Pareto chart and Pareto analysis in manufacturing

A Pareto chart is a bar graph in which the bars show frequency or cost, sorted from the largest on the left to the smallest on the right. ASQ counts it among the seven basic quality tools and also calls it Pareto diagram or Pareto analysis. A line for the cumulative share is usually added on top. According to Alkiayat (2021), Joseph Juran added that line and introduced the terms "vital few" and "trivial many".

The chart tells the team where to start. It does not say why a cause occurs. That needs a second step, such as a root cause analysis of the tallest bar.

The 80/20 principle behind the chart

Alkiayat (2021) traces the idea to the economist Vilfredo Pareto, who observed in 19th-century Italy that 80 percent of the land belonged to 20 percent of the population and generalized that about 80 percent of results come from 20 percent of the causes. In 1937 Joseph M. Juran put the idea to work in quality management, added the cumulative line and coined the terms vital few and trivial many. The same article calls the 80/20 rule a rough guide, so the numbers are not exact.

In practice the rule gives a stopping point. Read the cumulative line from the left and stop at the first bar that takes it past 80 percent. In the scrap example below that is the fourth bar, at 88.75 percent by count.

Build a Pareto chart in six steps

The ASQ procedure has nine steps; the last two, percentages and the cumulative line, are optional but useful. In a spreadsheet the work reduces to six steps.

• Fix the categories, for example the reasons for scrap on one line.
• Fix the measure and the period. ASQ names frequency, quantity, cost and time as common measures and suggests deciding whether the chart covers one work cycle, a day or a week.
• Collect the data and subtotal each category. Group many small categories as "other" and place that bar last.
• Sort the categories from largest to smallest.
• Calculate each category's share of the total, then the cumulative share. The last value must reach 100 percent.
• Draw the bars on the left axis, which runs from 0 to the grand total, and the cumulative line on a right axis from 0 to 100 percent, so that both scales line up. Add a reference line at 80 percent if you want to mark the vital few.

Example: scrap on a machining line, counted and costed

The numbers are invented for illustration. A machining line scrapped 400 parts in a month. Counting the rejected parts per reason gives this ranking.

Burrs and dimension errors together make up 58.75 percent, and three reasons reach 78.75 percent. Counting says to start with burrs. The parts do not cost the same, however. Assume the cost of a scrapped part rises with the work already invested: 4 euros for a burr, 12 for a dimension error, 6 for a scratch, 18 for a wrong thread and 30 for porosity, which is found late.

The ranking changes. Dimension errors lead with 1,140 euros, 30.4 percent of a total of 3,750 euros. Porosity moves from fifth place by count to second by cost, with 6.25 percent of the parts and 20.0 percent of the cost. Burrs fall from first to fourth. By the 80 percent rule the vital few are still four reasons, which together reach 84.5 percent, but they are a different four: porosity enters and surface scratches drop out. ASQ lists the weighted Pareto chart as a variation for this reason.

The sorting key is a decision. Count is right when every part hurts equally, for example complaints with the same effect. Cost, minutes of lost production or customer impact are better when the effects differ. State the key in the chart title, so nobody reads euros as counts.

Read the chart and take the second step

The NSW Clinical Excellence Commission gives a plain reading rule: each bar is a category, the bars are ordered by size, and where the cumulative line meets the 80 percent reference, the categories to the left are the vital few. The Alkiayat article adds that 80/20 is a rough guide, not an exact law, so do not expect a bar boundary to land on exactly 80 percent.

ASQ shows the next move in its own example: take the largest category and break it down into its parts in a second chart with its own cumulative values. In the scrap example, dimension errors could be split by feature, machine or shift. The first chart sets the priority, and the second one narrows down where to look.

Pitfalls that make a Pareto chart mislead

• An oversized "other" bar. If "other" is the tallest bar, the categories are too coarse. Split it before drawing conclusions.
• A period that is too short. One quiet or one bad week can reorder the bars. Compare at least two periods before acting.
• Mixed units on one chart. Counts, euros and minutes need separate charts, or a single weighted measure with a stated rule.
• Symptoms instead of causes. "Customer complaint" is a symptom. A chart of symptoms tells you where it hurts, not what to repair.
• No follow-up. Redraw the chart after the countermeasure, with the same categories and the same key, and check whether the bar shrank.

A table to fill in

Use one row per reason, sort the rows by the total column and keep the period in the heading of the sheet.

What SYMESTIC contributes

A Pareto chart needs counts, costs and times that someone has to collect. SYMESTIC records scrap and rework by reason, entered by hand at the workstation or derived automatically from the machine signal, and shows the top defect reasons together with the defect rate in percent or PPM. Stops are detected automatically and carry a reason, and setup appears as its own stop reason in the stop timeline. Stop records can be analyzed by machine, order and shift. Together they form the tally sheet a Pareto analysis starts from, without retyping.

More on downtime tracking and quality control software. For the cause analysis after the chart, see root cause analysis.

Sources

• ASQ: What is a Pareto chart?
• Alkiayat, M. (2021): A Practical Guide to Creating a Pareto Chart as a Quality Improvement Tool, Global Journal on Quality and Safety in Healthcare 4(2), 83-84
• Clinical Excellence Commission (NSW): Pareto chart

About the author

Christian Fieg

Head of Sales, SYMESTIC · Previously iTAC, Dürr, Visteon · Six Sigma Black Belt · LinkedIn

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