Six Sigma DMAIC process

Six Sigma Engineering

  • A Six Sigma Engineer develops efficient and cost effective processes to improve the quality and reduce the number of defects per million parts in a Manufacturing/Production environment.
  • Six Sigma Engineers determine and fine tune manufacturing process. Once a process is improved, they go back and re-tune the process and reduce the defects. This cycle is continued till they reach 3.4 or less defects per million parts.
  • Six Sigma is all about knowledge sharing. If a company has more than one manufacturing unit/plant, its more than likely that one of the plants produces better quality than others. The Six Sigma team should visit this higher quality plant and learn why its performing better than others and implement the techniques learned across all other units.
  • Research/Design department within a company can use the above techniques to learn from another R&D departments in the same company or affiliate companies and implement those techniques.
  • Motorola developed a five phase approach to the Six Sigma process called DMAIC.


  • Define opportunities
  • Measure performance
  • Analyze opportunity
  • Improve performance
  • Control performance

DMAIC Six Sigma Process

Six Sigma Statistics

  • Six Sigma uses a variety of statistics to determine the best practices for any given process.
  • Statisticians and Six Sigma consultants study the existing processes and determine the methods that produce the best overall results.
  • Combinations of these methods will be tested and upon determining that a given combination can improve the process, it will be implemented.
  • Six Sigma stands for “Six Standard deviations from the arithmetic mean”.
  • Six Sigma statistically ensures that 99.9997% of all products produced in a process are of acceptable quality.
  • Six Sigma allows only 3.4 defects per million opportunities.
  • If a given process fails to meet this criteria, it is re-analyzed, altered and tested to find out if there are any improvements.
  • If no improvement is found, the process is re-analyzed, altered and tested again.
  • This cycle is repeated until you see an improvement.

Once an improvement is found, its documented and the knowledge is spread across other units in the company so they can implement this new process and reduce their defects per million opportunities.

Advantages of Six Sigma

  • Save millions without capital investment (making what you have already work better for you)
  • Can be applied to almost business function (administration to production)
  • Leads to trust and higher employee morale within the corporation
  • Ensures customer the same results no matter the division of a large corporation
  • Makes company practices more standard.


  1. An FMEA is primarily considered a problem-solving tool.
    Incorrect. FMEA is primarily a reliability planning tool which considers the effects and causes of potential failure modes on the function or purpose of the part or service.
  2. A DFMEA evaluates the potential failure modes and causes associated with the manufacturing of a product
    Answer:  Incorrect.  A DFMEA evaluates the potential failure modes and causes associated with the design of a product
  3. The use of data to verify the relationships between root causes and effects is one of the critical-to-success factors in the FMEA process.
    Answer:  Correct
  4. FMEA teams will find themselves spending more time than usual early on in the planning process, which will usually lead to delayed product introductions.
    Answer:  Incorrect.  By spending the extra time on an FMEA early on in the planning process, there should be less time spent later debugging the product or service at its introduction to the market.
  5. At the DFMEA level, it is usually recommended to study each subsystem separately, and each component separately.
    Answer: Correct
  6. The objectives of a PFMEA include minimizing production process – based failure effects on the system but usually not minimizing  variation around the design specs due to the process. Answer: Incorrect.  The objectives of a PFMEA usually include both.
  7. When doing both a DFMEA and a PFMEA, it is important to keep the same team members throughout both FMEA processes.
    Answer: Incorrect.  It is typical for some (but not all) of the team members, and maybe even the team leader, to change for the PFMEA to reflect the emphasis on the process, rather than the design, of the part or service.
  8. Besides prioritizing improvement efforts, FMEA can also provide a formal record of reliability and safety analysis.
    Answer: Correct

The  FMEA Quality  Lever – Where  To  Put  The  Effort

If you apply the energy sooner, or further away from the introduction of the product or service, you will get much more leverage for your effort. Waiting to make the improvements or fixes after production starts will require a lot more effort.


In the above diagram, the further upstream you make changes, the more impact you will make.

Where  To  Spend  The  Effort? — Total  Time  Spent

In the sequential approach to product development, more time is typically spent on debugging the product afterit is released to the market.  In  the concurrent approach, more time is spent in the up-front planning.  However, there will usually be much less time spent later on the post-production problem solving.


