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# Weighted Pareto

Go to solution Solved by Vastupal Vashisth,

Pareto Chart

Pareto Chart is a graphical tool to help identify 'Vital Few from Trivial Many'. It is based on Pareto's principle which states that 80% of the defects are due to 20% of the causes. It is a bar chart depicting in descending order the frequency of the different defect categories. The bar chart is superimposed with a line graph which shows the cumulative percentage on a secondary y-axis. As per the principle, approximately 80% of my cumulative defects will be caused by 20% of the defect categories (starting with the categories from far left).

Weighted Pareto

Weighted Pareto is a modified Pareto which helps in assigning weightages to different defect categories thereby overcoming the limitation of a normal Pareto where all defects are considered to be of same severity. The most common parameter used for weightage is the cost of a defect but other parameters can also be used. Once the weightage is decided, the bar graph is plotted with the product of weightage and frequency (instead of frequency alone) in the decreasing order. Rest everything remains similar to a normal Pareto Chart.

An application oriented question on the topic along with responses can be seen below. The best answer was provided by Vastupal Vashisth on 15th September 2018.

## Question

Q. 93  One of the most commonly used approach to get more insights on a Pareto chart is to transform it into a “Weighted Pareto”. A weighted Pareto chart doesn’t solely highlight the most frequent defects, but also considers their importance. The frequency data is weighted by assigning attributes (e.g. Cost) to each defect type followed by prioritization using the weighted scores (e.g. frequency x cost). What are the different attributes we can use? Also, the modified approach may not point to the same problems that a Pareto based on frequency does. Explain one such practical example of a weighted Pareto chart from your experience?

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• Solution

Pareto Chart or Pareto Diagram,  is a excellent tool for  prioritizing potential root causes or number of defects/problems. It is based on Pareto Principle of 80-20 Principle. It is based on theory of unequal distribution of wealth. This principle dictates that 80% of the failures are coming from only 20% of the causes. This tool based on the present data, it does not provide any projected movement of any one of the contributing factor in coming future.

It is the visual representation of vital few against trivial many. A Pareto diagram is combination of bar and line graphs of accumulated data where data is associated with a problem are divided into smaller groups by causes.It is a dual scale chart. The length of bars represent frequency and arranged with longest bar on left and shortest to right in decreasing order.

On left side Y axis there is number of problems or defects and right side Y- axis cumulative percentage. Cumulative percentage of 100% should be equal to total no of problems or defects for getting accurate pareto Chart. On X- Axis types of defects or problems are defined. Cumulative % will be derived after arranging all types of defects/Problems in decreasing order.

We can use Pareto chart in following conditions:

1. When we are analysing data about the frequency of problems in a process.
2. When we want to compare results before and after taking countermeasure.
3. When we are communicating with other about our data to make them understand in better way,
4. When analysing causes in broad way by looking at their specific components.
5. When we have many problems and we want to focus only on significant problems.

A Weighted Pareto does not look like normal Pareto chart in which we look at how often defect occur but it considers how important they are. There are some of different attributes that we can use in weighted Pareto;

• Severity of defects
• Cost related to defect
• Detectability of defects

A Weighted  Pareto may change how we see the priority for improvement projects. It requires valuation, different attributes are needed to calculate valuation and these attributes can be objective to find out and fix cost to each type of defects/problem so that we can identify which type of defects is having more impact on company and its reputation. it will help you to identify where high cost defects occur. We reconstruct Pareto to draw Weighted Pareto by multiplying frequency to its assigned value of attributes and re-arrange all defects in decreasing order to calculate cumulative % of each defect type.

for example if we see a sheet metal industry, some defects are occuring like crack 10 cases, 25 dent, 30 deform. As per Pareto Chart we consider these defects as Deform, Dent and Crack in decreasing order. So if we consider cost related to these defects like we spend 5 rupee to repair one deform and 7 rupee to repair one dent but we can't repair crack so we loss 20 rupee for a crack.

so 10 Crack wasting 10* 20 = 200 rupees

25 Dent wasting  25* 7   =  175 rupees

30 Deform wasting  30 * 5 = 150 rupees.

so according to weightage of defects we are observing that Crack which was least important before now comes at top position and to focus more for taking countermeasure, similarly Deform which was on first position before now comes at end for taking action and least important.

So Weighted Pareto changes the scenario how we see the priority for improvement of projects.

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Apart from “Cost”, there could be other measures like “Amount of Rework involved”. This would depend on not just the type of error but also the point of time in the process life-cycle, when the error is discovered. Cost could depend on the amount of rework involved. Cost can also involve fines or penalties.

Further, there could be other factors like, “Show-stopper” or “Non-show-stopper”, with the obvious meaning that a “Show Stopper” error brings the entire process to a grinding halt and hence will warrant higher weight. But the problem with this and other error criticality-based weights including “Fatal”, “Critical”, “Non-critical” etc. is that of quantifying the conceptual criticality. This is a tricky question as while it is clear that a fatal error is more serious than a critical error, by how much is the question. Would a fatal error be rated twice as critical as a critical error? If so, why?

In the area of back-office documentation for container shipping process, some voyages involve declaring the contents of the containers in detail to the Customs of the destination country. Only after this declaration is cleared can the container be shipped. After this declaration is cleared if there are any changes to be done in the declaration, this will involve additional costs to be paid. If these changes are done after a certain point of time connected to the time of sailing, there will also be an additional fine involved. In some cases, no changes will be allowed and hence the container will have to be unloaded from the vessel and rolled over to the next voyage resulting in delayed revenue from the customer and perhaps loss of business in future. In this situation an error in documentation that necessitates re-declaration to customs or additional costs and / or fines or worse still rollover will have a higher weight than other errors even if the frequency of occurrence of such “costly” errors are lesser. Where relevant, additional audits for these errors are also justified.

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Hello Sir,

We are dealing with Insurance claim processing Data Capture. While working on the Pareto along with frequencies we tend to survey the field nature like how the claim is getting impacted with these field. Apart from this we also tend to look the nature of failure with the impact it creates like a same field what is the impact when it is miskeyed(Typo) and when it is not keyed. Based on this we prioritize our actions.

Thanks!

Vanchinathan M

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This was a tricky one as most people use the normal pareto chart only. The answers provided by Mohan PB and Vastupal are very close. The best answer selected is from Vastupal basis the detailed explanation provided for both Pareto and Weighted Pareto along with an example.

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