**1.0 Introduction**

In recent decades, industry has been fluctuated with different approaches to process improvement. Even though the suggested exercises by professional quality groups such as W. Edwards Demming and emphasized in the probe for the Baldridge Award were valuable, the results were often self-serving and difficult to measure. Six Sigma is a data-driven approach that trusts intensively on the “voice of the client” as a focus for improving operational businesses and work environments. Consequently, the process is far less subjective than previous “quality” programs and recognizes that measurable results are top to the influence of change. When employed effectively, Six Sigma is a part of a company’s culture and, from an organizational perspective; this means to solutions that notably improve the efficiency of business practices. Six Sigma was fugled by companies such as Motorola and General Electric and was focused on achieving efficiency gains in manufacturing processes. Today, the program has developed into an effective tool for a diverse range of businesses. For instance, nowadays construction companies also utilize the project management control system to perceive the differences between special and common causes of variation. In this paper, I have brought some examples in the field of construction projects and have matched the concept of Six Sigma with them.

**2.0 Literature Review**

**What is Six Sigma?**

Six Sigma is an approach to quality improvement in which it decreases the costs and increases productivity and profits through statistical and problem-solving tools that brings about breakthrough improvements with measurable influence on the bottom-line.

Sigma (s) is a measurement of quality which enables the determination of how effectively defects and variations from processes are eliminated. The various sigma levels are as follows: (Defects per million Error-free rate opportunities)

Two Sigma 308,537 69.2%

Three Sigma 66,807 93.3%

Four Sigma 6,210 99.4%

Five Sigma 233 99.977%

The processes in a Six Sigma-rated project operate at only 3.4 defects per million opportunities, or 99.9997% error-free.

**HISTORICAL PERSPECTIVE ON SIX SIGMA**

In the mid-1980s, Motorola, under the leadership of Robert W. Galvin, was the primary developer of Six Sigma. Bill Smith, a senior engineer and scientist within Motorola’s Communications Division, had subtilized that its final product tests had not anticipated the high level of system failure rates Motorola was experiencing. He recommended that the increasing level of complexity of the system and the resulting high number of opportunities for failure could be possible causes for this. He came to the conclusion that Motorola needed to require a higher level of internal quality, and he brought this idea to then-CEO Bob Galvin’s attention, persuading him that Six Sigma should be set as a quality goal. This high goal for quality was new, as was Smith’s way of viewing reliability of a whole process (as measured by mean time to failure) and quality (as measured by process variability and defect rates).

**3.0 Data Analysis and Discussion**

Before bring the examples, let me focus on some definitions and structure of Six Sigma as follows:

Each Six Sigma project follows the “DMAIC” which is depicted to below phases:

**Define phase**

· - Identify the problem

· - Define Requirement

· - Define goal / change vision

· - Set Goals

· - Clarity scope & customer requirements

**Measure phase**

· - Validate problem / process

· - Measure performance to requirements

· - Refine problem / goal

· - Gather process efficiency data

· - Measure key steps / input

**Analysis phase**

· - Develop Causal hypotheses

· - Identify Best practices

· - Identify Vital few Root causes

· - Assess process design

· - Validate hypothesis

· - Refine requirements

**Improve phase**

· - Develop Ideas to remove root cause

· - Design new process

· - Test solutions

· - Implement new process structure, systems

· - Standard solution measure results

**Control phase**

· - Establish standard measure to maintain performance

· - Establish measure & receives to maintain performance

· - Correct problem as need

· - Correct problem as needed

In here, I would like to introduce a Synthetic model of Six Sigma which is named Lean Six Sigma. It is a combination of Lean methods and Six Sigma approaches. It is also sometimes referred to as Six Sigma Lean. Lean Six Sigma builds on the knowledge; methods and tools derived from decades of operational improvement research and implementation.

measuring and eliminating defects. The Lean Six Sigma approach draws on the philosophies, principles and tools of both. The structure of Lean Six Sigma has been showed on below Figure (1):Lean approaches focus on reducing cost through process optimization. Six Sigma is about meeting customer requirements and stakeholder expectations, and improving quality by measuring and eliminating defects. The Lean Six Sigma approach draws on the philosophies, principles and tools of both. The structure of Lean Six Sigma has been showed on below Figure (1):**Figure (1)**

**Lean Six Sigma incorporates, and deploys, the key methods, tools and techniques of its predecessors**

*Lean focuses on waste elimination in existing processes*

*Six Sigma focuses on Continuous Process Improvement (DMAIC) to reduce variation in existing processes*

*Six Sigma also focuses on New Process Design/Complete Redesign (DMEDI) for wholesale redesign of processes as well as new products and services*
cc As you can see, DMAIC is the real structure of Six Sigma.