Spending more planning man hours up front does not mean that the product release time is pushed back. The cross-over point of these two overlaid graphs does not mean anything.  Q Which approach has less area under the curve? Why? A The concurrent approach very often results in 20-40% fewer man hours of total development time, due to the effectiveness of the up-front planning.

The main purpose of FMEA: Besides making customers happier by minimizing  potential failures, identifying necessary changes early, & prioritizing improvement  efforts, FMEA also provides:

  • A formal record of reliability and safety analysis ← The completed FMEA should become part of the design package.
  • A starting point in the preparation of field service policies ← And for preparing trouble-shooting guides.
  • A starting point for a preventive maintenance data base ← From the resulting prioritized preventive actions.
  • An indicator for test point location and sequencing ← From the identified
    causes, & also from the resulting prioritized preventive actions.

Types  Of  FMEA: Design FMEA (DFMEA), Process FMEA (PFMEA)

At the DFMEA level, it is usually recommended to study each subsystem separately, and each component separately.  Their inter-relations can be evaluated in the System FMEA.
The System FMEA examines system deficiencies caused by potential failure modes between the functions of the system.  This includes the interactions between the systems and the elements of the systems.
The PFMEA is conducted on a process, whether it be in a manufacturing or a service environment.  It is generally recommended to study each machine or sub-process separately.  Their inter-relationships can also be studied in a System FMEA.  Service FMEAs are usually not preceded by a DFMEA.

Types Of FMEA

Design FMEA DFMEA – Objectives

  • Maximize system quality and reliability
  • Minimize design-based failure effects on the system
  • Should also take into account DFM/A/(X) principles

Process FMEA PFMEA – Objectives

  • Maximize system quality, reliability, & productivity
  • Minimize production process – based failure effects on the system
  • Minimize variation around the design specs due to the process

The key difference in the objectives between the two is the focus of the FMEA.  When conducting a DFMEA, the team must remember to think in terms of the causes and effects of failure modes due to the design itself.   The causes usually involve product design variables that can be specified by the design team.

Design for Manufacturability/Assembly All other (DFM/A/(X) considerations should be included in the DFMEA as well, e.g., tooling access, robustness to sources of process variation, ability of product to be produced at planned production rates, maintainability, etc. In a PFMEA, the team will be focused on those failure modes and causes that could result from the production or service process itself rather than from the design of the product.

Typical Team Structure:

Design Team:

  • Responsible Design Engineer*  —  Leader
  • Test Engineer/Technician
  • Reliability/Quality Engineer
  • Marketing/Product Manager
  • Material Management/Purchasing
  • Field Service Engineer/Technician Process

the responsible designer will lead the DFMEA team. It is important to have cross-functional participation on the team, including at least some of the members from the after PFMEA team.

Process Team:

  • Responsible Manufacturing/Process Engineer**  —  Leader
  • Design Engineer*
  • Quality/Reliability Engineer
  • Tooling Engineer/Technician
  • Material Management/Purchasing
  • Responsible Operators
  • Maintenance Technician
  • Manufacturing/Process Engineer**

Usually, but not always, the leadership of the team changes to the responsible process engineer. This person ideally would have also been on the DFMEA team; and the DFMEA team leader would stay on as a member of the PFMEA team.  Several other team members, but not all, could change to reflect a heavier emphasis on the process under study.

FMEA – Failure Mode and Effects Analysis

Definition of Failure Mode and Effects Analysis

Failure Mode

The manner in which the product/part or service does not meet the customer’s expectations

Effects Analysis

A study of the effects of failure on the function or purpose of the product/part or service The customer could be external to the company, or internal (within the company). It is considered a reliability planning tool, but it has also become a method for prioritizing alternative actions (that do not deal with failure modes), e.g., in the Six Sigma process.

FMEA is a systematized group of activities intended to:

  • Recognize and evaluate the potential failure modes and causes associated with the designing and manufacturing of a product
  • Identify actions which could eliminate or reduce the chance of the potential failure occurring
  • Document the above process.

