Six Sigma Statistics

[Pages:20]Six Sigma

Six Sigma Statistics

Six Sigma Statistics

Companies often collect large amounts of data that are valuable sources of information to establish measures of process performance. But although customer surveys, rejection reports, expenses incurred in warranty claims, etc. are available, we often calculate the wrong indices. First Time Yield (the ratio of the number of accepted units to the number of units tested) has been traditionally used to assess process performance. However, this concept is flawed since the reality of rework and replacement of scrapped units is not considered, rendering management blind to the fact that we often do not produce quality products and services the first time.

Products or services are often the result of many process steps. It is rare to find products or services that are the direct result of a single process step. Final Yield is the calculation of First Time Yield at the last process step, and much like First Time Yield, it is not an accurate measure of process performance.

The concept of the Hidden Factory includes the amount of work required to produce a good unit above and beyond entitlement (the amount of work actually needed to produce a good unit of output the first time). The consequences of the Hidden Factory include longer cycle times, increased inventories, etc.

To uncover the Hidden Factory, Six Sigma introduces two measuring indices: Throughput Yield and Rolled Throughput Yield.

Throughput Yield represents the probability of producing a defect-free unit in a process step, while Rolled Throughput Yield represents the probability of producing a defect-free unit in a series of process steps. Both metrics can be calculated from either discrete or continuous data and the standard normal distribution tables.

When using discrete data, Throughput Yield is approximated using the formula YTP = e-DPU. From continuous data, it is calculated as YTP = 1 - probability (defect). The probability of producing a defect is calculated as the appropriate area under the standard normal curve.

Rolled Throughput Yield is calculated as the multiplication of the Throughput Yield values of each of the process steps involved in producing the output, or using the formula e-TDPU where TDPU stands for "Total Defects Per Unit".

Throughput Yield and Rolled Throughput Yield have deep business implications. We can now assess the true performance of our processes, no matter how unflattering this picture may be. In some instances a First Time Yield of 90% translates into a Throughput Yield of only 37%. On the bright side, once we know where we stand, we can set breakthrough targets and objectives. Moreover, we can track improvement over time using complete measuring indices.

The Normalized Yield is a single and equivalent value that is assigned to a series of process steps involved in producing an output. This is used to characterize all the steps involved in producing the output when the Total Defects Per Units at the final step is known. In this sense, we say that Normalized Yield represents a "kind of average" Yield value for a series of process steps.

Metrics Flow Down is a tool commonly used at the beginning of the life cycle of a product or service, typically during the design stage as a "what if" tool. For example, If we want to achieve a Six Sigma level and we know the

Copyright ? All Rights Reserved

process and product breakdown, then we can set targets at each of the lower levels in the breakdown that will render a Six Sigma product. Once data become available, later in the product life cycle, we can compare actual against target levels. Finally, Metrics Roll Up is a helpful tool for calculating the resulting Sigma value of a product or process. It is commonly used to benchmark products and services across groups or industries.

Key Questions

? What is "first-time yield" and how does it differ from "probability of zero defects"? ? What is "throughput yield", how is it computed, and what are its business implications? ? What is "rolled-throughput yield", how is it computed, and what are its business implications? ? What is "normalized yield", how is it computed, and what are its business implications? ? How can yield be converted into a "Sigma" value and how can this value be used? ? How can yield data be hierarchically pooled (or decomposed) and how can these values be used?

Key Questions First Time Yield (YFT) is the ratio of the number of units that pass inspection (S) to the number of units tested (U). It does not represent the probability of zero defects because units are accepted regardless of the presence of rework and replacement of scrapped units. Throughput Yield (YTP), represents the probability of producing a defect-free unit in a process step. It is calculated from discrete data (YTP = e-DPU where DPU means "Defects per Unit"), or continuous data (the appropriate area under the normal curve). The Hidden Factory is considered, thus providing a true picture of process performance. Rolled Throughput Yield (YRT) represents the probability of producing a defect-free unit in a series of process steps. It is calculated by multiplying the Throughput Yield values of each step, or using the formula YRT = e-TDPU where TDPU means Total Defects Per Unit. Normalized Yield (YNORM) is a single, equalized Yield value assigned to all steps in a group of "k" process steps. It is calculated as the kth root of Rolled Throughput Yield, and is used to benchmark processes and products. A Sigma value, Zst (Sigma short term) is used to compare performance across various products or processes. To obtain a Sigma value from a Yield value, we first calculate the probability of a defect (1 - Yield) and using the standard normal tables, we find the corresponding Z value. Then we perform the appropriate correction (shift and drift) using the "truth table". Yield values can be "Rolled Up" using the product or process hierarchy to characterize a product or process. Likewise, this hierarchy can be use to "Flow Down" Yield values and to set improvement targets for Quality levels.

