Process Performance Metrics Flashcards
Defect
An end result (often a product) that doesn’t fall within a pre-defined acceptable range of values. For a physical product, these values might be strength and/or size measurements. For a service, these values might be KPIs like turnaround time. In a general sense, think of a defect as a failure to meet customer expectations of quality.
Opportunity
A chance to add value for a customer. This applies to any situation in which your company can improve the perceived value of a product or service. For example, if you’re manufacturing a product to customer specifications, your opportunities might be:
- Matching customer’s physical requirements
- Meeting deadlines
- Providing a free courier service straight to the customer.
Unit
A tangible result to a customer: a single service or product.
-For example, a customer’s phone call to your service department is a unit.
Yield
The yield is the percentage of opportunities that were successfully met. Another way to look at yield is the percentage of processes that were defect-free.
Yield = (Opportunities - Defects) / Opportunities
Defects per Opportunity (DPO)
DPO = Defects / Opportunities
Express the ratio as a percentage
Worked example of Defects Per Opportunity
Let’s say Joe’s Burgers serves 1,000 customers a day. The company has identified its opportunity types as:
Accuracy
Speed
Freshness
Taste.
For example, in a single day, 50 customers had the wrong order, 75 felt they waited too long, 25 said their order was cold, and 50 more said their burgers just tasted bad. = 4 opportunities
Some of that feedback might have overlapped; customers might have received the wrong order and waited too long for it. That doesn’t matter for this metric, because each order has multiple opportunities attached to it.
To calculate the number of opportunities, multiply the number of orders (1000) by the number of opportunity types (4) to get 4000.
DPO = number of defects / number of opportunities = 200/4000 = 0.05 = 5%
Defects per Unit (DPU)
DPU = number of defects / number of units
Worked example of Defects Per Unit
Let’s say Joe’s Burgers serves 1,000 customers a day. In a single day, 50 customers had the wrong order, 75 felt they waited too long, 25 said their order was cold, and 50 more said their burgers just tasted bad.
-Number of Defects: 50+75+25+50= 200
Some of that feedback might have overlapped; customers might have received the wrong order and waited too long for it. That doesn’t matter for this metric. We’re just looking for a basic ratio.
(Note: it would matter if we were talking about defective units per 1000, for example.)
The number of units is the number of orders (1000).
DPU = number of defects / number of units DPU = 200/1000 = 0.2 DPU = 20%
Defects per Million Opportunities (DPMO)
DPMO = DPO * 1000000
Alternatively, you can use this equation:
DPMO = (Defects / Opportunities) * 1000000
Or:
DPMO = (Defects / (sample size * opportunities per unit)) *
1000000
Worked example of Defects Per Million Opportunities
Joe’s Burgers serves 1,000 customers in a day. The company has identified its opportunity types as:
Accuracy
Speed
Freshness
Taste.
In a single day, 50 customers had the wrong order, 75 felt they waited too long, 25 said their order was cold, and 50 more said their burgers just tasted bad.
Number of defects: 50 + 75 + 25 + 50 = 200
Sample size: 1000
Opportunities per unit: 4
DPMO = (Defects / (sample size * opportunities per unit)) *
1000000
DPMO = (200/(1000 * 4)) * 1000000
DPMO = 50000
How to Calculate 6 Sigma level based on DPMO
There are two basic ways that you can determine the Six Sigma level from your DPMO figure:
Look at an appendix table.
Use the equation.
Six Sigma Level Equation
Use this equation to calculate your process’s Six Sigma Level based on its DPMO:
Level = 0.8406 + √(29.37 – (2.221 * ln(DPMO)))
Note: If you’re wondering where the numbers 0.8406, 29.37 and 2.221 come from, they are constants that help us calculate the DMPO or level simply.
Process Sigma = 0.8406 + SQRT(29.37 – 2.221 * (ln(DPMO))).
Worked example of calculating Six Sigma Level
Let’s start with the DPMO figure from Joe’s Burgers: 50000.
Firstly, if you haven’t come across ln before, it means that you need to find the natural logarithm of the number – in this case, the DPMO. Use a scientific calculator. In this case, the natural logarithm of 50000 to 4 decimal places is 10.8198.
Secondly, we need to plug that into the equation:
Level = 0.8406 + √(29.37 – (2.221 * ln(50000)))
Level = 0.8406 + √(29.37 – (2.221 * 10.8198))
Level = 0.8406 + √(29.37 - 24.0307)
Level = 0.8406 + √(29.37 - 24.0307)
Level = 0.8406 + √5.3392
Level = 0.8406 + 2.3106
Level = 3.1513
First-Time Yield (FTY)
First-time yield is the most common way to calculate the process yield. It is the number of defect-free units coming out of a process, compared to the number of units manufactured. In other words, it is the probability of a defect-free output from a process.