It increases the likelihood that potential failures, and their effects and causes, will be considered prior to the final design and/or release to production. The key to the actions in this Reliability Analysis method is to plan preventive actions. A completed FMEA, which should be applied in an iterative process, contains a great deal of information about the product or process. It can be used as the starting point for later control plans, trouble-shooting guides, preventive maintenance plans, etc.

Key Things To Keep In Mind

“One of  the most important factors for the successful implementation of an FMEA program is timeliness…  Up front time spent properly completing an FMEA well, when product/process changes can be most easily and inexpensively implemented, will minimize late change crises.” AIAG FMEA Instruction Manual (3rd Edition)When going through the FMEA process, it is also important to remember to base your decisions on data, not on hunches! It should occur very early in the planning cycle.  FMEA teams will find themselves spending more time than usual early on, which will lead to leveraged savings later on. The use of data to verify the relationships between root causes and effects, to establish accurate rating criteria, and to determine effective preventive actions is one of the critical-to-success factors in the FMEA process.

Costs vs. Benefits

Lots of Tedious Work →  Increased success of implementation, & knowledge well captured by the cross-functional team.
Do not expect the up-front investigation and analysis to be quick or easy, but the extra initial work will typically provide an excellent payback.

Decision Tree for Selecting Type of Variables in Sampling Plan


Determine the AQL to use in the Master Table: Since there are standard AQLs used in the Master Tables, you need to convert the AQL per table below:


Determine the Sample-Size Code Letter to use in the Master Table: ANSI/ASQ Z1.9 Table A.2 Formulas for the Q Value:


Formulas for the Q Value:

For Section B – Standard Deviation Method (σ Unknown):


Note: For 2-sided spec limits, an AQL can be assigned to both limits combined, or to each end of the spec limit separately.
Table B-1 Standard Deviation Method Master Table B-1 for Normal and Tightened Inspection for Plans Based on Variability Unknown (Single Specification Limit)

Obtain the k Value from the Master Table:


Designing your own Variable Sampling Plan


What would be the variables sampling plan (sigma unknown) for the following conditions? High Pa (α = .05) for a fraction non-conforming (P1) of .005, with a low Pa (β = .05) for a fraction conforming (P2) of .03.



Note: with the same operating characteristics, an attribute sampling plan would require n = 274.

Example (Method: Population Sigma Known)

A lot of 1500 bobbins is submitted for inspection. Inspection level II, normal inspection, with AQL = .65%, is to be used. The specified minimum yield value for the tensile strength is 25.0 lbs. The variability σ is known to be 2.4 lbs.

The sample size code letter from Table A.2 is K. In Table D-2 (p. 86 in ANSI/ASQ Z1.9-2003), for reduced inspection, the required sample size is 7 and the k value is 1.80. The 7 sample specimen’s tensile strengths are 25.7, 26.4, 26.1, 27.2, 25.8, 28.3, and 27.4. QL = (X̄-LSL)/σ = 24.6 – 25.0 / 2.4 = 0.63

Since QL < k, the lot does not meet the acceptability criterion and should be rejected.

What are the alpha and beta risks for sampling letter K (p. 23 in ANSI/ASQ Z1.9-2003), for an AQL of .65, for various incoming quality levels (P)?

P Pa α β
Relatively Good Quality .25 99.5 .5
.50 96 4
Marginal .75 90 10 90
1.5 62 38 62
Poor 2.00 46 46
3.0 22 22
4.0 10 10
5.0 4.5 4.5

* All values are in Percentages

Why is the lot rejected even though none of the samples were out of spec? (Assuming this is a representative sample, a larger, +/- 3σ distribution would provide some product out of specification; in this case, in the left tail of the distribution.)

