Business Results/ Sigma level Business Results/ Sigma level CalculationsCalculations

Process performance metricsProcess performance metrics Typical example to illustrate the several Typical example to illustrate the several

measures used in Six Sigmameasures used in Six Sigma

A process produces 40,000 pencils. Three types A process produces 40,000 pencils. Three types of defects that can occur of defects that can occur

Their numbers are:Their numbers are: Blurred printing: 36Blurred printing: 36 Wrong dimensions: 118Wrong dimensions: 118 Rolled ends : 11Rolled ends : 11 Total number of defects = 36+118+11 =165Total number of defects = 36+118+11 =165

DPU/ DPMODPU/ DPMO DPU (Defects per unit) = (#defects) /(#units) DPU (Defects per unit) = (#defects) /(#units)

= 165/40000 = 0.004125= 165/40000 = 0.004125

DPMO (Defects per million opportunities)DPMO (Defects per million opportunities)

Formula for DPMO = (#defects x 1,000,000) / Formula for DPMO = (#defects x 1,000,000) / (total number of opportunities)(total number of opportunities)

Here we need to know the number of ways Here we need to know the number of ways each defect can occur on each item.each defect can occur on each item.

Blurred printing can happen only one way (pencils slip in the Blurred printing can happen only one way (pencils slip in the fixture).fixture).

Number of opportunities for this case =40,000x1 =40,000Number of opportunities for this case =40,000x1 =40,000

Three independent places where dimensions are checked and Three independent places where dimensions are checked and so in that case the opportunities for this batch are = 3 x so in that case the opportunities for this batch are = 3 x 40,000 =120,00040,000 =120,000

Rolled ends can occur at the top and bottom and in this case Rolled ends can occur at the top and bottom and in this case opportunities are = 2 x 40,000 = 80,000opportunities are = 2 x 40,000 = 80,000

Total number of opportunities are 40,000 + 120,000 + Total number of opportunities are 40,000 + 120,000 + 80,000 = 240,00080,000 = 240,000

Formula for DPMO = (#defects x 1,000,000) / (total number Formula for DPMO = (#defects x 1,000,000) / (total number of opportunities)of opportunities)

= 165,000,000/ 240,000 = 687.5= 165,000,000/ 240,000 = 687.5

DPO/DPMODPO/DPMODPO = DPO = # of defects# of defects

(#of units) x (#of opportunities)(#of units) x (#of opportunities)

E.g., #of units = 330E.g., #of units = 330

# of opportunities (type of defects) = 7# of opportunities (type of defects) = 7

# total number of defects = 59# total number of defects = 59

DPO = 59/ 330 x7 = 0.025DPO = 59/ 330 x7 = 0.025

DPMO = DPO x 10DPMO = DPO x 106 6

=0.025x1,000,000=25,000=0.025x1,000,000=25,000

In the earlier pencil exampleIn the earlier pencil example

DPMO = 165x 100,000/(40,000 X6)=687.5DPMO = 165x 100,000/(40,000 X6)=687.5

RTY/PPM RTY/PPM Throughput yieldThroughput yield, Also called yield, Also called yield This is given by the formula = This is given by the formula = e e - DPU- DPU

In the present case,In the present case,

throughput yield = e -0.004125 = 0.996throughput yield = e -0.004125 = 0.996

Rolled through put yield (RTY)Rolled through put yield (RTY) This applies to a series of processes and is This applies to a series of processes and is

found by multiplying the individual process found by multiplying the individual process yieldsyields

If a panel goes through four processes whose If a panel goes through four processes whose yields are .994, .987, .951 and .990yields are .994, .987, .951 and .990

RTY = .994 x .087 x .951 x.990 = .924RTY = .994 x .087 x .951 x.990 = .924

Normally when referring to defects we try Normally when referring to defects we try to indicate in PPM (Parts per million)to indicate in PPM (Parts per million)

PPM = DPU x 1,000,000PPM = DPU x 1,000,000

In the present case it is = 0.004125 x 1,000,000 = 4125In the present case it is = 0.004125 x 1,000,000 = 4125

It is also referred to as contaminants.It is also referred to as contaminants.

