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Lean Six Sigma Tools To Use With DMAIC

An organization requires good quality information to operate. It also needs the processes to meet these requirements. Organizations look for ways to improve the service they offer to their customers. It is their service that sets them apart from their competitors. The cost of quality (CoQ) is usually 25% of their sales, but this can easily be as high as 40 to 50%. What happens when quality is compromised? So, why is quality so important? Why do successful organizations put so much emphasis on quality? One way to answer this question is to consider the costs incurred by an organization when quality suffers. Here's a quick list of a few: Warranty costs - more goods returned for exchange Production rework - an overhead in the usage of production usage, Wastage - products components that cannot be reused in some manner Re-inspection - to assess the scope and scale of defectsWe must also look at intangible costs that may arise such as lost customer loyalty. You may also note an increase in sales cycle times and loss of revenue. Late deliveries and poor reviews from critical industries you serve may show up. Maintain a consistent quality standard One of the leading approaches in use today is Lean Six Sigma. Lean Six Sigma is a quality management process that uses a scientific method and a wide array of tools and techniques. Some Lean Six Sigma tools are more common than others. They all help to increase the quality of a product or service delivered. Lean Six Sigma is a five-phase process known as DMAIC — Define, Measure, Analyze, Improve and Control. The DMAIC phases and tools are for improving an existing process. Another process, DMADV, creates a new process, with the focus on customers throughout. In this article, our focus is on the DMAIC process. Define: What outcome does our customer expect from this process? Measure: What is the frequency of the defects in the highlighted process? Analyze: Why, When and Where do defects occur in the process? Improve: How best to fix this process for efficiency and with fewer defects? Control: Once improved, how can we keep the improvements in place? Phase # 1: DefineThe desired output of this phase is to establish a clear list of things that will be improved upon. You will determine how to measure improvement. Create a high-level process map as well as a list of what is important to customers (called Critical to Quality).  “Meaningful Impact BUT Manageable in Scope” is the theme while choosing a project. Select the least elaborate and complex process that can make the most impact on the clients. Remember that you are striving for measurable improvement. Do a high-level Value Added/Non-Value Added analysis. Look for the potential to reduce process time or defects.And now, here's a list of useful tools you might use in the Define Phase includes: Failure Modes and Effects Analysis: This tool identifies all the ways a process might fail. It then determines the impact(s) of each failure on other activities Suppliers/Inputs/Process/Outputs/Customers diagram: This tool will lay out the five key elements of any given process. It is critical to show who performs what tasks on what “materials” in the process Value Stream Analysis: A VSA compiles the activities necessary to produce and deliver a product or service. It will separate activities that contribute to value from activities that create waste. It identifies potential opportunities for improvement. To know more about Value Streams, take a look at this excellent article. High-Level Process Map: This tool will depict the process you focus on. It denotes all the steps, the sub-processes, activities, and results in the process. It shows the workflows and results and allows for a complete understanding of the process end-to-end. Voice of the Customer: This is a technique for gathering systematic information on the customer's "needs and wants". It employs surveys and interviews for purposes of validation. It helps to ensure that you include customer needs and requirements in any activity. It provides a project team with a “to be” idea based upon the needs of clients. Clients should be selected from a complete range of customers. Note that this tool requires a data cleaning method for analyzing customer feedback. Lean Six Sigma Project can often move back and forth between the Measure and Analyze phase. That is acceptable. This may be because the team will test a hypothesis in an iterative way. In the Measure Phase, use input gathered in VOC interviews to establish Performance Standards. Performance Standards translate the customer needs into quantified requirements for a process. Phase # 2: MeasureThis stage is vital in setting up an optimized process map. I employ a 5-step approach for this phase:- Develop a sampling strategy. Confirm the measurement system. Establish a baseline by collecting data on defects and possible causes. Are there any discernible patterns in the data? Do a close analysis to be certain. Determine process capability and create a more detailed process map.Now, let us take a look at some tools to use in this phase: Detailed Map of the Current Process and a Situation Assessment. This helps to define the