AQL Based Sampling Plans

  • ANSI/ASQ Z1.4-1993 (MIL-STD 105E was withdrawn in February 1995) sampling plans are based on the use of AQL – the percent defective that is considered acceptable as a process average for the purposes of acceptance sampling.
  • With these plans, it is not necessary to assume the provision of 100% screening (with replacement of all defective units) of all rejected lots.
  • To enter any of these tables, you must first decide on the AQL to use (and determine the sample size code letter); from the table you will get the acceptance number (Ac) and the rejection number (Re) for the plan.
  • There are also separate tables to provide the AQL for different values of AQL and sample code letters


– More serious defects should have a lower AQL as the acceptance criterion, and less serious defects can have higher AQLs – using a Classification of Defects system.
– Tightened inspection should be used whenever the quality history is unsatisfactory or when there are other good reasons for being suspicious about quality – keeping the beta risk down.
– Reduced inspection can be used when the quality history is shown to be good enough through Normal inspection.
– These plans are generally chosen to protect the producer under normal conditions, i.e., not to reject submitted lots that are at the AQL or better when there are no reasons to be suspicious about quality.

Double Acceptance Sampling Plans


• There is usually less sampling than for a single sampling plan
• The OC curve is better than the c = 0 curve for the single sampling plan with a smaller R (for better discrimination)

Designing your own double acceptance sampling plan


Desired α risk of .05 for a P1 of .008, along with a desired risk of .10 for a P2 of .06. Use Table 4-4.
1. Determine R:

R = P2/P1 = .060/.008= 7.5

2. Enter Duncan’s Double Sampling Tables and find the closest R to the calculated value in step 1.
The closest table value is 7.54 in Plan Number 2. This is very close to 7.5. Note the c1 value of 1 and the c2 value of 2.

3. For Pa1-α = .95, obtain the nP1 (Pn1 in the table) value. Then calculate n from:

n = nP2/P2 = 0.52/0.008 = 65.

The acceptance sampling plan is n1 = 65, c1 = 1; n2 = 65, c2 = 2.

Variables Sampling Plans

ANSI/ASQ Z1.9 (MIL-STD-414 is withdrawn) sampling plans are based on the use of variable data (from an assumed normal distribution).

Actual measurements are made on the samples : the sample data is used to calculate a statistic, such as X̄, R, or S and then the calculated statistic is compared to the critical value from a table.

Acceptance criteria must be applied separately to each quality characteristic (vs. overall lot accept vs. reject for attribute sampling), so it’s more expensive than attribute sampling for larger lots, so it’s generally best to use only on key characteristics, with attribute sampling on the rest.

Compared to attribute plans, these plans, for the same n, provide a greater quality protection in judging a single quality characteristic, or for the same amount of risk, a smaller n is OK.

The use of variable data can provide more information about the extent of nonconformity – How? (Hint: think frequency distribution and what you can do with this information).

These sampling procedures are based on the assumption that the quality characteristic is normally distributed (it is possible to use data transformation if it is not). Procedure:

To use any of these plans, you must first decide on the:

  • Inspection level (II is the default for Z1.9)
  • Method to use – S or R, with variability (population sigma) known or unknown (see Decision Tree)
  • AQL
  • Lot size

Determine the sample-size code letter from the table

Calculate the Q value

Enter the Master Table by sample size code letter and AQL, and look up the k value.
Compare the k and Q values – if the calculated Q value is ? than the critical k value from the table, accept the lot. If not, reject it.

Sampling Plan Variation vs Lot Size Variation in Acceptance Sampling

If the lot size N changes, the below curves change very little. However, the curves will change quite a bit as sample size n changes. So, basing a sampling plan on a fixed percentage sample size will yield greatly different risks. For consistent risk levels, it is better to fix the sample size at n, even if the lot sizes N vary. Question: If n = 10 & c = 2, what is the alpha risk for a vendor running at p = .02? Answer: Pa is about .55, so alpha is about .45. Question: What is the beta risk if the worst-case quality the customer will accept is 3%? Answer: (about 15%). To lower alpha and beta, you can increase n and c.


Is c = 0 the best plan for the producer and the consumer?


At the 2.8% lot defect rate, both plans give the producer equal protection: Pa = 11%, or Prej = 89%. Which one gives better protection against rejecting relatively good lots, e.g., at the .5% lot defect rate, and why?

For (1), α = about 8% and for (2), α = about 30%.

(1) has a lower α error so less chance of rejecting good lots. With (2), you will reject any lot of 500 if there is even 1 defect in the sample, but it will lead to higher costs.