E.g., 0.23 grams of insect parts are found E.g., 0.23 grams of insect parts are found in 25 kgs of a product:in 25 kgs of a product:

PPM = 0.23 x 1,000,000 /25,000 = 9.2 PPM = 0.23 x 1,000,000 /25,000 = 9.2 ppmppm

COPQ/Sigma LevelsCOPQ/Sigma Levels

Cost of Poor Quality (COPQ)Cost of Poor Quality (COPQ)

This is helpful in prioritizing projects in This is helpful in prioritizing projects in terms of their impact on the enterprise terms of their impact on the enterprise in terms of money.in terms of money.

It should include costs involved in re-It should include costs involved in re-work, warranty, late deliveries, work, warranty, late deliveries, customer dissatisfaction some of the customer dissatisfaction some of the main things one should always consider. main things one should always consider.

Sigma LevelsSigma Levels E.g., Tolerance for a part are given as 5.000 E.g., Tolerance for a part are given as 5.000 ++ 0.012 (4.98 to 0.012 (4.98 to

5.012)5.012)

Data from a particular shift indicates that the process mean is Data from a particular shift indicates that the process mean is 5.000 and standard deviation 5.000 and standard deviation σσ = 0.004 = 0.004

++ 3 3σσ fits inside the tolerance = fits inside the tolerance = + + 0.0120.012

Capability calculations will show Capability calculations will show

Cp = Cpk =1Cp = Cpk =1

Traditional way you would use standard normal table to determine Traditional way you would use standard normal table to determine the area under the normal curve between the area under the normal curve between ++33σσ..

From experience the mean could shift and for Six Sigma From experience the mean could shift and for Six Sigma process, it is allowed to shift to process, it is allowed to shift to ++1.51.5σσ or yield is 0.9332 or yield is 0.9332

Suppose the variation has reduced to Suppose the variation has reduced to σσ =0.002 and area =0.002 and area under a normal curve is to the right of - 4.5under a normal curve is to the right of - 4.5σσ

This turns out to be 0.9999966 This turns out to be 0.9999966

The defect level = 1-0.99999966 =0.0000034 or 3.4 ppm.The defect level = 1-0.99999966 =0.0000034 or 3.4 ppm.

This is the often quoted as defect level for Six Sigma This is the often quoted as defect level for Six Sigma processes.processes.

Easy way is to refer the Sigma table given to all and go by Easy way is to refer the Sigma table given to all and go by different criteria data you have to assign the Sigma levels for different criteria data you have to assign the Sigma levels for your process.your process.

Safe is to first look for the % yield or Safe is to first look for the % yield or success to find out the process sigma.success to find out the process sigma.

If you are sure about the different ways If you are sure about the different ways defects could occur and perceived in your defects could occur and perceived in your organization calculate DPMO. organization calculate DPMO.

Still I would advice cross-check with Sigma Still I would advice cross-check with Sigma other method.other method.

If you want to know the throughput yield, If you want to know the throughput yield, use the formula involving DPU.use the formula involving DPU.

Another Example: Another Example:

Your department performed 535 specific operations last month. Of Your department performed 535 specific operations last month. Of these, 43 were defective (they fell outside the acceptable range of these, 43 were defective (they fell outside the acceptable range of outcomes). This means that 492 of the operations were outcomes). This means that 492 of the operations were successful. successful.

The yield was: 492 ÷ 535 = 91.9%The yield was: 492 ÷ 535 = 91.9%

Referring to Table 1, we discover that this outcome represents Referring to Table 1, we discover that this outcome represents Sigma somewhere between 2.5 and 3. Sigma somewhere between 2.5 and 3.