metrics we will gather and measure. For each stage of the process, the map delineates the activities conducted. It also shows the intended output, result or effect of the steps. Data Collection Plan and Data Table –A data collection plan provides a written strategy for collecting data you will use. The plan creates a clear strategy to collect reliable data. This plan gives all team members a reference for clear communication. It outlines the purpose and methods for data collection and links it to project goals. You will use this step to analyze the current measurement system (if any). This will help to determine its accuracy. To complement your Data Table, consider a Trend Chart. Trend Charts, also run charts, can show trends in data over a period of time. Many processes can vary due to different locations or different shifts. Single point measurements can be misleading. Trend Charts can show a "dip" or "spike" you may need to study. When you display process data over time, you understand the real performance versus a target. Process Capability is a tool I like to use in my analysis of an existing process. Process Capability is a test to measure if a process will meet customer requirements. Will it meet or exceed what customers expect from the process? Using throughput is one way to determine existing capability. If you are gathering large amounts of data, a histogram can display it in a useful visual summary. Another useful chart is the Pareto Chart. This chart can display an uneven distribution of defects. Think of the 80-20 rule. "20% of the clients cause 80% of the problems". Many defects can follow a similar type of pattern. A few steps in a process can account for a large percentage of defects. This will show how frequently a defect occurs. It helps rank steps and allows you to go after "easy pickings". Phase # 3: Analyze The third phase in Lean Six Sigma DMAIC is the Analyze phase. The tools for the Analyze phase make sense of the data collected during the Measure phase. The team uses the data to confirm a source of waste such as delays or quality defects. One challenge to be aware of is sticking to the data. The experiences of members can point in a specific direction for root causes. The aim of this phase is to note any patterns for the Improve phase. Now let us take a look at the tools. Fish-bone or Cause and Effect Diagram. This provides a visual display of all possible causes of a specific problem. Use it in the context of a group. It can expand discussion for all possible causes, to cover all the bases. It allows a team to do a better job of identifying correct causes, rather than what may appear to be “most obvious”. A 5-Why analysis method couples well with a Cause and Effect Diagram. You use it to move past symptoms you detect and understand the true root cause of waste. The 5-Why analysis is more than an iterative process or a simple question asking activity. The purpose is to get the right people discussing any possible root causes of a given defect in a process. Many times teams will stop once a reason for a defect appears to them. The problem's root cause can still hide below this initial layer. I like to use a Cost of Poor Quality Calculation on Marketing and Sales LSS projects. Cost of Poor Quality Calculation will quantify money lost due to waste. It is important because it can provide insight into potential value when you make changes. Phase # 4: Improve This is the phase where improvement strategies are put into place. You characterize and examine the variables you've identified. In developing a solution, you design and pilot this solution to test it. You test this solution as a hypothesis and confirm if it works before a large scale roll-out. The roll-out includes training, support, technology changes, and the process/documentation changes. The tools in the Improvement phase are quite varied. You match the tool to the problem you face. Depending on the project you will look at a tool based on many factors. These factors might be complexity, data availability or business impact. Sometimes, an acceptable solution can come from a tool in an earlier phase. Other times you need a more complex tool. An entire article can be a dedication to going through the list. Here are some common tools for this phase. Phase # 5: Control The Control Phase is the last phase of DMAIC that is most vital. Unless you add documentation to a process it will degrade over time and lose any gains from the project. The outcome you look for is to make sure the new process stays in control after you implement the new solution. I detail several of these tools below in a previous article about business requirements documents. Below is a list of some plans that need to be incorporated as part of the Control Phase. Control plan Monitoring plan Response plan Training plan When you complete a DMAIC project, you will want to assess whether the process improvement met the requirements of the customer. You will understand whether the solution resulted in any benefits that are unexpected or in addition to goals set out in the beginning. You will be equipped to leverage the solution to other projects in your operation with clarity on whether there’s buy-in to keep the intended change or solution in place.