FTY does not capture how many defects are reworked in each stage. In other words, It doesn’t include units that need to be reworked in the defect-free units. It will not detect the effect of hidden factors.
Simply, FTY is the number of good parts produced divided by the total number of parts going into the process.
How to calculate First-Time Yield for a process
Calculate the first-time yield for each step in the process, based on the number of defect-free units going into each step (typically each step will have fewer units than the preceding step).
Multiply the FTYs together to get the total first-pass-yield.
FTYt = FTY1 * FTY2 * FTY3 * … * FTYn
Where:
FTYt is the total First Time Yield for the process.
n is the number of steps in the process.
Worked example of calculating FTY
Example: In a manufacturing plant, 100 parts are entered into the first process, 2 are scrapped, and 98 defect-free parts go to the next stage. 98 parts enter the second process, 5 are scrapped, and 93 defect-free parts go to the next stage. 93 parts enter into the third process, 10 scrapped and 83 defect-free parts are going to the next stage. Find the First time yield.
First process: 100 parts enter into process; 2 scrapped, So output 98 parts; FTY1 = (100 – 2)/100 =98/100= 0.98
Second process: 98 parts enter into process; 5 scrapped, So output 93 parts; FTY2 = (98 – 5)/98 =93/98= 0.9489
Third process: 93 parts enter into process; 10 scrapped, So output 83 parts; FTY3 = (93 – 10)/93 =83/93= 0.8924
Total First Time Yield = 0.98*0.9489*0.8924= 0.829 ~ 83% yield
FTY also can calculate the final number of defect-free parts divided by the number of parts in the start of the process = 83/100 = 83%
Rolled Throughput Yield (RTY)
Rolled Throughput Yield is a great way of seeing how healthy a process is. RTY provides a probability that a unit will be generated by a process with no defects. In other words, it’s the probability that a multi-step process will produce a defect-free unit.
Rolled Throughput Yield is more powerful as it is sensitive to defects, which means instead of being based on the yield on units, it uses the number of defects at each step (even the defective part is corrected, but still it will count in the calculation of RTY). It is valuable to the organizations as most of them consider only the successful/passed units although inherent muda are present. RTY considers total defects in the entire process.
Before calculating RTY, you need to complete two important steps:
Map the process so that you know how many steps it has.
Take samples at each stage of the process and test for defects, so that you have data for the calculation.
Rolled Throughout Yield (RTY) Example
A sequence of 3 operations has first pass yield (right first time) rates as follows:
1st step: 93%
2nd step: 87%
3rd step: 92%.
In other words, the first step in a process has a 93% chance of completing correctly. The 2nd has only an 87% chance. And the third process step has a 92% chance.
The first pass yield rate for the whole process is the chance of each step multiplied.
RTY = 93% * 87% * 92% = 74%
Each step by itself had a good chance of being acceptable. But when you take a look at the entire system, you see that the cumulative errors take a toll. In the above example, any item that the process produced only had a 74% chance of passing through without error or rework.
Worked example of calculating Rolled Throughput Yield
Example: In a manufacturing plant, 100 parts are entered into the first process, 2 are scrapped, and 5 are reworked to get the 98 parts to the next stage. 98 parts enter into the second process where 5 are scrapped and 10 reworked to obtain 93 parts. 93 parts enter into third process, where 10 scrapped and 5 reworked to get 83 parts. Find the Rolled throughput yield.
First process: 100 parts enter into process; 2 scrapped and 5 reworked, So output 98 parts; RTY1 = (100 – (2+5))/100 =93/100= 0.93
Second process: 98 parts enter into process; 5 scrapped and 10 reworked, So output 93 parts; RTY2 = (98 – (5+10))/98 =83/98= 0.85
Third process: 93 parts enter into process; 10 scrapped and 5 reworked, So output 83 parts; RTY3 = (93 – (10+5))/93 =78/93= 0.84
So, the Total Rolled Throughput Yield = 0.93*0.85*0.84= 0.664 ~ 66% yield
Calculating DPU from Rolled Throughput Yield
In addition to the Defects Per Unit calculations above, you can use a process’s RTY to calculate its Defects Per Unit. Use this equation:
DPU = -ln(RTY)
Reminder: ln is the natural log.
Worked example of calculating DPU from RTY
From the above manufacturing example, RTY is approximately 69.5%. Then to get the DPU, we plug that into the equation:
DPU = -ln(0.695) DPU = 0.3638