If you were able to reduce the number of defects by half, ending If you were able to reduce the number of defects by half, ending up with 21, your acceptable outcomes would then grow to 514 out up with 21, your acceptable outcomes would then grow to 514 out of 535 operations, and your yield would increases well: of 535 operations, and your yield would increases well:

The yield is 514 ÷ 535 = 96.1%The yield is 514 ÷ 535 = 96.1%

Now the Sigma is between 3 and 4, a significant improvement. Of Now the Sigma is between 3 and 4, a significant improvement. Of course, if you cut defects in half, you are going to know your course, if you cut defects in half, you are going to know your outcomes have improved, so what purpose does Six Sigma outcomes have improved, so what purpose does Six Sigma provide beyond the obvious scorekeeping?provide beyond the obvious scorekeeping?

As the preceding example demonstrates, improvement in As the preceding example demonstrates, improvement in quality can be specifically measured. quality can be specifically measured.

In practice, you may be dealing with a much greater volume of In practice, you may be dealing with a much greater volume of outcomes, and the incremental rate of success is likely to be outcomes, and the incremental rate of success is likely to be smaller than that shown in the example; smaller than that shown in the example;

and Six Sigma is far more than a measuring system. and Six Sigma is far more than a measuring system.

It is a way of doing things, a change in cultural attitude that is It is a way of doing things, a change in cultural attitude that is designed to create a company-wide team in practical terms. designed to create a company-wide team in practical terms.

As far as the scorekeeping aspects of Six Sigma go, if you As far as the scorekeeping aspects of Six Sigma go, if you begin with an assumption that a change in procedures will begin with an assumption that a change in procedures will produce an expected change in outcomes, you can then produce an expected change in outcomes, you can then compare actual to projected results to judge the success of compare actual to projected results to judge the success of your work.your work.

Key Point Key Point What makes Six Sigma different from most other What makes Six Sigma different from most other quality control programs? quality control programs? It is more than just a way to improve It is more than just a way to improve performance; it is a method for changing the corporate culture, performance; it is a method for changing the corporate culture, from top to bottomfrom top to bottom..

An “operation” can be any function you performAn “operation” can be any function you perform— delivery of goods, telephone contact, — delivery of goods, telephone contact, balancing accounts, or executing a repair, for balancing accounts, or executing a repair, for example. example.

Any operation is measurable in Sigma terms. Any operation is measurable in Sigma terms. The desired outcome represents satisfaction of The desired outcome represents satisfaction of the customer’s expectation, and any time that the customer’s expectation, and any time that expectation is not met, the outcome is defective.expectation is not met, the outcome is defective.

While measuring results is a crucial part of the While measuring results is a crucial part of the process, you will be more concerned with how process, you will be more concerned with how Six Sigma is applied and what role you and other Six Sigma is applied and what role you and other employees will perform within that process. employees will perform within that process.

So the idea of Six Sigma is much more than the So the idea of Six Sigma is much more than the latest approach to quality control; it represents a latest approach to quality control; it represents a change in philosophy that affects everyone.change in philosophy that affects everyone.

It is designed to bring everyone into a single team It is designed to bring everyone into a single team with the same overall goals. So many corporate with the same overall goals. So many corporate employees— especially in large organizations—employees— especially in large organizations—have a sense of isolationhave a sense of isolation

or view their relatively small department as a realm or view their relatively small department as a realm unto itself. Six Sigma encompasses the entire unto itself. Six Sigma encompasses the entire corporation as a single team and is aimed at corporation as a single team and is aimed at removing that sense of isolation.removing that sense of isolation.

Key Point Key Point

Cost savings are an important aspect of quality Cost savings are an important aspect of quality control, but they are only control, but they are only one one aspect; aspect;

a permanent, effective, and rewarding quality a permanent, effective, and rewarding quality program requires more work.program requires more work.

So many quality programs have been devised, So many quality programs have been devised, named, and put into effect over many years. named, and put into effect over many years.

