Measure

1. Process Definition - Overview and Objectives

Measurement Phase Section Overview and Objectives At the end of this phase, you will learn what the different process definitions are. What are six-sigma statistics? How do we perform measurement system analysis? How do we calculate process capability? Process definition Section Overview and Goals At the end of this session, you will learn what cause and effect are and the fishbone diagram. What is process mapping? SIPOC and value stream mapping? What is an XY? A Diagram What is the failure mode and effect Cause and Effect or the Fishbone Diagram cause-and-effect diagrams are effective team-based tools to determine the potential root causes of a problem.

A cause and effect or fishbone diagram breaks problems down into bite-sized pieces and graphically displays many possible causes; it is also known as an Ishikawadiagram and shows how various causes interact when brainstorming ideas. A fishbone session is divided into three parts: brainstorming, prioritizing, and development of an action plan. Identify the problem statement and brainstorm the categories in a fishbone diagram.

To priorities problem causes, polling is often used. The three most probable causes may be outlined for the development of an action plan. Generally, the four MS, that is, manpower, material, method, and machine version of the fishbone diagram, will suffice. Occasionally, the expanded version must be used in a laboratory environment. Measurement is a key issue when discussing brown grass in the lawn. The environment is important. A five-M and-E schematic is shown in the figure. In the figure you will also observe the problem statement: the eye of the fish has several bones, such as measurement, material, machine method, manpower, and environment. Here is an example of a fishbone analysis for high turnaround time or Tat.

As you can see in the diagram, the possible root causes categorized under "methods" are staffing, training, approval, processing, and escalation. The categorization under people includes inadequate staffing, inadequate skills, lack of experience, and lack of process knowledge. The categorization of measurement includes collection, consistency, and CTPs not measured. The categorization under Mother Nature includes the day of the week, week of the month, month of the year, and holiday season.

The category under materials includes lack of documentation, lack of knowledge base, and lack of escalation matrix, and the category under machine includes server downtime and workstation downtime. Measurements of process inputs and outputs can be used to optimize the process being measured. Process inputs may be raw materials, human resources, or services. All inputs have some quantifiable measurement, including human effort and skill level. Process input requirements should be stated so that key measures of input quality can be controlled. Measurements within the process can also be used as effective controls. Once process capabilities are known, output measures can be used to monitor if the process has remained in control.

Figure Two One C In this figure, the process starts when the upstream process provides the inputs that are processed for outputs to the downstream process. The process database of the organization has details of input measures, process controls, process measures, and output measures. Feedback from downstream process measurements can be used to improve an upstream process. For example, electrical testing for solder shorts can be used to optimize a circuit board soldering operation even if it involves several processes upstream from the testing operation. When considering the entire organizational feedback system, complex interrelationships are likely to exist. This is where planned experimentation and design for Six Sigma come into play. Planned experimentation deals with isolating the effects of several different independent variables on a process. Designing for Six Sigma includes eliminating potential sources of error. SIPOC. A key concept in Six Sigma methodology is the IPOC high-level process map, in which SIPOC stands for suppliers, inputs, process outputs, and customers.

This diagram identifies the major core processes. Refer to figure two. Two below. The advantages of using an Si POC model include a display of cross functional activities in a single simple diagram, a big picture perspective from which additional details can be added, and a framework applicable to both large and small organizations.

As you can see in the diagram, the suppliers provide inputs which are processed as outputs and received by the customer. The feedback is shared when inputs and outputs are provided. Similarly, the knowledge repository is updated with the process details. The ultimate goal is to identify essential workflows and sources of variation in work overtime. The diagram can also be adapted to a number of essential support processes. SIPOC captures the key components of success from suppliers through internal processes and to key customers. Other tools such as process mapping, flowcharting, and affinity diagrams can be used to further identify the major steps in a process or system. S IPOC The S IPOC process map is designed to be a high-level process view with four to seven displayed steps. This is a flowchart viewed at the 500-foot level.