Increasing Protection from Rejecting Good Lots in Acceptance Sampling

Is c = 0 the best plan for the producer and the consumer?


At the 2.8% lot defect rate, both plans give the producer equal protection: Pa = 11%, or Prej. = 89%. Which one gives better protection against rejecting relatively good lots, e.g., at the .5% lot defect rate, and why? For (1), α = about 8%; for (2), α = about 30%. (1) has a lower α error so less chance of rejecting good lots. With (2), you will reject any lot of 500 if there is even 1 defect in the sample, but it will lead to higher costs.

Discrimination in Acceptance Sampling Plans

Discrimination is the ability of a sampling plan to distinguish between relatively good levels of Quality and relatively bad levels of quality. In other words, having

  • A high Pa (e.g., 95%, 1-α) associated with a good level of quality P1 (e.g., .5% or better)
  • A low Pa (e.g., 10%, β) associated with a bad level of quality P2 (e.g., 3% or worse)

The Operating Ratio is defined as
R = P2/P1 = Pβ/P1-αExample: R = .03/.005 = 6.0

Designing your own single acceptance sampling plan

Derive a plan that comes as close as possible to satisfying two points on the OC curve. The two points are (P1, 1-α) and (P2, β). The derived plan will contain an n and a c value.
Desired α risk of .05 for a P1 of .005, along with a desired risk of .05 for a P2 of .03.
1. Determine R:

R = P2/P1 = .030/.005 = 6.0

2. Enter the Values of Operating Ratio Table with α and β and find the closest R to the calculated value in step 1.
For α = .05 and β = .05, the closest table value is 5.67. This is acceptable since it is slightly more discriminating than 6.0. Note the c value of 3 in the far left column.

3. Obtain the nP1 value in the far right column. Then calculate n from:

n = nP1/P1 = 1.366/.005 = 273.2 or 274.

The acceptance sampling plan is n = 274, c = 3.

Six Sigma Acceptance Sampling

What is acceptance Sampling

Acceptance sampling is a method in which we use statistical sampling to determine whether to accept or reject an outcome.

Operating Characteristic Curve or The OC Curve

The OC curve quantifies the α and β risks of an attribute sampling plan. Below is an ideal OC curve (the bold line) for a situation in which we might want to accept all lots that are, say, ≤ 1% defective and reject all lots that are > 1% defective:


With this ideal (no risks) curve, all batches with ≤ 1% defective incoming quality level would have a probability of acceptance (Pa) of 1.0. And, all lots with > 1% defective would have a Pa of 0. The Pa is the probability that the sampling plan will accept the lot. It is the long-run % of submitted lots that would be accepted when many lots of a stated quality level are submitted for inspection. It is the probability of accepting lots from a steady stream of product having a fraction defective P.

Typical OC Curve

Since there will always be some risks, a more typical looking OC curve looks more like the one listed in the next page. It is based on the Poisson distribution* (with the defective rate < 10% and n is relatively large compared to N).

Acceptance Quality Level (AQL), Rejectable Quality Level (RQL) and Lot Tolerance Percent Defective (LTPD)

AQL – Acceptance Quality Level

The AQL (Acceptance Quality Level), the maximum % defective that can be considered satisfactory as a process average for sampling inspection, here is 1%. Its corresponding Pa is about 89%. It should normally be at least that high.

RQL – Rejectable Quality Level

The RQL (Rejectable Quality Level) is the % defective, here at 5%, that is associated with the established β risk (which is usually standardized at 10%). It is also known as the Lot Tolerance Percent Defective (LTPD).

LTPD – Lot Tolerance Percent Defective

The LTPD of a sampling plan is a level of quality routinely rejected by the sampling plan. It is generally defined as that level of quality (percent defective, defects per hundred units, etc.) which the sampling plan will accept 10% of the time.


* The hyper geometric and binomial distance are also used. The alpha risk is the probability of rejecting relatively good lots (at AQL). The beta risk is the probability of accepting relatively bad lots (at LTPD/RQL). It is the probability of accepting product of some stated undesirable quality; it is the value of Pa at that stated quality level. The OC curves are a means of quantifying alpha and beta risks for a given attribute sampling plan. The Pa value obtained assumes that the distribution of defectives among a lot is random – either the underlying process is in control, or the product was well mixed before being divided into lots. The samples must be selected randomly from the entire lot. The alpha risk is 1 − Pa. The shape of the OC curves is affected by the sample size (n) and accept number (c) parameters. Increasing both the accept number and sample size will bring the curve closer to the ideal shape, with better discrimination.

