Pareto Chart

Goal

The Pareto chart answers one question: among a problem's categories, which ones account for most of the effect? Where the cumulative line bends, the first categories separate from the rest.

Juran calls the first categories the vital few and the rest the useful many. He had first written trivial many. He changed the term so that managers would not dismiss the small categories out of hand: they still have to be tackled once the first ones are done. The name comes from Vilfredo Pareto, who observed in 1890s Italy that about 20% of the population owned 80% of the land. Juran carried this distribution over to quality in the 1940s: a minority of causes produces the majority of defects.

The technique prepares a decision: where to put the improvement effort first and which category to analyse further. It delivers the chart and the table it is calculated from, with the period, the measure and the category definitions. When the team breaks down the tallest bar, it delivers a second-level Pareto, built only on that bar's data.

Usage

When to use it

• Defects, incidents or complaints already recorded by reason: rank them before choosing where to put the effort.
• Choosing the problem for an improvement project: in the Measure phase of a DMAIC project, select the category that accounts for most of the effect.
• Before a fishbone diagram: the selected category becomes the effect at the head.
• Software defect backlog: rank by module or by cause to decide where to fix first.
• Trade-offs in a steering committee: show with figures why the team tackles two categories out of seven.
• After an improvement: redraw on the next period and compare the counts, category by category.

When not to use it

• No data classified by category: first keep a check sheet over a period of normal operation.
• Process unstable over the period: a one-off incident skews the ranking; check stability with a control chart first.
• Severe failure that is rare or has never occurred: the tally cannot count it; anticipate it with an FMEA.

Description

The elements of the chart

Each bar stands for one category. Its height gives the number of occurrences or the cost, read on the left axis. The bars run from tallest to shortest. An Other bar groups the small categories and goes last, even when it is taller than the bar before it.

The cumulative line starts at the top of the first bar and adds that category's share at each bar. It reaches 100% on the last one. The right axis carries the percentages. Its 100% sits level with the total on the left axis: with the two scales aligned, the line reads against the bars.

Many teams draw a horizontal line at 80%. It helps the eye and decides nothing. The reader finds the first categories at the bend of the line, where its slope drops sharply. According to the Juran Institute, this point most often lies between 70% and 80% of the total.

Building the chart

1. Name the effect, the measure and the period. "Supplier invoices rejected at ERP import, by count, from 1 January to 31 March." A period that is too short ranks a one-off event. A period that is too long mixes successive states of the process. A control chart drawn before the Pareto checks that the process stayed stable over the period ranked.
2. Define the categories before counting. Each one gets a written definition. Each occurrence goes into one category only. A category created after the fact fits its author's hypothesis.
3. Collect. A system that already records the reason is enough. Otherwise a check sheet kept at the workstation counts the occurrences as they happen.
4. Sort and calculate. Sort the categories in descending order, Other last. Calculate each one's share of the total, then the cumulative share.
5. Draw. The bars on the left axis, scaled from zero to the total. The line on the right axis, scaled from 0% to 100%.
6. Read. Find the bend and the categories before it. Check that the Other bar is not among the tallest.
7. Act and redraw. Tackle the first categories, then draw the chart for the next period with the same categories and the same measure.

The table delivered with the chart carries the exact counts that the graph rounds for the eye. The team works from it when it breaks down a bar.

Counting or costing

The number of occurrences is the simplest measure. It ranks a frequent, cheap category ahead of a rare, costly one. Juran ranks contributions by their size, in count or in cost, and the team chooses the measure that serves its decision. To reduce a workload, it counts hours. To reduce a loss, it counts francs. Weighted by the time it takes to handle a rejection, the same quarter changes order.

A team tasked with freeing up time in accounts payable would, on the count alone, tackle the unreadable QR code third: 2.2% of the time spent.

When the bars look alike

A flat chart, with bars of similar height and an almost straight line, points to no category. The problem exists; the classification does not show it. The Juran Institute then recommends re-sorting the same data by another variable: reason, department, period, customer or person. This operation is called stratification. The team repeats it until an uneven distribution appears.

Sorting by person shows who handles the most cases, rarely why. Shown in a meeting, it names culprits, and staff stop reporting cases. The team reviews it in a small group and looks for the cause in what the person receives: their files, their tools, their instructions.

Breaking down the tallest bar

The first chart says neither why the category dominates nor what to do. "Amount mismatch with order" names a symptom.