The map enables all team members to view the process in the same light. Various Six Sigma authors warn against making the diagram too detailed and thereby losing the ability to focus on a Six Sigma improvement project that has a significant reward. As you can see in the diagram, IPOC is an acronym of suppliers, inputs, process, outputs, and customer. The following steps can be used for developing an SIPOC diagram Have the team create the process map.

The process may have four or five key steps The process list's outputs are the process list's customers, the process list's inputs, and, as an optional step, the process's suppliers. Identify some preliminary requirements of the customers; involve the team leader, champion, and other stakeholders for verification. Process mapping is the graphic display of steps, events, and operations that constitute a process. A pictorial illustration which identifies the steps, inputs and outputs, and other related details of a process. Providing a step-by-step picture of the process As is a graphics technique for dissecting a process by capturing and integrating the combined knowledge of all parties associated with the process. It is a team effort and is documented by everyone who contributes to the process and/or is a part of the process.

Process maps help characterize the functional relationships between various inputs and outputs. Flowcharting Tools Three commonly used process mapping tools to create detailed process maps are flowchart deployment Flowchart Alternate Path Flowcharts are frequently used. flowcharting tools process As you can see in the diagram, the process flow chart is a regular flow chart of the process. In this example, an individual lifts a receiver and dials a number. It rings on the opposite phone. If the call is answered, we hear a hello, and then we have a conversation, and finally we hang up the phone. If the phone is not answered, we will hang up the phone.

An Example of a Deployment Flowchart In the deployment flowchart, a dealer places an advertisement. An agent will initiate a call and the buyer will answer. We'll discuss the details, agree on the details, and then hang up. Similarly, the agent and the buyer discuss this further. There is an agreement and then a hang-up. We write the contract and the attorney reviews the contract. In a deployment flowchart, we create a flowchart using swim lanes, and each swim lane represents the role of each individual. An Example of an Alternate Path Flowchart In this example, it is decided whom to call. If we have the number, we dial the number. If we do not have the number, we look up the number in the telephone directory and then dial the number. If the receiver is picked up, we say hello, have a conversation, and then hang up.

Likewise, if the phone is not picked up and the voicemail is set up, we will leave a message and then hang up. If the voicemail is not set up, the phone is hung up. Process Analysis Tools Flowchart and Process Mapping: There are advantages to depicting a process in a schematic format. The major advantage is the ability to visualize the process being described. Process mapping, or flowcharting, has the benefit of describing a process with symbols, arrows, and words without the clutter of sentences. Many companies use process maps to outline new procedures and review old ones for viability and thoroughness. Most flowcharting uses standardized symbols. Computer flowcharting software may contain 15 to 185 shapes, with customized variations extending to the 500 range. Many software programmers have the ability to create flowcharts or process maps, although the information must come from someone knowledgeable about the process. Some common flowcharts or process maps are shown below. Start or end database external data decision or preparation connector off page connector manual input extract merge process decision data document sub process or predefined process start or end database.

2. Process Definition - Value Stream Mapping

Measure phase process definition, value stream mapping, flowcharts, process maps, written procedures, and work instructions are tools used for process analysis and documentation. Other lean techniques, such as value stream mapping and spaghetti diagrams, are also often used. Value Stream Mapping A value stream map is created to identify all of the activities involved in a product's manufacturing from start to finish. This value stream may include suppliers, production operations, and the end customer. VSM typically focuses on material and information flow for product development. Value stream mapping includes the design flow from product concept to launch. This was the large view, looking at the entire system for improvement opportunities. A value stream map includes seeing the complete process flow identifying sources and locations of waste, providing common terminology for process discussions. Multiple lean concepts and techniques, when combined, form a blueprint for lean ideas. showing the linkage between information and material flows, describing how the process can change, determining effects on various metrics The value stream mapping process includes defining a product family where we can use an equipment matrix. A product family is defined as a group of products that pass through similar processing steps and overcome an equipment draw. A current state map, which can be done personally, A current state map of the process is developed to facilitate a process analysis. Create a future state map where we can use creative concepts. A future value stream map is an attempt to make the process lean for implementation, which can take months or years. The final step in the value stream mapping process is to develop an implementation plan for establishing the future state. specify the product family The recommended value stream approach is to map one product family.

