Pareto Analysis

Pareto analysis is particularly useful in dealing with chronic problems because it helps us to decide which of several chronic problems to attack. We can also make a Pareto analysis at the end of the problem-solving process to see whether our solution worked.
We may already know the idea behind Pareto analysis, even though we haven’t heard it called by that name. We see it when 20% of our customers account for 80% of our business. To give another example, it’s when only a few branches of a bank, out of many branches, conduct most of the business for the bank.
Problems tend to sort themselves out this way, too. When we do some investigating, we usually find that of the 12 or so problems we have looked at, only one or two, maybe three cause the most dollar loss, happen the most often, or account for the most trouble.
An example of a special type of bar graph called Pareto diagram is on the problem-solving team of a hotel room attendants. The problem-solving team of the hotel room attendants has collected data about items for which there were shortages during their weekend cleaning. The team looked at the past month’s reports and recorded the data in a Pareto diagram. Among the 68 recorded shortages, they found 33 instances where they didn’t have enough sheets; 18 times they were short of pillowcases; towels, 7 times; shampoo, 5 times; toilet tissue, 3 times; and twice they didn’t have a vacuum cleaner. Sheets accounted for 33 of the 68 shortages, or 48.5%.
If this team wants to improve the availability of supplies and equipment during weekend, which problem do you think they should tackle first, vacuum cleaners or sheets? A missing vacuum cleaner is an obvious problem, but the team discovered that missing sheets was far more frequent. Therefore, to improve both quality and productivity, the best approach to use is to tackle missing sheets, the biggest problem. Pareto analysis helped the team make this decision.
What is the difference between Pareto analysis and a Pareto diagram? As we said before, a Pareto diagram is a special type of bar graph. In this graph, the problem that occurs most frequently is shown by the first vertical bar at the left, the tallest bar. The next most frequently problem is represented by the second tallest bar. The third bar shows the third most frequent problem, and so on. “Frequency” might mean cost in dollars, number of errors, or how often a computer program fails. Each bar represents a specific category, day of the week, or even employee.
Pareto analysis will help you see that there is a need for change and improvement. The Pareto diagram is the picture part of the analysis. Pareto analysis helps set priorities on problems that needs to be solved and helps bring agreement on what to do first. It helps you to make decision based on data, not on “squeaking wheels”. An example of Pareto diagram is as shown below:

HOW TO CONSTRUCT A PARETO DIAGRAM

Step 1. Specify your goal clearly.

Let’s suppose our company is a retailer. We are a member of a task force that has been asked to improve the quality of handling customer orders. Our team is not responsible for improving the quality of the actual merchandise itself, but we are asked to look at such things as the following: Did the customer receive the correct product? Was it delivered on time? Was it billed properly? This might require our group to address billing errors, shipping errors, or any of a host of other potential problems. Our team has been instructed to look at quality from the customer’s viewpoint. Pareto analysis will help you decide which specific problem area to address first.

Step 2. Collect data.

First determine whether data are already available. If not, then collect the data.
Lets see an example:
In our example, we know that the accounting department has copies of all credits issued to customer’s view of quality, reviewing credits is a good beginning. One member of our team volunteers to obtain data for the last 6 months from accounting. Sandy’s list is shown in below:

	Recorder: Sandy				Source: Corporate Accounting
	Date: Nov.5

	Customer 		Date		Reason			Dollars
	
	Buckman 		3/25		Pricing error		25.00
	Natural 		4/20		Late shipping		816.00
	Natural 		6/03		Shipping error		520.00
	Shamers 		6/17		_			69.00
	Johnstone		3/13		Billing error		20.00
	Printographics 	        5/07		Billing			126.00
	Providential		2/20		Late shipment		134.00
	Artistic		1/12		Short one carton	6.00
	Custom		        3/30		Wrong shipment	8.00
	Banker			5/15		_			40.00
	Niceties		2/23		Shipping shortage	105.00
	Natural			2/17		Order entry error	278.00

Step 3. Tally the data.

Count up the items in each category.

In our example, the group decided to look at “dollars” first, although this is not the only way the data could be analyzed. A tally sheet is shown in table below.

                                          Table 3
                                       Tally of data
	Pricing: $25							$25.00
	Shipping: $816, $520, $134, $8, $105			        $1583.00
	No reason given: $69, $40					$109.00
	Billing: $20, $126						$146.00
	Shortage: $6							$6.00
	Order entry: $278						$278.00

		Total dollars						$2147.00

Step 4. Rank the categories by size.