Lean Six Sigma Tools To Use With DMAIC
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Lean Six Sigma Tools To Use With DMAIC

An organization requires good quality information to operate. It also needs the processes to meet these requirements. Organizations look for ways to improve the service they offer to their customers. It is their service that sets them apart from their competitors. The cost of quality (CoQ) is usually 25% of their sales, but this can easily be as high as 40 to 50%. What happens when quality is compromised? So, why is quality so important? Why do successful organizations put so much emphasis on quality? One way to answer this question is to consider the costs incurred by an organization when quality suffers. Here's a quick list of a few: Warranty costs - more goods returned for exchange Production rework - an overhead in the usage of production usage, Wastage - products components that cannot be reused in some manner Re-inspection - to assess the scope and scale of defectsWe must also look at intangible costs that may arise such as lost customer loyalty. You may also note an increase in sales cycle times and loss of revenue. Late deliveries and poor reviews from critical industries you serve may show up. Maintain a consistent quality standard One of the leading approaches in use today is Lean Six Sigma. Lean Six Sigma is a quality management process that uses a scientific method and a wide array of tools and techniques. Some Lean Six Sigma tools are more common than others. They all help to increase the quality of a product or service delivered. Lean Six Sigma is a five-phase process known as DMAIC — Define, Measure, Analyze, Improve and Control. The DMAIC phases and tools are for improving an existing process. Another process, DMADV, creates a new process, with the focus on customers throughout. In this article, our focus is on the DMAIC process. Define: What outcome does our customer expect from this process? Measure: What is the frequency of the defects in the highlighted process? Analyze: Why, When and Where do defects occur in the process? Improve: How best to fix this process for efficiency and with fewer defects? Control: Once improved, how can we keep the improvements in place? Phase # 1: DefineThe desired output of this phase is to establish a clear list of things that will be improved upon. You will determine how to measure improvement. Create a high-level process map as well as a list of what is important to customers (called Critical to Quality).  “Meaningful Impact BUT Manageable in Scope” is the theme while choosing a project. Select the least elaborate and complex process that can make the most impact on the clients. Remember that you are striving for measurable improvement. Do a high-level Value Added/Non-Value Added analysis. Look for the potential to reduce process time or defects.And now, here's a list of useful tools you might use in the Define Phase includes: Failure Modes and Effects Analysis: This tool identifies all the ways a process might fail. It then determines the impact(s) of each failure on other activities Suppliers/Inputs/Process/Outputs/Customers diagram: This tool will lay out the five key elements of any given process. It is critical to show who performs what tasks on what “materials” in the process Value Stream Analysis: A VSA compiles the activities necessary to produce and deliver a product or service. It will separate activities that contribute to value from activities that create waste. It identifies potential opportunities for improvement. To know more about Value Streams, take a look at this excellent article. High-Level Process Map: This tool will depict the process you focus on. It denotes all the steps, the sub-processes, activities, and results in the process. It shows the workflows and results and allows for a complete understanding of the process end-to-end. Voice of the Customer: This is a technique for gathering systematic information on the customer's "needs and wants". It employs surveys and interviews for purposes of validation. It helps to ensure that you include customer needs and requirements in any activity. It provides a project team with a “to be” idea based upon the needs of clients. Clients should be selected from a complete range of customers. Note that this tool requires a data cleaning method for analyzing customer feedback. Lean Six Sigma Project can often move back and forth between the Measure and Analyze phase. That is acceptable. This may be because the team will test a hypothesis in an iterative way. In the Measure Phase, use input gathered in VOC interviews to establish Performance Standards. Performance Standards translate the customer needs into quantified requirements for a process. Phase # 2: MeasureThis stage is vital in setting up an optimized process map. I employ a 5-step approach for this phase:- Develop a sampling strategy. Confirm the measurement system. Establish a baseline by collecting data on defects and possible causes. Are there any discernible patterns in the data? Do a close analysis to be certain. Determine process capability and create a more detailed process map.Now, let us take a look at some tools to use in this phase: Detailed Map of the Current Process and a Situation Assessment. This