Now, I would like to illustrate two examples of Construction projects compatible with DMAIC as follows:

**Example (1): An executive method for embankment layers in roads and yards**

**Define of the problem (D phase):**

In this example, I have tried to show what is the distance between two consecutive soil storage area that they have been unloaded by Damp Trucks for reaching to designing specifications in the roads and yards.

It is possible only with having results of laboratory tests.

Easily, we can see that above problem is independent of optimum moisture. When we proceed to execute a compacted layer, for example: soil, Base, Sub base layer in road and yards, we should

**know how much the soil or aggregate (as a base or sub base layer) per square meter is need for reaching to specifications of design (thickness, percentage of compaction).****Measure phase (M):**

In this phase we approach on validate and refine problem accompanied by measuring of requirements. In this example it has been raised: “what is the distance between unloading of two consecutive Damp Trucks a long road so that two important specifications are produced?”

What are the two important specifications? (Measuring of requirements)

After designing of a pavement for roads or yards, civil engineer obtains several layers of aggregates (base or sub base) and soil that they must be compacted and

**executed under asphalt. Each one of these layers has its own specifications included: thickness, percentage of compaction, maximum dry density, optimum moisture, atterburg limits, sandy equalent, crashing percentage and etc.**
Two specifications of them are very important: thickness and compaction percentage

**.****Analysis phase (A):**

In order to execute a filling layer on sub grade in the road, we start it in accordance with four

**stages as follows:****A) Unloading of soil or aggregate on required area (XY) of sub grade with required volume (V**

_{1}) by a Damp Truck.**B) To distribute storage area of soil (Unloaded by Damp Truck) by a Grader so that the soil or aggregate layer reaches to thickness of design specifications.**

**A) Spraying on soil by watering - Can Truck in order to reach the soil or aggregate to optimum moisture.**

**B) To compact the soil or aggregate by a Roller in order to reach to compaction percentage of design specifications.**

**In this analysis, the target is to obtain the required area (XY) for unloading soil of each Damp Truck or the required volume (V**

_{1}) of unloading soil on area (XY) by each Damp Truck for reaching to specifications of design.

**Improve phase (I):****In this phase, we should develop our idea to remove root cause or to solve the problem in which we have to use some tests and standards. At the first, we should define some parameters in accordance with the standards as follows:**

**- w% Natural moisture of the soil**

**- Dn Natural unit weight (Free unit weight of the soil)**

**- Dm Maximum dry density**

**- R % Compaction Percentage (Design Specification)**

**- Z Thickness of layer (Design specification)**

**- V**

_{2}Volume of dry compacted soil after filling**- m**

_{2}Weight of dry compacted soil after filling**- m**

_{1}Weight of natural soil (Free)**- A required Area (XY) for unloading soil of each Damp Truck**

**- V**

_{1}required Volume of unloading soil on Area (XY) by each Damp Truck**In order to solve above problem, I has used from returning analyze as follows:**

**An element of soil (X, Y, Z) has been considered after executing of the last stage (stage D).**

**Where:**

**V2 = Z.X.Y (1)**

**m**

_{2 =}Dm. Z.X.Y.R (2)**m**

_{1 = }m2 + (m2 * w %) = m2 (1_{ + }w %) (3)**Therefore, it could be used from below formula:**

**V1 = m1 / Dn= Dm.Z.X.Y.R((1**

_{ + }w %) / Dn (4)**X.Y = A = V1. Dn / Dm.Z.R((1**

_{ + }w %) (5)**Now, we can solve two samples as follows:**

**Sample (1):****w = 3 %**

**Dm = 2.17 gr / cm3**

**R = 95 %**

**Dn = 1.53 gr / cm3**

**A = 10000 cm2**

**Z=15Cm**

**V1 = 2.17 * 15 * 10000 * 95 % * (1 + 3 %) / 1.53**

**V1 = 0.2 m3**

**Sample (2):****w = 3 %**

**Dm = 2.17 gr / cm3**

**R = 95 %**

**Dn = 1.53 gr / cm3**

**V1 = 6 m3 = 6000,000 cm3**

**Z=15Cm**

**6000,000 = 2.17 * 15 * 95 % * (1 + 3 %) A / 1.53**

**A = X.Y= 288226 cm2**

**A # 29 m2**

**Control phase (C):****In this phase, we proceed toward to check and control our solution by executing real job at the site. We assume that it has been done the embankment of 10000 m3 on the road and according to the results of tests; there are 2 m3 of embankment as defects incompatible with our solution. We can calculate DPMO (Defects per million opportunities), Sigma Levels as follows:**