A product family is defined as a group of products that pass through similar processing steps and over common equipment. A product and equipment matrix can be used to indicate common features. See the table for an example of the matrix. The matrix shows products that go through a series of common processes. A work cell could be formed to handle a particular flow. Another method is to create a pared chart of the various products. The product with the highest volume should be used for the model line. In the table provided in the product family matrix, there are five products and four processes. In this example, the equipment is used in four processes. Process One uses its equipment for all five products. Process Two use equipment in process A and process D. Process Three use equipment in processes A, B, and E, and finally, process Equipment used in processes A and B. Value Stream The value stream for a product family may cross department boundaries in the company. This creates the potential for difficulties in coordinating an effective value stream project. Such problems call for the creation of a new position for a value stream manager. This manager must have the authority to make things happen and should report to the plant manager. It is recommended that a production person handle the job of value stream manager.

This manager would monitor all aspects of the project. Being a hands-on person, the manager should be on the floor on a regular basis. Current State Map A current state map of the process is developed to facilitate a process analysis. Basic tips on drawing a current state map start with a quick orientation of the process. I personally monitor the flow of materials and information. I mapped the process with a backward flow from the shipping dock to the beginning. Personally, I collected the data personally. Do not trust the engineering standard times map of the whole stream. Create a pencil drawing of the value stream. Some of the typical process data included are cycle time, CT changeover time, cot uptime, UT, number of operators, pack size, working time that is minus breaks in seconds, WIP, and scrap rate. An analysis of the current status can provide the amount of lead and value-added time. In many situations, teams take on the task of data collection. Both individuals and teams find it beneficial to develop a VSM data box in advance. Value Stream Mapping definitions worth noting include Customers are willing to pay for lead time, which is defined as the time it takes one piece of product to cycle through all processes or the time it takes a piece to complete an individual process. Future State Map A future value stream map is an attempt to make the process lean.

This involves creativity and teamwork by the value stream manager and the lean team to identify creative solutions. Everything the team knows about lean manufacturing principles is used to create the process of the future. Questions to ask when developing a future state map are: What is the required tax time? Do manufactured items move directly to shipping? Are items sent to a finished supermarket for customer pickup? Is continuous flow processing applicable? Where is the pacemaker process? This process controls the tempo of the value stream. Can the process be leveled? What is the increment of work to be released for Kanban use? What process improvements can be used, i.e., changeover machine uptime, kaizen events, SMED, etc.? Implementation Planning The final step in the value stream mapping process is to develop an implementation plan for establishing the future state. This includes a STEPBYSTEP plan, measurable goals, and checkpoints to measure progress. A Gantt chart may be used to illustrate the implementation plan. Several factors determine the speed of the plan. These include available resources and funding. The plan could take months or years to complete, and even then there may be a need to improve upon it in the future.

Value Stream Mapping Icons The following icons may be used with value stream mapping, Kanban, and other lean manufacturing areas FIFO: first in, first out. Kaizen burst Kanban withdrawal electronic Kanban production Flow Kanban Supermarket production signal safety buffer stock control source sequenced pull ball inventory shipment arrow shipment truck value is defined by the customer. Quite often, manufacturers cannot provide appropriate customer value. In many cases, senior business managers in the United States have lost touch with the customer. They want customers to purchase products at reasonable prices in order to keep the company profitable. They attempt to increase the performance of the firm while reducing costs. What is the value of a German mindset? The German mindset is more product, feature, and process-oriented. The technical people or engineers are in control of the businesses. Thus, the Germans are very strong technically. Therefore, features and enhancements are of the utmost importance.