helps to define the metrics we will gather and measure. For each stage of the process, the map delineates the activities conducted. It also shows the intended output, result or effect of the steps. Data Collection Plan and Data Table –A data collection plan provides a written strategy for collecting data you will use. The plan creates a clear strategy to collect reliable data. This plan gives all team members a reference for clear communication. It outlines the purpose and methods for data collection and links it to project goals. You will use this step to analyze the current measurement system (if any). This will help to determine its accuracy. To complement your Data Table, consider a Trend Chart. Trend Charts, also run charts, can show trends in data over a period of time. Many processes can vary due to different locations or different shifts. Single point measurements can be misleading. Trend Charts can show a "dip" or "spike" you may need to study. When you display process data over time, you understand the real performance versus a target. Process Capability is a tool I like to use in my analysis of an existing process. Process Capability is a test to measure if a process will meet customer requirements. Will it meet or exceed what customers expect from the process? Using throughput is one way to determine existing capability. If you are gathering large amounts of data, a histogram can display it in a useful visual summary. Another useful chart is the Pareto Chart. This chart can display an uneven distribution of defects. Think of the 80-20 rule. "20% of the clients cause 80% of the problems". Many defects can follow a similar type of pattern. A few steps in a process can account for a large percentage of defects. This will show how frequently a defect occurs. It helps rank steps and allows you to go after "easy pickings". Phase # 3: Analyze The third phase in Lean Six Sigma DMAIC is the Analyze phase. The tools for the Analyze phase make sense of the data collected during the Measure phase. The team uses the data to confirm a source of waste such as delays or quality defects. One challenge to be aware of is sticking to the data. The experiences of members can point in a specific direction for root causes. The aim of this phase is to note any patterns for the Improve phase. Now let us take a look at the tools. Fish-bone or Cause and Effect Diagram. This provides a visual display of all possible causes of a specific problem. Use it in the context of a group. It can expand discussion for all possible causes, to cover all the bases. It allows a team to do a better job of identifying correct causes, rather than what may appear to be “most obvious”. A 5-Why analysis method couples well with a Cause and Effect Diagram. You use it to move past symptoms you detect and understand the true root cause of waste. The 5-Why analysis is more than an iterative process or a simple question asking activity. The purpose is to get the right people discussing any possible root causes of a given defect in a process. Many times teams will stop once a reason for a defect appears to them. The problem's root cause can still hide below this initial layer. I like to use a Cost of Poor Quality Calculation on Marketing and Sales LSS projects. Cost of Poor Quality Calculation will quantify money lost due to waste. It is important because it can provide insight into potential value when you make changes. Phase # 4: Improve This is the phase where improvement strategies are put into place. You characterize and examine the variables you've identified. In developing a solution, you design and pilot this solution to test it. You test this solution as a hypothesis and confirm if it works before a large scale roll-out. The roll-out includes training, support, technology changes, and the process/documentation changes. The tools in the Improvement phase are quite varied. You match the tool to the problem you face. Depending on the project you will look at a tool based on many factors. These factors might be complexity, data availability or business impact. Sometimes, an acceptable solution can come from a tool in an earlier phase. Other times you need a more complex tool. An entire article can be a dedication to going through the list. Here are some common tools for this phase. Phase # 5: Control The Control Phase is the last phase of DMAIC that is most vital. Unless you add documentation to a process it will degrade over time and lose any gains from the project. The outcome you look for is to make sure the new process stays in control after you implement the new solution. I detail several of these tools below in a previous article about business requirements documents. Below is a list of some plans that need to be incorporated as part of the Control Phase. Control plan Monitoring plan Response plan Training plan When you complete a DMAIC project, you will want to assess whether the process improvement met the requirements of the customer. You will understand whether the solution resulted in any benefits that are unexpected or in addition to goals set out in the beginning. You will be equipped to leverage the solution to other projects in your operation with clarity on whether there’s buy-in to keep the intended change or solution in place.
