode of failure and is open to opinion rather than being a fact.)
- Looking at this analysis it would appear that the biggest problem faced by the company is oversized spacers since it is the most re-curing problem. This would indicate that this should be the crucial problem in need of solution. However if we look at the following analysis...
- Although oversize spacers is the most re-occurring problem it is useful to look at the method of correcting all these problems. In the case of oversize spacers these items are likely to be thrown away and replaced at minimal cost. All the other faults are likely to involve some sort of rework procedure - some more complicated than others. If we know look at this analysis it becomes apparent that the cost to correct one poor body coating far outweighs the cost of replacing all oversize spacers. In essence this suggests that poor body coating is the true vital problem which needs to be addressed.