However, some of the new complex enhancements have failed to attract the customer's interest. Often, the German mindset is that the customer is not sophisticated enough to understand the new features. What is the value of a Japanese mindset? The Japanese define value in the context of where value is created. As the proportion of the products made in the Japanese homeland increases, the greater the value that is retained at home for their society. Customers in general do not define value based on where it is made. Customers want their needs satisfied quickly. As the yen strengthened, the previous advantages of Japanese companies using Japanese suppliers disappeared. This has resulted in the weakening of many Japanese companies. In the long run, value must be defined by the customer. The customer wants specific products with specific capabilities at specific prices. Specifying value is the first step in lean thinking. New methods must be developed to communicate with customers, to get closer to them, and to find out what they want. Once value is determined, a firm must go back again and again to determine if they really have the right answers. The target cost of the product may be determined after defining customer value. This target cost is higher than the market cost of the product. The market cost is typically the manufacturing cost of the product plus the selling expenses and profit.

In lean banking, the target cost is the mixture of the current selling prices by competitors and the examination and elimination of mud through lean methods. This analysis results in a target price that is below current selling prices. The firm then applies lean thinking to its processes. Each firm in the value stream is reluctant to disclose too much information to the others for fear of price concession requests. A voluntary alliance of the members of the value stream must be developed in order to eliminate the mud hidden in the value stream. The value chain, as described by Porter in 1985, is at a high operating level. A generic value chain involves key components of human resources, technology, procurement, inbound logistics, operations, outbound logistics, marketing, sales, and service. The discussion and analysis centers on methods to differentiate the firm. However, an organization gains a competitive advantage by performing certain strategic activities better or at a lower cost than its competitors. The value stream or chain, as used in lean manufacturing efforts, goes into greater detail. It involves a single product stream which is analyzed for reduction of waste, reduction in cycle time, or improvement in quality. A value stream map is created to identify all of the activities involved in the product.

This value stream can include the various suppliers, production activities, and the final customer. The activities are viewed in terms of the following criteria: It adds value as perceived by the customer. It adds no value but is required by the process. It adds no value and can be eliminated. Connor identifies the steps for documenting the value stream mapping as product development in 2001. Identify customer requirements, methods of delivery, and typical quantities. Process Design: Perform a walkthrough of the process, recording each step. Start from the shipping dock and work your way back through the process to the receiving dock. Make note of machine time and cycle times. Operators change over time, I'm WIP available, scrap rate, machine reliability, etc. Record the current status on an 11 x 17 inch sheet of paper. Planning. Develop a future state map. Traditional mass production is often accomplished by the batch method. The objective is to produce many units of a specific part at a given time in order to maintain the production efficiency of the machines and the overall efficiency of the departments. However, optimization of the individual operation unknowingly leads to suboptimisation of the process as practiced by nonplan companies. The lean effort requires the conversion of the batch process to a continuous flow process. In some cases, converting the batch process into a one-piece flow is ideal.

Some of the obstacles to overcome include the fact that the plant has always done it in batches or lots. The plant has a multitude of departments and functions the plant can't afford. Quick changeover Tooling the plant with high momentum and inflexible machinery. The plant machinery would be expensive to move, ideally in a continuous flow layout. The production steps for single piece flow without WIP are arranged in a straight-line shape or cellular sequence. Inside this flow, the work of each station operator must be performed with reliability. When the machinery is performing as expected, there are zero breakdowns. This is the concept of TPM, or total Productive Maintenance. The quality level of each operation is very high, near perfect, using a variety of defect elimination and detection techniques. The activities needed for production should be a steady continuous flow with no pauses, no batches, and no WIP. There should be flexibility to meet the present needs. The work of people, functions, departments, and firms will require adjustments to the value stream to make it flow and to create value for the customer. Instead of creating a product in response to an estimated sales forecast, the plant manufacturers a product as the customer requires it. This is the full system in action.