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Lean Six Sigma Tools To Use With DMAIC

An organization requires good quality information ... Read More

Project Quality Management: The Key Indicator of Project Success

The PMBOK® defines quality as the degree to which a set of inherent characteristics fulfills requirements.  A project is said to be meeting its quality expectations when all the project requirements agreed at the inception of the project are met, and thus the resulting product or service is usable for the relevant stakeholders.  Quality is Subjective  Quality for one individual will not be adequate for another. For example, the youth will consider a mobile phone as being of high quality based on its look and feel, brand name and its specification such as camera quality, memory capacity, screen resolution, ability to connect with other devices etc. and based on the support to run applications on the phone. However, for someone in the age group of 60 and above, the ability to take a phone call or send an SMS and whether this can be done without much hassle alone may define the quality of the mobile phone.  To understand the quality requirements tailored to projects, it is necessary to have an exhaustive Quality Management training such as the Certified Manager of Quality Training. Quality has many faces The definition of quality depends on the context and the business domain. For a service-oriented organization such as a bank, a restaurant, an airline etc. quality of service is identified through the level of customer satisfaction. For a product such as a mobile phone, a vehicle, a computer etc. quality means conformance to product specifications and its fitness for use.  In the context of healthcare sector, mission-critical military activities etc. quality is measured through precision and accuracy. Precision refers to the granularity of measurement and how fine the outcome can be measured. Accuracy simply put is the correctness of the output or being close to the desired value.   Here are the four things #CIOs need to know about quality https://t.co/gRfqoTEUB7 #Qualitymanagement pic.twitter.com/KHMz5iC6RN — CIOReview (@cioreview) January 7, 2018 Quality is everybody’s responsibility  Quality in project management is two-fold. Project Quality and Product Quality. Project quality is to ensure that the project is executed in line with the triple constraints of time, cost, and scope. If the project is within the defined tolerance levels of these three dimensions, then we can say that the project is of high quality. Projects are carried out to develop a solution; i.e. product, service or a result. If this solution meets its specification or meets the needs of the stakeholders then it is said that the solution is of high quality.   Meeting the quality expectations is not merely the responsibility of the project manager, but of everyone involved in the project. Achieving quality involves cost where it is the responsibility of everyone involved in the project to manage the same. Increased efforts and costs can increase the quality of output but a ceiling on this investment has to be fixed. Yes, it is the responsibility of the project manager to manage this ceiling value and to ensure optimal levels of quality within the project but he or she can only do this with the support of his team members. The optimal level of quality can be achieved when the incremental cost of achieving quality is equal to the incremental revenue from such quality improvements.    What digital transformation means for the future of #qualitymanagement: https://t.co/0gyCaHsKtb — Sparta Systems (@SpartaSystems) January 17, 2018 Cost of Quality In order to achieve this, the project will have to incur some cost and this is known as Cost of Quality. This includes all costs incurred over the life of the product by investment in preventing non-conformance to requirements, appraising the product or service for conformance to requirements and failing to meet requirements or in other words rework. Thus, the cost of quality is of two main types- Cost of Conformance – This is the money spent during the project to avoid failures through prevention or appraisal. Prevention costs are costs incurred to prevent errors by the way of training, documentation, maintenance of equipment, quality control etc. Appraisal costs are incurred to assess the quality by the way of testing (quality assurance), inspections, etc. Cost of Non-Conformance – This involves the money spent during and after the project because of failures. Two main types of such costs are cost of internal failure and cost of external failures. Internal failure costs involve rework, scrap costs that are incurred before the solution is released. External failure costs are more critical where these are incurred to rectify damages of products failing once released to the customer. Such costs include liabilities, warranty, loss of business, damage to image etc.   Quality Management is an important aspect of Project Management. PMI® thus has given a central position to the same when defining the knowledge areas in the PMBOK™. It is thus important for project managers and team members alike to understand the importance of quality and to better manage projects to achieve all expectations pertaining to quality.  
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Project Quality Management: The Key Indicator of P...