**DPMO = (2 / 10000) * 1000000 = 200**

**The number of DPMO can be converted to the Sigma level. For instance, in this example, 200 DPMO converts to slightly better than a 5 Sigma process.**

**Example (2):****An Executive method for concrete placing (Cast - in - Place)**

**In Small building Sites**

**Define of the problem (D phase):****There is the lack of the executive method for concrete placing at small building sites. Since there is not a mechanized and automatic systems for concrete placing ( Cast - in - place ) in small building sites (included : Batching plant , Batch mixer , Truck mixer , … ) , a contractor has to utilizes from drum mixer or handling mixer by volume batching method . When you use the drum mixer, you cannot produce the fresh concrete in accordance with weight batching and standards. In fact, you have to use from the volume batching by scaling of a bushel so that you will lose the accuracy of your job and increase errors.**

**Measure phase (M):****Since we have the standards to prepare the formula of the concrete mix design by using of weight batching, I has tried to show changing of weight batching to volume batching of concrete materials (cement, water, aggregates) so that weight batching has already obtained by using of ACI 211 (Concrete Mix Design). In order to execute concrete placing (cast-in-place) at the sites, it is needed to be obtained a mix design of concrete.**

**A mix design of concrete (in accordance with ACI-211) introduces us only the weight batching of cement, water, aggregates.**

**We can use from weight batching, if we have had a batching plant, batch mixer, truck mixer…**

**
**

In fact, if we have had a mechanized and automatic system for concrete placing, it can be used only in big and large sites.

But we have to use volume batching instead of weight batching in small sites. In this example, I have presented a method for changing of weight batching to volume batching in which we should measure the compressive strength and workability (slump) of fresh concrete as two important quality factors after using of this executive method.

**Analysis phase (A):**

The analysis of this method is included three following steps in which we need to determine the weight batching in accordance with ACI -211:

1) We should get the results of simple tests on aggregates as follows:

- Sieve analysis of coarse and fine aggregates

- Free unit weight of coarse aggregate

- Free unit weight of fine aggregate

- Free unit weight cement

2) According to above tests results and tables of ACI-211, we can estimate weight batching of concrete materials.

3) We assume weights batching of concrete materials per one cubic meter of the concrete in according with point (2) are as follows:

- Weight of coarse aggregate / 1 m

- Weight of fine aggregate / 1 m^{3}concrete^{3}concrete**- Weight of cement / 1 m**

^{3}concrete

**- Weight of water / 1 m**

^{3}concrete**
**

**Improve phase (I):**

In this phase, we should obtain the solution for the problem mentioned in the phase of Define (D). At the first, we should get the volume of a batch that it is available for us and total volume of Drum Mixer should be recognized that it depends on to type of Drum Mixer (It is Standard).

- Volume of an available batch

- Total Volume of Drum mixer (Volume capacity of Drum mixer)

According to above stated, we have:

- Free Unit weight of coarse aggregate

- Free Unit weight of fine aggregate

- Free Unit weight of Cement

- =1000 Kg / m

^{3}Free Unit weight of Water
In this step, we can get the volume of each one of the concrete materials for one cubic meter of the concrete:

- The volume of coarse aggregate / 1 m

^{3}concrete
- The volume of fine aggregate / 1 m

^{3}concrete
- The volume of Cement / 1 m

^{3}concrete
- The volume of Water / 1 m

^{3}concrete
- Sum of concrete materials volumes

According to Volume of Drum Mixer, we should calculate the volume of concrete materials for one Drum Mixer batch:

- The volume of coarse aggregate / 1 unit Drum Mixer batch

- The volume of fine aggregate / 1 unit Drum Mixer batch

- The volume of Cement / 1 unit Drum Mixer batch

- The volume of Water / 1 unit Drum Mixer batch

We should get number of batches:

Number of total batches

Now, we can get number of batches for each material of the concrete with using of below formula:

Where:

- Each one of the concrete materials (aggregate, cement, water)

- Number of batches for each material of the concrete

- Number of total batches

- Weight of each one of the concrete material / 1 m

^{3}concrete
(According to ACI-211 Tables)

- Free Unit weight of each one of concrete material

In here, I would like bring a sample as follows:

**Sample:**

According to ACI-211 Tables, we have obtained amount of materials per one cubic meter of the concrete as follows:

**
**

And so, free unit weight of above materials is below cited:

The volume of Drum Mixer and the Volume of the batch sample are:

Therefore, we have:

Number of Total batches

Now, we can calculate number of batches for each materials of the concrete:

Batches number of coarse aggregate

Batches number of fine aggregate

Batches number of Cement

Batches number of Water

According to above mentioned, we can execute concrete placing by using of ACI-211 or another standard and volume batching method in small sites where there is not any mechanized or automatic system.