Copyright ? All Rights Reserved

First Time Quality

First Time Quality is not ... - After Discarding and Starting over Again - After Rework - After Corrections - After Force-Fitting - After Scrap - After ...

1_04_01_002

Analyze

Six Sigma Statistics

3

First Time Quality

A Champion and a Six Sigma Master Black Belt reflect on the concept of First Time Quality, highlighting the fact that historically we used mathematical ratios and proportions to represent the status and health of our processes.

"I remember", says the Champion "...how we used to plot many graphs depicting the amount of scrap and rework for a given month. We used to show trends and set objectives to contain and lower the number of rejections, ultimately controlling labor and cost".

"Yes, that was prior to implementing Six Sigma. Today the objective remains the same, but we plot DPMO (Defects Per Million Opportunities), Sigma values and other metrics that help us measure our products and processes and, by identifying and solving problems,quality improves, cost goes down and we keep our customers satisfied".

"It is interesting to see how much one factor (variation) can influence our processes. After we began to understand and started to control variation, our processes started improving. Adopting metrics such as Yield (the probability of producing good units of output), Throughput Yield, Rolled Throughput Yield and Normalized Yield helps to measure, uncover, and eliminate the Hidden Factory".

"Now that we are on our way to becoming a Six Sigma company, we understand the importance of using the proper metrics, operating robust processes and having defect free units of output... the first time!"

Copyright ? All Rights Reserved

Finding Artifacts to Estimate Capability

1_04_01_003

Analyze

Six Sigma Statistics

4

Findings Artifacts to Estimate Capability

During the implementation of Six Sigma, we often believe that there is no readily available information or numbers to estimate our existing level of process performance. We believe that a considerable effort is required to measure the existing situation and to identify trends, strengths, and areas for improvement. However, companies .measure certain activities and record the data which could provide valuable information as a starting point for a capability evaluation.

Among the many sources of information, there are:

Quality records (rejection reports): Customer surveys:

? Records of Cost of Poor Quality (COPQ); ? Records of customers' complaints; ? Records of returned goods or items: ? Warranty replacements and repairs, etc.

Much like an archaeologist looks for artifacts of past civilizations to discover how ancient societies lived, Six Sigma practitioners can "dig out" existing records to begin assessing the performance of our existing processes and products.

All these sources provide a "ball park" figure of the number of defects per unit. From this number, we can calculate Throughput Yield or Rolled Throughput Yield values, which in turn lead to Sigma values.

Copyright ? All Rights Reserved

The Hidden Factory

Input

Operation

Rework Scrap

Quality = Customer satisfaction

= Profits

OK Inspect

NOT OK

Output

Hidden Factory

1_04_01_004

Analyze

Six Sigma Statistics

5

The Hidden Factory

When a Six Sigma Black Belt inquires about the Hidden Factory, the Master Black Belt clarifies, "The Hidden Factory is a concept related to productivity, value and money. It includes all work and costs invisible to our accounting system. In practice, the constituents of the Hidden Factory vary depending on how we measure costs and business performance. Another way of defining the Hidden Factory is all work required to produce one good unit of output above and beyond entitlement (the amount of work actually needed to produce a good unit of output the first time)".

Hidden Factories are not exclusive to manufacturing. They in any department, shop, or but its effects are felt across the business. Longer cycle times, increased costs, and inefficient use of resources are some of the consequences of the Hidden Factory. In Six Sigma, we strive to uncover and eliminate this Hidden Factory.

A team member says, "As part of my weekly tasks, I compile data recorded in the Non Conformance Reports. I see that report no. C320363 indicates that for the rejection of certain parts, we incurred material costs of $4,678 and labor costs of $4,700. Is this part of Hidden Factory"?

The Master Black Belt answers, "Not really. These costs are measured and reported, so they are visible. However, other costs, such as the amount of time the operator correcting defective units, are not specified anywhere, therefore they are part of the Hidden Factory.

Copyright ? All Rights Reserved

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download