The PMBOK® defines quality as the degree to which... Read More

General Concepts And Goals Of Hypothesis Testing

Hypothesis means a supposition or an assumption or a claim. Hypothesis testing forms a critical part while conducting Statistical test and is a part of “DMAIC” methodology in Six Sigma, Analyse phase. Let us look at simple examples where we make assumptions : Increase in price will increase the sales revenue of an organization Pizza delivery outlet has sample of delivery times for the last one month and would like to compare with the competitors target time of 30 minutes In all the above cases we make an assumption and with the help of Statistical tests, we arrive at a conclusion whether the assumption is true or false. So let us see how we can develop the hypothesis and the different criteria used to arrive at conclusion. There are 2 types of Hypothesis: Null and alternative. Null Hypothesis : It means No difference, No effect, Zero impact. Null hypothesis is an assumption that there is no difference in two or more populations with reference to their means or variances. It is denoted by Ho. Thus in the above examples our Ho is : Increase in price does not affect the sales revenue of the organization Target delivery time of the outlet # 30 minutes Alternative hypothesis is exactly the opposite of Null hypothesis. The alternative hypothesis is the hypothesis which the belt is trying to prove. It is denoted by Ha or H1. In the above cases the alternative hypothesis is : Increase in price affects the sales revenue of the organization Target pizza delivery time = 30 minutes Now we need to test the supposition or prove whether the Null hypothesis is true or the alternative hypothesis. Following are the steps which will help us arrive at a decision. Step I : Set up a hypothesis Step II : Set up a Suitable Significance level Step III : Setting a test criterion Step IV : Doing computations Step V : Decision making We have seen how to set up a Null and alternative hypothesis. Step II: Having set up the hypothesis, next step is to test validity of Null against Alternative Hypothesis i.e. Ho vs H1 at a certain level of significance. The confidence with which an experimenter rejects or accepts Ho depends upon the significance level. Here we need to look at Type 1 and Type II errors. Type I error : Rejecting the Null hypothesis when it is true.  is the level of significance and is the probability of rejecting the Null hypothesis when it is true and is usually at 5%. When the hypothesis is accepted at 5% level, we are running the risk in the long run of making a wrong decision 5% of the time. Type II error : Accepting the null hypothesis when it is false. is the probability of accepting the null hypothesis when it is false. (Type I and Type II error is an extensive topic which can be considered for a separate session). Step III : Setting a test criterion After we have decided the Hypothesis and the significance level, we need to understand which is the statistical test to be conducted. One of the most widely used test is the Student t-test. Other tests are F, Chi square etc. Each test makes assumption about your data and the sample drawn from the population. Step IV : Doing computations Depending upon the selection of the test we go ahead and do the computations. There are very good statistical software available and the most commonly used is “Minitab”. We can also perform these tests with the help of Excel. Excel add-in has good features. The statistical significance of the test result is given by the p value. If the p value is less than alpha (significance level) we reject the Null hypothesis. Step V : Decision making The rejection of Ho means the differences are statistically significant and the acceptance means they are due to chance. Depending upon the outcome we then take decision of our sample and the population. Many frameworks exist for implementing the Six Sigma methodology. Six Sigma Consultants all over the world have developed proprietary methodologies for implementing Six Sigma quality, based on the similar change management philosophies and applications of tools.
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General Concepts And Goals Of Hypothesis Testing

Hypothesis means a supposition or an assumption or... Read More

Six Sigma Methods and Formulas For Successful Quality Management

Six Sigma is basically the application of Statistical formulas and Methods to eliminate defects, variation in a product or a process. For example if you want to find the average height of male population in India, you cannot bring the entire population of more than 2 billion into one room and measure their height for a scenario like this we take samples that is we pick up sample(people) from each state and use statistical formulas to draw the inference about the average height of male population in a population which is more than 2 billion. One more example would be say a company manufactures pistons use d in motor cycles the customer demand is that the piston should not a diameter more than 9 cm and less than 5 cm anything manufactured outside this limits is said to be a variation and the six sigma consultant should confirm that the pistons are manufactured within the said limits else if there is variation in the range then the company is not operating at 6 sigma level it is operating at a very low level. A company is operating at six sigma level implies that there are only 3.4 defects per million opportunities for example an airline company operating at six sigma level means that it loses only 3.4 baggage’s per million of the passenger it handles. Below is Shown the Six Sigma Table and a graph explaining the meaning of various levels of Six Sigma. Sigma Level