This results in many positive things for the organization's cycle times, which decreases from concept to launch, sales, to delivery, etc. Finished inventories are reduced, work in progress or WIP is reduced. The customer stabilizes their order. Pricing is stabilized. The majority of mass-production manufacturing companies are in push mode. Each operation produces as much as possible and sends it on to the next operation. The goal is to maximize machine efficiency with a maximum amount of in-process inventory sitting around the plant. Contrast the above manufacturing firm with a factory that is dependent on the pull of the market. The receipt of a customer order initiates activities. Each operation produces parts as needed through a signal from downstream. There is a minimal amount of WIP in the process stream. This arrangement enables flow through the plant using the principles of lean thinking. Quality, machinery, downtime, absenteeism, etc. are all of concern. Problems in any area will stop the process, disrupting the pull process. Problems of any sort are magnified and must be immediately corrected. Wilma in 1996 suggests that reductions in cycle times which are due to lean thinking methods can equal those shown in table five.

5% reduction in product development 50% Order % reduction in processing 75% Physical production Percent reduction 90% perfection The customer is searching for a value-added product. The pursuit of the first four principles of lean thinking allows the firm to move toward perfection. Solving customer value problems, working the value stream, converting to flow, and making poll occur all help eliminate mud. As the process continues, more medias are eliminated, and perfection seems possible. Perfection is accomplished via product teams working with customers to find better ways to specify, enhance flow, and achieve pull. Using collaboration between the value stream partners, that is, suppliers, distributors, customers, and employees, to uncover more value. Using technologies to eliminate mud, developing new products Lean thinking principles are the cornerstones of higher performance and economic growth. Perfection is a journey. Some possible improvement results from lean thinking are: improvement area versus reduction or improvement in labor productivity. Throughput times have increased by 100%. Inventory reduction of 90% 90% reduction in household waste, 50% reduction Safety injuries Product with a 50% reduction Development time: 50% reduction in capital Investment is modest It may take years to implement lean thinking principles in a company, and even longer to implement lean thinking throughout the entire value chain.

Tactile tack time is the available production time divided by the rate of customer demand. A discussion of the hypothetical process is presented below in order to understand the measurement of Tactile and how it can be improved, a discussion of hypothetical process is presented below. Consider a sequential operation with five operators or stations. The times allocated for each station are indicated in table 5.6. If the tax time for the line is 60 seconds, the immediate observation is that station four exceeds the tax time and will not be able to maintain the pace. One option would be to have some of the time eliminated by moving work to another station. Upon further examination, some thought has to be given to stations one, two, and five that do not align with the current time.

Because of the existing slack Station three has a full 60 seconds of work. A keen lean Six Sigma specialist will seize this opportunity to review the entire line for another redesign. The total work time used at the current time is 265 seconds. With five operators, this equates to 53 seconds on a balanced line. Another perspective indicates that four operators will require 66.25 seconds. This is slightly more than the desired tax time of 60 seconds. However, the initial task will be to reexamine the content of the operations by looking at the value-added and nonvalue-added elements. A thorough study may reveal that a significant portion of time can be eliminated, leading to a reduction of one operator and possibly a reduction in floor space. The following three cases assume a series of three operations with each processing one unit per minute. Case one orders are manufactured in batches of 100 units. Only batches of 100 units are transferred from operation to operation. The total processing time is 201 minutes before the first unit is available. Total order time through the entire process is 300 minutes for 100 units.

Two orders are manufactured in batches of ten units. Only batches of ten units are transferred from operation to operation. The total processing time is 21 minutes before the first unit is available. Total order time through the entire process is 30 minutes for ten units. In this case, three orders are manufactured in batches of one unit. Each unit is transferred from operation to operation. The total processing time is three minutes before the first unit is available. Total order time through the entire process is three minutes for one unit. The above three cases illustrate the power of one-piece flow. If a customer changes their requirements, the shop will not have 300 units in queue in partial stages of production. The shop will be able to shift production requirements and provide the first units rapidly. Quality equipment, personnel, materials, and supplier resources must be coordinated and made available as needed. The layout of the line or cell is a starting point. The line should be examined as necessary to improve cycle times, reduce product defects, correct long-term changes, and address equipment reliability issues.