Therefore, we can speak about optimum slump, W/C, quality of concrete even in small building sites.

Small building sites could be meant even when we are using of concrete in our homes.

But we should notice, for producing the concrete with high quality, all of aggregates, cement and water should be tested in laboratory before using of them.

**Control phase (C):**

**In this phase, we should control our solution by preparing the samples of fresh concrete or to place the concrete as the real job at the site. We assume that we have executed about 5000 m3 of fresh concrete at the working place and according to the results of tests; there are 1.2 m3 of fresh concrete as defects incompatible with our solution. We can calculate DPMO (Defects per million opportunities), Sigma Levels as follows:**

**
**

DPMO = (1.2/ 5000) * 1000000 = 240

The number of DPMO can be converted to the Sigma level. For instance, in this example, 240 DPMO converts to slightly better than a 5 Sigma process.

**4.0 Conclusion**

Regarding to the examples mentioned in this paper, there are many methods for solving of the problems. At the first, we should know if the problem is actually the problem . It means: Which problem should be solved by us? Further more, we should simplify the complex problem to be perceived easily. Besides,we should know that there are so many ways to solve the problem and we should choose the best one by balancing of Time and Energy (cost).

One of the best ways to solve the problems is to go along step by step as follows:

Step1) To find out exact definition of the problem.

Step2) To make a sentence that is exactly included all of the problem basic concepts (To summarize exact definition of the problem by a sentence).

Step3) To search the guiding channels of knowledge for each word or perfect sentence just like to use of the search engines.

Step4) To select of collected knowledge so that we find out the logical relation among them.

Step5) To find out assumptions, dependent and independent variables (unknowns) by using of Step (4).

Step6) To establish the differential equations by using of Step (5) and the points A to T mentioned in this paper.

Step7) To solve the differential equations by deleting of many variables (unknowns) so that we must observe balance of the Time and Energy (Cost).

Concerning to above steps, we can use of “Equilibrium Theory” for solving of the problems in the world. Maybe, one day we will be able to find out an opportunity of the Reference Frame with datum coordinates by using of Equilibrium Theory and Returning Analysis. We know that all of Equilibrium systems are the unstable and we must spend the energy for increasing of Equilibrium stability time.

Step1) To find out exact definition of the problem.

Step2) To make a sentence that is exactly included all of the problem basic concepts (To summarize exact definition of the problem by a sentence).

Step3) To search the guiding channels of knowledge for each word or perfect sentence just like to use of the search engines.

Step4) To select of collected knowledge so that we find out the logical relation among them.

Step5) To find out assumptions, dependent and independent variables (unknowns) by using of Step (4).

Step6) To establish the differential equations by using of Step (5) and the points A to T mentioned in this paper.

Step7) To solve the differential equations by deleting of many variables (unknowns) so that we must observe balance of the Time and Energy (Cost).

Concerning to above steps, we can use of “Equilibrium Theory” for solving of the problems in the world. Maybe, one day we will be able to find out an opportunity of the Reference Frame with datum coordinates by using of Equilibrium Theory and Returning Analysis. We know that all of Equilibrium systems are the unstable and we must spend the energy for increasing of Equilibrium stability time.

Every project will smoothly move and be successfully fulfilled the least Time and Energy (Cost), if all of people involved in this project as well as know and accept the target of project. In the circumstances, the attractive concepts similar to Excessive Generosity, Hardworking, Perseverance, Honest, Reliable, Love, Truthfulness and so no will be raised. Of course, it is very hard because we have five cases as follows:

1)Training: All of people involved in the project should be familiar and learn about the target of the project.

2)To define the aim of the project (What is the problem): All of people involved in the project should accept the target of the project and it is very difficult (Actually, what is the problem?).

1)Training: All of people involved in the project should be familiar and learn about the target of the project.

2)To define the aim of the project (What is the problem): All of people involved in the project should accept the target of the project and it is very difficult (Actually, what is the problem?).

3) To choose the method for internal process. What is the best way to reach our target? How can we measure the best way?

4) Are all people satisfied with the target and output of the project?

What is our strategic plan to satisfy all people such as stakeholders, staff, customers, government, and so on?

5) What area our financial benefits to be obtained of outputs?