Most fail after a while because employees lose Most fail after a while because employees lose faith in those programs. It becomes obvious to faith in those programs. It becomes obvious to employees that “quality control” really represents employees that “quality control” really represents management’s attempt to cut costs and expenses management’s attempt to cut costs and expenses and get more work from its labor force.and get more work from its labor force.

In other words, the program applies to the In other words, the program applies to the worker but there is no change in worker but there is no change in management itself. If the final result of a management itself. If the final result of a quality program is to achieve increased quality program is to achieve increased efficiency, and that results in layoffs, who efficiency, and that results in layoffs, who benefits? benefits?

With Six Sigma, everyone is involved and With Six Sigma, everyone is involved and everyone is expected to change (for the everyone is expected to change (for the better) as part of one overall team. The better) as part of one overall team. The purpose is not assigned to the rank and purpose is not assigned to the rank and file, but is shared from top to bottom.file, but is shared from top to bottom.

Calculate Process Sigma firstCalculate Process Sigma first

How to Calculate Process SigmaHow to Calculate Process SigmaConsider a power company for Consider a power company for illustration purposes: A power illustration purposes: A power company measures their company measures their performance in uptime of available performance in uptime of available power to their grid. Here is the 5 step power to their grid. Here is the 5 step process to calculate your process process to calculate your process sigma.sigma.

Steps involved Steps involved Step 1: Define Your OpportunitiesStep 1: Define Your Opportunities

An opportunity is the lowest defect noticeable by a customerAn opportunity is the lowest defect noticeable by a customer. . This definition, of course, is debatable within the Six Sigma This definition, of course, is debatable within the Six Sigma community. community.

"Typically, most products (and services) have more than one "Typically, most products (and services) have more than one opportunity of going wrong. opportunity of going wrong.

For example, it is estimated than in electronics assembly a For example, it is estimated than in electronics assembly a diode could have the following opportunities for error: 1) diode could have the following opportunities for error: 1) Wrong diode and 2) wrong polarity (inserted backwards), so Wrong diode and 2) wrong polarity (inserted backwards), so for each assembly shipped, at least two defect opportunities for each assembly shipped, at least two defect opportunities could be assigned for each diode. could be assigned for each diode.

Apparently, some manufacturers of large complex equipment Apparently, some manufacturers of large complex equipment with many components prefer to [count two opportunities in with many components prefer to [count two opportunities in this case]. “This approach dilutes Six Sigma metrics."this case]. “This approach dilutes Six Sigma metrics."

Many Six Sigma professionals support the counter Many Six Sigma professionals support the counter point. I always like to think back to the pioneer of point. I always like to think back to the pioneer of Six Sigma, Motorola. They built pagers that did not Six Sigma, Motorola. They built pagers that did not require testing prior to shipment to the customer. require testing prior to shipment to the customer.

Their process sigma was around six, meaning that Their process sigma was around six, meaning that only approximately 3.4 pagers out of a million only approximately 3.4 pagers out of a million shipped did not function properly when the shipped did not function properly when the customer received it. The customer doesn't care if customer received it. The customer doesn't care if the diode is backwards or is missing, just that the the diode is backwards or is missing, just that the pager works.pager works.

Returning to our power company example, an Returning to our power company example, an opportunity was defined as a minute of uptime. That opportunity was defined as a minute of uptime. That was the lowest (shortest) time period that was was the lowest (shortest) time period that was noticeable by a customer.noticeable by a customer.

Step 2: Define Your DefectsStep 2: Define Your Defects

Defining what a defect is to your customer is not Defining what a defect is to your customer is not easy either. You need to first communicate with easy either. You need to first communicate with your customer through your customer through focus groups, , surveys, or , or other other voice of the customer tools. To Motorola pager . To Motorola pager customers, a defect was defined as a pager that did customers, a defect was defined as a pager that did not function properly.not function properly.

