A. Performance Metrics: purpose
What are the ways you can measure how successful your Six Sigma project has been in improving quality or decreasing the number of defects?
Before we go into the metrics and definitions, let’s say what “defects” and “defective” mean. Something has a defect if the result or outcome of a process is not what is expected. Something went wrong. The product may still be usable: a car with chipped paint can still be driven.
So some engineers use “defective” to mean a product which is not usable. Oops, we forgot to put an engine in that car: well, that’s a defective car because it can’t be driven. However, for the purpose of quality control, “defective” simply means “contains a defect,” whether that defect is cosmetic or whether it actually affects the function of the part as intended. (So just be careful to make sure you are on the same page in terms of your definition as those you are communicating to).
There can be different types of defects in a single part based on different causes.
B. Performance Metrics–Definitions
Here is a list of the Performance Metrics which are spelled out and then given an acronym if one is commonly used. The description is given of what this metric means.
Performance Metric | Description | |
1. | Percentage Defective | What percentage of parts contain one or more defects? |
2. | Parts per Million (PPM) | What is the average number of defective parts per million? This is the same figure in metric 1 above of “percentage defective” multiplied by 1,000,000. |
3. | Defects per Unit (DPU) | What is the average number of defects per unit? |
4. | Defects per Opportunity (DPO) | What is the average number of defects per opportunity? (where opportunity = number of different ways a defect can occur in a single part |
5. | Defects per million Opportunities (DPMO) | The same figure in metric 3 above of defects per opportunity multiplied by 1,000,000 |
6. | Rolled throughput yield (RTY) | The yield stated as a percentage of the number of parts that go through a multi-stage process without a defect. |
7. | Process sigma | The sigma level associated with either the DPMO or PPM level found in metric 2 or 5 above. |
8. | Cost of poor quality | The cost of defects: either internal (rework/scrap) or external (warranty/product) |
C. Performance metrics–Discussion and examples
1. Percentage Defective
This is defined as the
(Total number of defective parts)/(Total number of parts) X 100
So if there are 1,000 parts and 10 of those are defective, the percentage of defective parts is (10/1000) X 100 = 1%
2. PPM
Same as the ratio defined in metric 1, but multiplied by 1,000,000. For the example given above, 1 out of 100 parts are defective means that 10,000 out of 1,000,000 will be defective so the PPM = 10,000.
NOTE: The PPM only tells you whether or not there exists one or more defects. To get a clear picture on how many defects there are (since each unit can have multiple defects), you need to go to metrics 3, 4, and 5.
3. Defects per Unit
Here the AVERAGE number of defects per unit is calculated, which means you have to categorize the units into how many defects they have from 0, 1, 2, up to the maximum number. Take the following chart, which shows how many units out of 100 total have 0, 1, 2, etc., defects all the way to the maximum of 5.
Defects | 0 | 1 | 2 | 3 | 4 | 5 |
# of Units | 70 | 20 | 5 | 4 | 9 | 1 |
The average number of defects is DPU = [Sum of all (D * U)]/100 =
[(0 * 70) + (1 * 20) + (2 * 5) + (3 * 4) + (4 * 9) + (5 * 1)]/100 = 47/100 = 0.47
4. Defects per Opportunity
How many ways are there for a defect to occur in a unit? This is called a defect “opportunity”, which is akin to a “failure mode”. Let’s take the previous example in metric 3. Assume that each unit can have a defect occur in one of 6 possible ways. Then the number of opportunities for a defect in each unit is 6.
Then DPO = DPU/O = 0.47/6 = 0.078333
5. Defects per Million Opportunities
This is EXACTLY analogous to the difference between the Percentage Defective and the PPM, metrics 1 and 2, in that you get this by taking metric 4, the Defects per Opportunity, and multiplying by 1,000,000. So using the above example in metric 3:
DPMO = DPO * 1,000,000 = 0.078333 * 1,000,000 = 78,333
6. Rolled through Yield
This takes the percentage of units that pass through several subprocesses of an entire process without a defect.
The number of units without a defect is equal to the number of units that enter a process minus the number of defective units. Let the number of units that enter a process be P. The number of defective units is D. Then the first-pass yield for each subprocess or FPY is equal to (P – D)/P. One you get each FPY for each subprocess, you multiply them altogether.
If the yields of 4 subprocesses are 0.994, 0.987, 0.951 and 0.990, then the RTY = (0.994)(0.987)(0.951)(0.990) = 0.924 or 92.4%.
7. Process Sigma
What is a Six Sigma process? It is the output of process that has a mean of 0 and standard deviation of 1, with an upper specification limit (USL) and lower specification limit (LSL) set at +3 and -3, respectively. However, there is also the matter of the 1.5-sigma shift which occurs over the long term.
The result is the following two charts, one without and one with the 1.5-sigma shift.
This is from ASQ’s website under Quality Process. Refer to this site for more detailed information on the theory and mathematics behind this 1.5-sigma shift.
http://asq.org/quality-progress/2009/08/34-per-million/perusing-process-performance-metrics.html
8. Cost of poor quality
Also known as the cost of nonconformance, this takes the cost it takes to take care of defects either
a) internally, i.e., before they leave the company, through scrapping, repairing, or reworking the parts, or
b) externally, i.e., after they leave the company, through costs of warranty, returned merchandise, or product liability claims and lawsuits.
This is obviously more difficult to calculate because the external costs can be delayed by months or even years after the products are sold. It’s best, therefore, to measure those costs which are relatively easy to calculate and quickly available, i.e., the internal costs of poor quality.
The above are some of the metrics you can use BEFORE your Six Sigma Project and then AFTER your project to show that the countermeasures you have devised have had a positive effect. How certain can you be of this? That is the subject of the measurement section, which comes after this Define section of the Body of Knowledge is done.
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