List the most frequent category first, whether it’s the most dollars, as in our example, or the largest number of defects, or whatever we are looking at. Use the top part of the Pareto Diagram Worksheet. When we have rearranged the tally by frequency of dollars, our worksheet will look like:

                          PARETO DIAGRAM – WORKSHEET

	Category 	Frequency	Cumulative         Cumulative
			(Dollars)	frequency          percentage

	shipping	1583.00
	order entry	278.00
	billing		146.00
	no reason given	109.00
	other		31.00

	total dollars	2147.00

Step 5. Prepare the chart for the data.

On the graph portion of the Pareto Diagram Worksheet, draw horizontal and vertical scales. Then, mark the numbers on the left-hand vertical scale so that the largest category will fit comfortably. Our largest category is “shipping”, with $1583.00, so run our vertical scale up to at least $1600.00. We ran it up to $2000.00. Label the scale “dollars”.
Next, subdivide the horizontal scale into equal-width intervals so that we have enough intervals for our categories. We may decide to combine the smallest categories into a single group called “other”. We recommended that the total of those combined in “other” should not be more than 10% of the overall total.
In our example, we have six categories or reasons for credits. The two smallest, ”shortage” and “pricing”, have very small dollars amounts, so they can be combined into one category – “other”. As a result, we will need only five equal width intervals.

Step 6. Draw the bars.

For the first interval on the left, draw in a bar to represent our largest category. “shipping” is the largest category with $1583.00, so draw in with height of $1583.00 and label it “shipping”.
For the second interval on the left, draw in a bar for “order entry”, the next largest category, at height of $278.00 and label it.
Continue this manner with all the other categories.

Step 7. Make calculation based on tallies.

On the top of the worksheet, first add the dollars, starting with $1583.00 (“shipping”), the largest. Add the next largest entry, $278.00 (“order entry”), for a total of $1861.00. When we add the dollar amounts for “shipping” and “order entry”, the cumulative frequency, or amount, is $1861.00. The third entry, $146.00 (“billing”), gives a cumulative amount of $278.00, and “billing” - $146.00. Make a note of each cumulative amount and keep adding until we reach the last entry. The last cumulative amount should be $2147.00, the total of all the credits.
Now that we have calculated the cumulative dollars, the next step is to find the cumulative percentage for each entry. To do this we use a simple formula:

		Cumulative percentage equals cumulative amount divided by the 
		total amount times 100%

As we have already seen, the first cumulative amount is $1583.00. Divide $1583.00 by $2147.00, the total of all credit dollars. The result is 0.74. Multiply this figure by 100% to find the cumulative percentage.
To find the second cumulative percentage, take $1861.00 divided by $2147.00. The cumulative percentage is higher this time because now we are using the cumulative amounts from two categories.

		
			1861/2147 = 0.87
			0.87 * 100% = 87%

Continue in this way to find the cumulative percentage on the basis of each cumulative amount, and make a note of each cumulative percentage. The last one should equal 100%.

Step 8. Complete the Pareto diagram.

Finally, set a scale on the diagram to show the cumulative percentages. We can use 10 major subdivisions of graph paper. We recommended that you use an easy method or use a scale that is easy to read, fits the graph well, and looks good. The following method is simple and clear.
Draw a vertical scale for cumulative percentages on the right-hand side of the graph. Label it “cumulative %”. Mark off 10 divisions to represent 10 percentage point each. Mark some cumulative percentages on it – at least 0%, 50% and 100% - so that the reader will understand the scale.
Next, draw in the cumulative percentages. At the bar for “shipping”, mark a small dot at a height of 74%, our first cumulative percentage. Over the “order entry” bar, draw a dot at 87%, and so on. Then connect the dots with straight lines to make the chart easier to read.
Finally, label the chart “Pareto Diagram of Credits, Jan1 – June 30”. This completes the Pareto diagram.

HOW TO INTERPRET THE PARETO DIAGRAM

Your Pareto diagram is a document of quality problems: it can be duplicated, put on an overhead transparency for a presentation, or otherwise copied and stored.
The Pareto diagram is also a communication tool based on data, and it can help to bring agreement about which problems should be solved first. The diagram allows the process to tell its own story without politics or personal feelings. In our example, anyone – management, supervisors, hourly employees – can see that shipping is by far the highest dollar category of credit in the time period we studied and should be tackled before anything else.
Finally, the Pareto diagram serves as a way to compare problems that existed before we worked to improve the process with problems that exist after we worked on the process. After we tackle the problem of shipping, a new Pareto diagram should show shipping as a minor or nonexistent problem.

Brainstorming
Cause and Effect Diagrams
Flowcharts
Storyboarding
Scatter Diagram

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