Returning to our power company example, a defect Returning to our power company example, a defect is defined by the customer as one minute of no is defined by the customer as one minute of no power. An additional defect would be noticed for power. An additional defect would be noticed for every minute that elapsed where the customer every minute that elapsed where the customer didn't have power available.didn't have power available.

Step 3: Measure Your Opportunities and DefectsStep 3: Measure Your Opportunities and Defects

Now that you have clear definitions of what an opportunity Now that you have clear definitions of what an opportunity and defect are, you can measure them. and defect are, you can measure them.

The power company example is relatively straight forward, The power company example is relatively straight forward, but sometimes you may need to set up a formal data but sometimes you may need to set up a formal data collection plan and organize the process of data collection. collection plan and organize the process of data collection.

Returning to our power company example, here is the data Returning to our power company example, here is the data we collected:we collected:Opportunities (last year): 525,600 minutesOpportunities (last year): 525,600 minutesDefects (last year): 500 minutesDefects (last year): 500 minutes

Step 4: Calculate Your YieldStep 4: Calculate Your Yield

The process yield is calculated by The process yield is calculated by subtracting the total number of defects subtracting the total number of defects from the total number of opportunities, from the total number of opportunities, dividing by the total number of dividing by the total number of opportunities, and finally multiplying the opportunities, and finally multiplying the result by 100.result by 100.

Returning to our power company example, Returning to our power company example, the yield would be calculated as:((525,600 - the yield would be calculated as:((525,600 - 500) / 525,600) * 100 = 99.90%500) / 525,600) * 100 = 99.90%

Step 5: Look Up Process Step 5: Look Up Process SigmaSigma

The final step (if not using the The final step (if not using the Process Sigma Calculator) is to Process Sigma Calculator) is to look up your sigma on a sigma look up your sigma on a sigma conversion table, using your conversion table, using your process yield calculated in Step 4.process yield calculated in Step 4.

Customer CTQs - Defining Customer CTQs - Defining Defect, Unit and OpportunityDefect, Unit and Opportunity

Start With The CustomerStart With The Customer

Before you can define your process defects, units and Before you can define your process defects, units and opportunities, you need to understand the needs of your opportunities, you need to understand the needs of your customers. customers.

Voice of the Customer (Customer Needs, eSurveys, Focus Voice of the Customer (Customer Needs, eSurveys, Focus Groups, Surveys) is the process of gathering customer Groups, Surveys) is the process of gathering customer comments/quotes and translating them into issues and comments/quotes and translating them into issues and specifications. specifications.

From these comments, issues and specifications come the From these comments, issues and specifications come the customer CTQ (Critical To Quality) customer CTQ (Critical To Quality) – a product or service – a product or service characteristic that must be met to satisfy a customer characteristic that must be met to satisfy a customer specification or requirement.specification or requirement.

CTQ Examples Including Defect, Unit and Opportunity Area: Call Center Customer Quote: 'I consistently wait too long to speak to a representative.' CTQ Name: Representative Responsiveness CTQ Measure: Time on hold (seconds) CTQ Specification: Less than 60 seconds from call connection to the automated response system Defect: Calls with hold time equal and greater than 60 seconds Unit: Call Opportunity: 1 per call

Calculate Your Sigma (Plug in the values below to calculate Sigma)

Defects: 263 calls

Units: 21,501 calls

Opportunities: 1 per call

Sigma: 3.75

Area: Book Publisher Customer Quote: 'I can't stand typos in books I purchase.' CTQ Name: Typographic Quality CTQ Measure: Number of typographical mistakes CTQ Specification: Zero typographical mistakes Defect: Any typographical mistakes Unit: A word Opportunity: Words per book

Calculate Your Sigma (Plug in the values below to calculate Sigma)

Defects: 2 typographical mistakes

Units: 100,000 (500 words/page x 200 pages/book)