Defect Rate Yield Percentage 2 σ 308,770 dpmo (Defects Per Million 69.10000 %   Opportunities)   3 σ 66,811 dpmo 93.330000 % 4 σ 6,210 dpmo 99.38000 % 5 σ 233 dpmo 99.97700 % 6 σ 3.44 dpmo 99.99966 % Six Sigma is Denoted by the Greek alphabet σ which is shown in the table above and is called as Standard deviation. The father of Six Sigma is Bill Smith who coined the term Six Sigma and implemented it in Motorola in the 1980’s. Six Sigma is implemented in Five Phases which are Define, Measure, Analyze, Improve, Control and we will discuss each phases in brief and the various methods used in Six Sigma. Define The objectives within the Define Phase which is first phase in DMAIC framework of Six Sigma are:- Define the Project Charter Define scope, objectives, and schedule Define the Process (top-level) and its stake holders Select team members Obtain Authorization from Sponsor Assemble and train the team. Project charters the charter documents the why, how, who and when of a project include the following elements Problem Statement Project objective or purpose, including the business need addressed Scope Deliverables Sponsor and stakeholder groups Team members Project schedule (using GANTT or PERT as an attachment) Other resources required Work break down Structure It is a process for defining the final and intermediate products of a project and their relationship. Defining Project task is typically complex and accomplished by a series of decomposition followed by a series of aggregations it is also called top down approach and can be used in the Define phase of Six Sigma framework. Now we will get into the formulas of Six Sigma which is shown in the table below. Central tendency is defined as the tendency for the values of a random variable to cluster round its mean, mode, or median. Where mean is the average for example if you have taken 10 sample of pistons randomly from the factory and measured their diameter the average would be sum of the diameter of the 10 pistons divided by 10 where 10 the number of observations the sum in statistics is denoted by ∑. In the above table X, Xi are the measures of the diameter of the piston and µ , XBar is the average. Mode is the most frequently observed measurement in the diameter of the piston that is if 2 pistons out 10 samples collected have the diameter as 6.3 & 6.3 then this is the mode of the sample and median is the midpoint of the observations of the diameter of the piston when arranged in sorted order. From the example of the piston we find that the formulas of mean, median , mode does not correctly depict variation in the diameter of the piston manufactured by the factory but standard deviation formula helps us to find the variance in the diameter of the piston manufactured which is varying from the customer mentioned upper specification limit and lower specification limit. The most important equation of Six Sigma is Y = f(x) where Y is the effect and x are the causes so if you remove the causes you remove the effect of the defect. For example headache is the effect and the causes are stress, eye strain, fever if you remove this causes automatically the headache is removed this is implemented in Six Sigma by using the Fishbone or Ishikawa diagram invented by Dr Kaoru Ishikawa. Measure Phase: In the Measure phase we collect all the data as per the relationship to the voice ofcustomer and relevantly analyze using statistical formulas as given in the above table. Capability analyses is done in measure phase. The process capability is calculated using the formula CP = USL-LSL/6 * Standard Deviation where CP = process capability index, USL = Upper Specification Limit and LSL = Lower Specification Limit. The Process capability measures indicates the following Process is fully capable Process could fail at any time Process is not capable. When the process is spread well within the customer specification the process is considered to be fully capable that means the CP is more than 2.In this case, the process standard deviation is so small that 6 times of the standard deviation with reference to the means is within the customer specification. Example: The Specified limits for the diameter of car tires are 15.6 for the upper limit and 15 for the lower limit with a process mean of 15.3 and a standard deviation of 0.09.Find Cp and Cr what can we say about Process Capabilities ? Cp= USL-LSL/ 6 * Standard deviation = 15.6 – 15 / 6 * 0.09 = 0.6/0.54 = 1.111 Cp= 1.111 Cr = 1/ 1.111 = 0.9 Since Cp is greater than 1 and therefore Cr is less than 1; we can conclude that the process is potentially capable. Analyze Phase: In this Phase we analyze all the data collected in the measure phase and find the cause of variation. Analyze phase use various tests like parametric tests where the mean and standard deviation of the sample is known and Nonparametric Tests where the data is categorical for example as Excellent, Good, bad etc. Parametric Hypothesis Test – A hypothesis is a value judgment made about a circumstance, a statement made about a population .Based on experience an engineer can for instance assume that the amount of carbon monoxide emitted by a certain engine is twice the maximum allowed legally. However his assertions can only be ascertained by conducting a test to compare the carbon monoxide generated by the engine with the legal requirements. If the data used to make the comparison are parametric data that is data that can be used to derive the mean and the standard deviation, the population from which the data are taken are normally distributed they have equal variances. A standard error based hypothesis testing using the t-test can be used to test the validity of the hypothesis made about the population. There are at least 