3. Process Definition - X Y Diagram

Process phase measurement definition process The XYdiagram The idea of the XY matrix is to multiply the weight with the score. If you look at the XY matrix example, the score of 208 for input two is calculated as eight score times ten weight plus eight. Eight times eight plus four times seven plus nine times four equals 208. Similarly, for others, the highest ranking can be used to identify the most important few factors. In this example, an XY diagram is used to identify the key actionable. The output variables are described on the x axis.

The output variables are weld strength, weld appearance, pinhole density, and weld flexibility. A weight is given for each of the variables, such as ten, eight, seven, and four, respectively. Ultrasonic weld frequency, power amplitude, initial gap, contact pressure, dwell time, and hold time are factors impacting the variables on a scale of one to 10. The impact of x variables on variables is identified and documented. Finally, the ranking numbers are created. Failure Mode and Effect Analysis and Understanding An FMEA provides the design engineer, reliability engineer, and others a systematic technique to analyses a system subsystem or item for all potential or possible failure modes. This method then places a probability that the failure mode will actually occur and what the effect of this failure is on the rest of the system. If the criticality of failure is considered, the technique is called FMECA. The criticality portion of this method allows one to place a value or rating on the criticality of the failure effect on the entire system.

It is not uncommon to omit the criticality portion from the methodology. An FMEA or FMECA, in most cases, little difference, is a detailed analysis of the system down to the component level. Once all items are classified as to the one failure mode and two effective failures and three probabilities that failure will occur, they are rated as to their severity via an index called an RPN or risk priority number. This RPN is dimensionless in the sense that a value of 600 versus 450 has no real meaning other than the difference in magnitude. Once all components or items have been analyzed and assigned an RPN value, it is common to work from the highest RPN value down. There will be more discussion on the RPN later. FMEA Failure Mode Effect Analysis: A Definition of Failure Mode When a specific process input fails, the impact on the critical quality parameter is assessed, as is the source of variation that caused the process to fail. The current control systemized devices in place to prevent or detect the failure severity importance of effect on critical quality parameters range from one to ten. The frequency with which a cause occurs varies; one is not likely, and ten is very likely.

The current control's detection ability to detect the cause before creating a failure mode that one is likely to detect. TEN is not likely to be detected. The following are the steps that are taken to prepare an FMEA FMEA number. This should be a log controlled number assigned for tracking the document, the part number, name, or other appropriate description. The design The FMEA is responsible for this design. The person responsible for the FMEApreparation, the date the FMEA was prepared, and any necessary revision level The subsystem or component part number being analyzed is the component function The potential failure mode The potential effect of failure What is the potential cause of failure? What are the current controls in place to prevent the cause from occurring? Mode and Effect of Failure The next major step is to weigh the risks associated with the current component effect and cause with the controls that are currently in place. P is the probability that this failure mode will occur.

Values for this index generally range from one to ten, with one being virtually no chance of occurrence and ten being near certainty of occurrence. S is the severity of the effect of the failure on the rest of the system. If the failure occurs, these values are often indexed from one to ten. A value of one means the user will be unlikely to notice, with a value of ten meaning that the safety of the user is in jeopardy. D is a measure of the effectiveness of the current controls that are in place to identify potential weaknesses or failures prior to release to production. This index may also range from one to 10. A value of one means this will be caught, whereas a value of ten indicates the design weakness would most certainly make it to final production without detection. RPN The risk priority number is the product of the indices from the previous three columns. RPN equals P times S times D. Actions are then based upon which items either have the highest RPN and/or have the highest major safety issues.

There is a column for actions to be taken to reduce the risk, a column for this responsibility, and finally a column for the revised RPN once corrective actions are implemented. In summary, FMEA provides a disciplined approach for the engineering team to evaluate designs to ensure that all the possible failure modes have been taken into consideration. Risk Assessment Risk assessment is the combination of the probability of an event or failure and the consequences of that event or failure on a system's, operators, users, or environment. The analysis of the risk of failure It normally utilises two measures of failure. These measures are the severity of failure and the effect of the failure on the system, operators, or mission. The probability of failure is the likelihood of the failure occurring. A number of systems are used to combine the probability of failure and the hazard category. These systems are based on accepting a degree of risk of occurrence with respect to the severity of the hazard. Frequently, catastrophic failure modes have additional safety measures such as redundant components, frequent inspection during service, etc.