Opportunities: 1 per word

Sigma: 5.61

Area: Printed Circuit Board Manufacturing Customer Quote: 'Boards must work when I plug them in.' CTQ Name: Board Functionality CTQ Measure: Non-functioning or improperly functioning boards CTQ Specification: All boards function properly (a board wil not function properly if any individual component is bad) Defect: Any non-functioning or improperly functioning board Unit: A board Opportunity: Total number of parts plus solder points

Calculate Your Sigma (Plug in the values below to calculate Sigma)

Defects: 18 boards

Units: 1,000 boards

Opportunities: 58 (1 board + 13 resistors + 4 capacitors + 2 diodes + 38 solder points)

Sigma: 4.92

Current Method for Calculating Sigma Score

In the current method used to calculate process performance on the sigma scale, the area on a standard normal curve extending from a point some Z-value to the right of center (the mean line) to infinity represents the percent of defects. Figure 1 illustrates this definition of Z-score.

Figure 1: Illustrated Z-Score Calculation

It becomes a bit more confusing once the 1.5 shift in sigma value is considered to account for long- and short-term conversions. Short-term performance is obtained by adding 1.5 to the long-term value. The shift of 1.5 is attributed to a Motorola conclusion that a process has tighter variance in the short term. Over the long term, however, because of issues such as weather, set-up changes, shift changes, batch changes and operator changes, the variation in the process increases – leading to a performance impact of about 1.5 on the Z-scale.

The traditional calculation method The traditional calculation method results in the following Z-scores for results in the following Z-scores for error free processes:error free processes:

0 percent error-free yield = negative 0 percent error-free yield = negative infinity Z-score infinity Z-score

50 percent error-free yield = 1.5 Z-50 percent error-free yield = 1.5 Z-score score

99.99966 percent error-free yield = 6.0 99.99966 percent error-free yield = 6.0 Z-score Z-score

100 percent error-free yield = positive 100 percent error-free yield = positive infinity Z-scoreinfinity Z-score

Figuring the sigma for most processes is pretty easy. A Figuring the sigma for most processes is pretty easy. A calculator is helpful, but no advanced math is needed. calculator is helpful, but no advanced math is needed. What is needed is basic data and definitions for the What is needed is basic data and definitions for the following:following:

The “unit,” or item being delivered to the customerThe “unit,” or item being delivered to the customer

The “requirements” that make the unit good or bad for The “requirements” that make the unit good or bad for the customerthe customer

The number of requirements, or defect opportunities, for The number of requirements, or defect opportunities, for each uniteach unit

For example, in the pizza business, our unit is a pizza! We For example, in the pizza business, our unit is a pizza! We determine the four main “requirements”: determine the four main “requirements”:

correct ingredients, hot, on time, and undamaged.correct ingredients, hot, on time, and undamaged.

These four requirements are also the four “defect These four requirements are also the four “defect opportunities” for each pizza.opportunities” for each pizza.

We collect data on 500 delivered pizzas and find that 25 were late, We collect data on 500 delivered pizzas and find that 25 were late, 10 were too cold, 7 were damaged, and 16 had wrong ingredients. 10 were too cold, 7 were damaged, and 16 had wrong ingredients.

To calculate sigma, we take the total number of defects counted, To calculate sigma, we take the total number of defects counted, divide by the total number of units, and multiply by the number of divide by the total number of units, and multiply by the number of defect opportunities:defect opportunities:

(25+10+7+16)(25+10+7+16) 500 x 4500 x 4

This gives us 58 / 2000, or 0.029; we call this defects per This gives us 58 / 2000, or 0.029; we call this defects per opportunity (DPO).opportunity (DPO).

As we explained earlier, we usually consider 1 million opportunities, As we explained earlier, we usually consider 1 million opportunities, soso

that would be 29,000 defects per million opportunities (DPMO). that would be 29,000 defects per million opportunities (DPMO).

Now all you do is look up that DPMO number in a table to find what Now all you do is look up that DPMO number in a table to find what sigma it represents.sigma it represents.

In this case, the pizza process is performing at about 3.3 sigma.In this case, the pizza process is performing at about 3.3 sigma.