3 steps to follow when conducting hypothesis. Null Hypothesis: The first step consists of stating the null hypothesis which is the hypothesis being tested. In the case of the engineer making a statement about the level of carbon monoxide generated by the engine , the null hypothesis is H0: the level of carbon monoxide generated by the engine is twice as great as the legally required amount. The Null hypothesis is denoted by H0 Alternate hypothesis: the alternate (or alternative) hypothesis is the opposite of null hypothesis. It is assumed valid when the null hypothesis is rejected after testing. In the case of the engineer testing the carbon monoxide the alternative hypothesis would be H1: The level of carbon monoxide generated by the engine is not twice as great as the legally required amount. Testing the hypothesis: the objective of the test is to generate a sample test statistic that can be used to reject or fail to reject the null hypothesis .The test statistic is derived from Z formula if the samples are greater than 30. Z = Xbar-µ/σ/ √n If the samples are less than 30, then the t-test is used T= X bar -µ/ s/√n where X bar and µ is the mean and s is the standard deviation. 1-Sample t Test such as an ideal off center (Mean v/s Target) this test is used to compare the mean of a process with a target value goal to determine whether they differ it is often used to determine whether a process is 1 Sample Standard Deviation This test is used to compare the standard deviation of the process with a target value such as a benchmark whether they differ often used to evaluate how consistent a process is 2 Sample T (Comparing 2 Means) Two sets of different items are measured each under a different condition there the measurements of one sample are independent of the measurements of other sample. Paired T The same set of items is measured under 2 different conditions therefore the 2 measurements of the same item are dependent or related to each other. 2-Sample Standard This test is used when comparing 2 standard deviations Standard Deviation test This Test is used when comparing more than 2 standard deviations Non Parametric hypothesis Tests are conducted when data is categorical that is when the mean and standard deviation are not known examples are Chi-Square tests, Mann-Whitney U Test, Kruskal Wallis tests & Moods Median Tests. Anova If for instance 3 sample means A, B, C are being compared using the t-test is cumbersome for this we can use analysis of variance ANOVA can be used instead of multiple t-tests. ANOVA is a Hypothesis test used when more than 2 means are being compared. If K Samples are being tested the null hypothesis will be in the form given below H0: µ1 = µ2 = ….µk And the alternate hypothesis will be H1: At least one sample mean is different from the others If the data you are analyzing is not normal you have to make it normal using box cox transformation to remove any outliers (data not in sequence with the collected data).Box Cox Transformation can be done using the statistical software Minitab. Improve Phase: In the Improve phase we focus on the optimization of the process after the causes are found in the analyze phase we use Design of experiments to remove the junk factors which don’t contribute to smooth working of the process that is in the equation Y = f(X) we select only the X’s which contribute to the optimal working of the process. Let us consider the example of an experimenter who is trying to optimize the production of organic foods. After screening to determine the factors that are significant for his experiment he narrows the main factors that affect the production of fruits to “light” and “water”. He wants to optimize the time that it takes to produce the fruits. He defines optimum as the minimum time necessary to yield comestible fruits. To conduct his experiment he runs several tests combining the two factors (water and light) at different levels. To minimize the cost of experiments he decides to use only 2 levels of the factors: high and low. In this case we will have two factors and two levels therefore the number of runs will be 2^2=4. After conducting observations he obtains the results tabulated in the table below. Factors Response     Water –High Light High 10 days     Water high – Light low 20 days     Water low – Light high 15 days     Water low – Light low 25 days     Control Phase: In the Control phase we document all the activities done in all the previous phases and using control charts we monitor and control the phase just to check that our process doesn’t go out of control. Control Charts are tools used in Minitab Software to keep a check on the variation. All the documentation are kept and archived in a safe place for future reference. Conclusion: From the paper we come to understand that selection of a Six Sigma Project is Critical because we have to know the long term gains in executing these projects and the activities done in each phase the basic building block is the define phase where the problem statement is captured and then in measure phase data is collected systematically against this problem statement which is further analyzed in Analyze phase by performing various hypothesis tests and process optimization in Improve phase by removing the junk factors that is in the equation y = f(x1, x2,x3…….) we remove the causes x1, x2 etc. by the method of Design of Experiments and factorial methods. Finally we can sustain and maintain our process to the optimum by using control charts in Control Phase.
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2049
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Design For Six Sigma Methodology: A Toolset To Add...

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