The team then takes only the occurrences of the tallest bar and sorts them by a finer variable: sub-reason, supplier, product, site. This second-level Pareto has its own line and its own bend. The team repeats the operation, level by level, until a category is precise enough to name an action or a cause to verify. When the bars hold only a few occurrences each, the ranking is down to chance: the team stops and goes to observe the work on site.

When the cause remains to be found, the selected category becomes the effect of a fishbone diagram. The Pareto names the effect, the fishbone searches for its possible causes and the data settle between them.

Checking the effect of an improvement

After the action, the team redraws the chart over a period of the same length, with the same categories and the same measure. It compares the counts on the same scale. Percentages mislead: once the first bar shrinks, another takes its place and the chart keeps its shape. If the total has dropped and the bar the team tackled has shrunk, the action worked. If another bar has risen by as much, the problem has moved.

The share of the missing order number rises from 27% to 35% without a single extra rejection. The total, from 600 to 462, and the bar the team tackled, from 246 to 108, show that the action worked.

Common mistakes

Reading 80/20 as a law. The ratio varies from one problem to the next: three categories out of ten can make up 60% of the total or 95%. The team reads the bend on the line, wherever it falls.

Leaving the Other bar among the tallest. The classification then hides a category. The team opens the Other bar and pulls out the reasons that recur.

Mixing periods or sources. Adding up the rejections of two systems or those from before and after a process change ranks two problems in one chart.

Comparing raw counts when the volume has changed. If the next quarter handles 30% more invoices, a stable number of rejections hides an improvement. The team then compares a rate, for example rejections per 1'000 invoices imported, and states it in the table.

Counting an invoice under two reasons without saying so. An ERP can record two reasons on the same invoice. The team sets a rule along with the category definitions. It counts the first blocking reason, or it counts every reason and states that the total exceeds the number of rejected invoices.

Abandoning the useful many. A small category that takes an hour to fix gets fixed right away, without waiting for its rank.

AI considerations

A language model classifies free text. In a few minutes it sorts 2'000 complaints or tickets into a list of categories set by the team. The team gives it the list, the definitions and the Other category, then checks a random sample of about fifty cases. Without a given list, the model invents its own categories and applies them unevenly from one batch to the next.

It suggests stratification variables from the columns of an export. It writes the spreadsheet formula or the script that draws the chart. The analyst checks that the calculation sorts before it computes the cumulative share and that the Other bar stays last.

A model has none of the organisation's figures. Asked about the usual causes of a problem, it returns a plausible ranking without a single data point. Nor does it choose the measure: counting or costing depends on the decision the team is preparing.

Complaints and tickets contain names, addresses and sometimes health data. These are personal data, and health data are sensitive personal data (Art. 5 let. c FADP). They go to an external AI service only under a data processing agreement (Art. 9 FADP) and, if the provider processes them outside Switzerland, only to a country with adequate protection or with sufficient safeguards (Art. 16 FADP).

Examples

The case continues with the quarter's 600 rejected invoices.

The first level points to the amount mismatch, 41% of rejections. Sorted by supplier, these 246 rejections concentrate on one carrier: 138 rejections, 56% of the bar and 23% of the quarter's rejections. Its invoices add a fuel surcharge that the order does not provide for. The purchasing department adds the surcharge to the order. At the first level, the same bar would have triggered a review of the whole ordering process.

Visualisations

The Pareto chart is itself a figure: bars and a line on two axes. The diagrams show its anatomy, the effect of stratification and the second-level Pareto. The calculation table, the count-versus-time ranking and the before-and-after comparison are rows and columns, so they are tables.

Cost

Tooling

A spreadsheet is enough in most cases. Excel has offered a Pareto chart type since version 2016. Elsewhere a combo chart, with bars and a line on a secondary axis, does the same job.

Minitab and JMP draw the chart in one command. Minitab groups the small categories into Other beyond a cumulative percentage that the analyst sets. R, with the qcc package, and Python, with matplotlib, produce the chart in a script that the team reruns each period.

At the workstation, a paper check sheet and a whiteboard are enough: the team counts over the week and draws the bars by hand.

Sources

• Juran Institute, "A Guide to the Pareto Principle": the definition of the chart, its origin with Vilfredo Pareto and then Joseph Juran, the change from trivial many to useful many, the construction steps and the re-sorting of the data when the categories are close.
• Kaoru Ishikawa, Guide to Quality Control, Asian Productivity Organization (original Japanese edition, 1968): the Pareto chart among the seven basic tools of quality, designed so that a quality circle can run the analysis without statistical training.