# Six Sigma Metrics

## Introduction

Six Sigma is a disciplined, data-driven approach and methodology for process improvement. In addition, it aims to minimize defects, reduce process variations, and improve overall quality and efficiency in organizations. Further, Six Sigma metrics, also known as key performance indicators (KPIs), are used to measure and assess the performance and effectiveness of processes.

## Here are some common Six Sigma metrics:

#### Defects per Unit (DPU):

DPU measures the average number of defects per unit produced or processed. Additionally, it helps quantify the quality level and provides a baseline for improvement efforts.

Formula: Number of Defects / Number of Units

Example: In a software development project, if 20 defects were found in a total of 500 units of code, the DPU would be 20 / 500 = 0.04 defects per unit.#### Defects per Million Opportunities (DPMO):

DPMO is a normalized version of DPU that represents the number of defects per million opportunities. Further, it allows organizations to compare different processes or products with varying numbers of opportunities.

Formula: (Number of Defects / Number of Opportunities) * 1,000,000

Example: Let’s say a manufacturing process produces 2,000 defective products out of 100,000 opportunities. The DPMO would be (2,000 / 100,000) * 1,000,000 = 20,000 DPMO.#### Parts Per Million (PPM):

PPM is a common metric used to quantify the defect rate or quality level in various manufacturing and business processes. In addition, it measures the number of defective or non-conforming units or parts per million units or parts produced.

PPM (Defects): Formula: (Number of Defects / Total Number of Units) * 1,000,000

Example: Let’s say a manufacturing process produces 50 defective parts out of a total of 10,000 parts. The PPM (Defects) would be (50 / 10,000) * 1,000,000 = 5,000 PPM.PPM (Defectives): Formula: (Number of Defective Units / Total Number of Units) * 1,000,000

Example: Consider a quality inspection where 25 out of 500 units fail to meet the specifications. The PPM (Defectives) would be (25 / 500) * 1,000,000 = 50,000 PPM.#### Process Capability (Cp and Cpk):

Process capability indices, such as Cp and Cpk, assess the capability of a process to consistently produce within the desired specifications. Cp measures the potential capability, while Cpk considers both the process average and variation.

Formula: (USL – LSL) / (6 * Standard Deviation)

Example: If the upper specification limit (USL) is 10, the lower specification limit (LSL) is 8, and the standard deviation of the process is 0.5, the Cp would be (10 – 8) / (6 * 0.5) = 1.#### Rolled Throughput Yield (RTY):

RTY calculates the probability of producing a defect-free unit through multiple process steps. In fact, it accounts for the cumulative effect of process variations and helps identify improvement areas in a multi-step process.

Formula: Yield1 * Yield2 * … * YieldN

Example: In a manufacturing process with three stages, if the yield of each stage is 0.95, 0.98, and 0.99, respectively, the RTY would be 0.95 * 0.98 * 0.99 = 0.9216.#### Sigma Level (Z-Score):

Sigma Level, also known as Z-Score, is a metric used in Six Sigma methodology to measure process performance and quantify the level of defects or variations in a process. Further, it indicates how well a process is performing relative to its specifications.

Formula: (Process Mean – LSL) / (Process Standard Deviation * DPMO Conversion Factor)

Example: Let’s say the process mean is 80, the lower specification limit (LSL) is 75, the process standard deviation is 5, and the DPMO Conversion Factor for a normal distribution is 2,691. The Z-Score would be (80 – 75) / (5 * 2,691) ≈ 0.004.#### First Pass Yield (FPY):

FPY measures the percentage of units that pass through a process without any rework or repair. It indicates the process’ ability to produce defect-free outputs on the first attempt.

Formula: (Total Units Produced – Total Defective Units) / Total Units Produced

Example: If a manufacturing process produces 1,000 units and 50 of them are defective, the FPY would be (1,000 – 50) / 1,000 = 0.95 or 95%.

## Summary

It’s essential that you carefully analyze these metrics to understand the process’ current state fully. This understanding will lay the groundwork for making data-driven decisions and targeting improvements during the Analyze and Improve phases of your Six Sigma project. Remember that accurate data collection and analysis are key to success in the Measure phase.