# Pareto Analysis

Pareto diagrams are very specialized forms of column graphs. They are used to prioritize problems (or opportunities) so that the major problems (or opportunities) can be identi?ed. Pareto diagrams can help six sigma teams get a clear picture of where the greatest contribution can be made

History

There is a very interesting story behind the name of Pareto diagrams. The word “Pareto” comes from Vilfredo Pareto (1848-1923). He was born in Paris after his family had fled from Genoa, ltaly, in search of more political freedom. Pareto, an economist, made extensive studies about the unequal distribution of wealth and formulated mathematical models to quantify this maldistribution. He also wrote a political book on nationalism which helped lead to fascism in ltaly. Dr. Joe M. Juran, world renowned leader in the quality ?eld, was preparing the Quality Control Handbook in the l 1940s. He needed a short name to apply to the phenomenon of the “vital few” and the “trivial many.” He depicted some cumulative curves in this manuscript and had put a caption under them, “Pareto’s principle of unequal , distribution…”

The text makes it clear that Pareto only applied this principle in his studies of income and wealth; Dr. Juran applied this principle as “universal. ” To complicate matters more, the cumulative curve diagram itself was first used by M.O. Lorenz in 1904. Briefly stated, the principle suggests (in most situations) a few problem categories (approximately 20%) will present the most opportunity for improvement (approximately 80%).

Pareto diagrams are used to:

Analyze a problem from a new perspective

Focus attention on problems in priority order

Compare data changes during different time periods

Provide a basis for the construction of a cumulative line

BASICS OF SIX SIGMA METRICS

Q. What is a Unit?

A. It is an Item being processed

A.What is a Defect?

A. It is defined as the failure to meet a customer Requirement or a Performance standard

Q. What is an Opportunity?

A. Any product / service characteristics which is measured to a standard is an Opportunity

Q. What is Defective?

A. It is a unit that has s defect

Q. What are Defects Per Million Opportunity?

A. Number of defects that would arise given a million opportunity

DPU, DPO and DPMO:

Defects Per Unit (DPU)

DPU = D / U

D = Total No. of Defects

U = Total No. of Units

Defects Per Opportunity (DPO)

DPO = D / (U*O)

D = Total No. of Defects

U = Total No. of Units

O = Opportunities for defects per unit

Defects Per Million Opportunities (DPMO)

DPMO = 1,000,000 * DP = 1,000,000 * D / (U*O)

Yield

Different types of fulfillment can impact the quality level we measure in our processes

Yield can be understood as follows:

Classical Yield

Classic Yield (YC ) – Units Passed / Units Tested

First Pass Yield

First Time Yield (Yft ) – Units Passed / Units input for First time

Rolled Throughput Yield

Rolled Throughput Yield (Ytp ) – Yield 1* Yield 2* Yield 3* Yield 4

Cycle Time

Cycle Time = 1 / Throughput Rate