Download Acceptance Sampling Tutorial in MS Word format

Six Sigma Tutorial

What Is Six Sigma?

Six Sigma stands for Six Standard Deviations (Sigma is the Greek letter used to represent standard deviation in statistics) from mean.  It is a methodology that provides the techniques and tools to improve the capability and reduce the defects in any process.

It was started in Motorola, in its manufacturing division, where millions of parts are made using the same process repeatedly. Eventually Six Sigma evolved and applied to other non manufacturing processes. Today you can apply Six Sigma to many fields such as Services, Medical and Insurance Procedures, Call Centers.


Six Sigma uses a methodology known as DMAIC (Define opportunities, Measure performance, Analyze opportunity, Improve performance, Control performance)  to improve any existing business process by constantly reviewing and re-tuning the process.


Six Sigma methodology can also be used to create a brand new business process from ground up using DFSS (Design For Six Sigma) principles. Six Sigma Strives for perfection. It allows for only 3.4 defects per million opportunities for each product or service transaction. Six Sigma relies heavily on statistical techniques to reduce defects and measure quality.

Six Sigma experts (Green Belts and Black Belts) evaluate a business process and determine ways to improve upon the existing process. The experts can also design a brand new business process using DFSS (Design For Six Sigma) principles. Typically it’s easier to define a new process with DFSS principles than refining an existing process to reduce the defects.

Six Sigma incorporates the basic principles and techniques used in Business, Statistics, and Engineering. These three form the core elements of Six Sigma. Six Sigma improves the process performance, decreases variation and maintains consistent quality of the process output. This leads to defect reduction and improvement in profits, product quality and customer satisfaction.

Six Sigma methodology is also used in many Business Process Management initiatives these days. These Business Process Management initiatives are not necessarily related to manufacturing. Many of the BPM’s that use Six Sigma in today’s world include call centers, customer support, supply chain management and Project Management.

Lean Six Sigma

Some Six Sigma practitioners have In recent years combined Six Sigma ideas with lean manufacturing to invent new a methodology. This new methodology is called Lean Six Sigma.

Key Elements of Six Sigma

Customer requirements, design quality, metrics and measures, employee involvement and continuous improvement are main elements of Six Sigma Process Improvement.

Customer Satisfaction

Defining Processes and defining Metrics and Measures for Processes

  • Using and understanding Data and Systems
  • Setting Goals for Improvement

Team Building and Involving Employees

Involving all employees is very important to Six Sigma. The company must involve all employees. Company must provide opportunities and incentives for employees to focus their talents and ability to satisfy customers.

Defining Roles: This is important to six sigma. All team members should have a well defined role with measurable objectives.

Six Sigma in Business

Even though it was initially implemented at Motorola to improve the manufacturing process, all types of businesses can profit from implementing Six Sigma.

Businesses in various industry segments such as Services industry (Example: Call Centers, Insurance, Financial/Investment Services), Ecommerce industry (Example: B2B/B2C websites), Education can definitely use Six Sigma principles to achieve higher quality. Many big businesses such as GE and Motorola have successfully implemented Six Sigma but the adaptation by smaller businesses has been very slow.

Here are some of the reasons to consider:

  • Bigger companies have resources internally who are trained and also have ‘Train the Trainer’ programs using which they churn out many more Six Sigma instructors. Also many bigger companies encourage the employees to learn Six Sigma process by providing Green Belts/Black Belts as mentors.
  • Effectively applying the Six Sigma techniques is difficult compared to actually learning the techniques in a class. Big companies make it a part of the goal for employees and provide incentives for employees who undergo training and mentor colleagues.
  • Many assume that that SS works for bigger companies only as they produce in volumes and have thousands of employees. This notion is not true and Six Sigma can be effectively applied for small businesses and even companies with fewer than 10 employees.
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