Note that no hazard category has an allowable failure probability of frequent or probable failure mechanisms. Modes The failure mode is the actual symptom of the failure. That is, the failure mode may be premature engine shutdown or 70% degradation of function, or any other description of what an external occurrence will be defined as a failure. These failure modes are the result of failure mechanisms. Failure mechanisms are the individual or multiple reasons that cause the failure mode. For instance, failure mechanisms might be corrosion, contamination, or any other description of reasons that might cause a failure mode. Failure mechanisms cause failure modes,failure modes, and effect analysis. Types of FMEA There are four types of FMEAsdesign FMEAs process FMEAs systems FMEAs functional The following is an abbreviated description of the types. Design FMEAs are performed on the product, service, or system at the design level. The purpose is to analyses how failure modes affect the system and to minimise failure effects upon the system.

Design FMEAs are used before products are released to the manufacturing operation. All anticipated design deficiencies should be detected and corrected by the end of the process. Process FMEAs are performed on the manufacturing processes. They are conducted through the quality planning phase as an aid during production. The possible failure modes in the manufacturingprocess, limitations on equipment, tooling, gauges, operator training, or potential sources of error are highlighted and corrective action is taken. System FMEAs comprise part-level FMEAs All of the part-level FMEAs will tie together to form a system. As an FMEA or part level FMEA goes lower into the system into more detail, more failure modes will be considered. A system FMEA needs only to go down to the appropriate level of detail. Functional FMEAs are also known as black box FMEAs.

This type of FMEA focuses on the performance of the intended part of the device rather than the specific characteristics of the individual parts. As an example, if a project is in the early design stages, a black box analysis would focus on the function of a device rather than on the exact specifications. That is, the color must be blue, the grey knob is 215 millimeters to the left, etc. All of the above FMEAs can be applied to software systems. Summary: Process Definition In this session, you will learn about the following What is the cause and effect in the Fishbone diagram? What is process mapping? SIPOC and value stream mapping? What is an XY? A Diagram What is a failure mode and effect and analysis?

4. Six Sigma Statistics

Six Sigma Statistics Section Overview and Objectives By the end of this session, you will learn what basic statistics are, what descriptive statistics are, and what normal distribution and normality What are the different graphical analyses? Basic Statistics: Basic Terms Measurements of process inputs and outputs can be used to optimize the process being measured. Process inputs may be raw materials, human resources, or services. All inputs have some quantifiable measurement, including human effort and skill level. Process input requirements should be stated so that key measures of input quality can be controlled. Measurements within the process can also be used as effective controls. Once process capabilities are known, output measures can be used to monitor if the process has remained in control. Feedback from downstream process measurements can be used to improve an upstream process.

For example, electrical testing for solder shorts can be used to optimize a circuit board soldering operation even if it involves several processes upstream from the testing operation. When considering the entire organizational feedback system, complex interrelationships are likely to exist. This is where planned experimentation and designing for six sigma comes into play. Planned experimentation deals with isolating the effects of several different independent variables on a process. Designing for six sigma includes eliminating potential sources of error. Continuous Distribution A distribution containing infinite or variable data points that may be displayed on a continuous measurement scale, normal, uniform, exponential, and way bowl distributions. Discrete Distribution A distribution resulting from countable or attribute data that has a finite number of possible values. The true numeric population value is frequently unknown and estimated by a statistical population, for example, binomial cocoon and hyper geometric distributions.

From all possible observations of similar items, a sample is drawn. A statistic is a numerical data value taken from a sample that may be used to make an inference about a population six sigma Statistics Descriptive Statistics Descriptive statistics include measures of central tendency, measures of dispersion, probability, density, function, frequency distributions, and cumulative distribution functions. Measures of Central Tendency Measures of central tendency represent different ways of describing the central value of a collection of data. Three of these measures will be addressed here: mean, mode, and median. Measures of Dispersion: The other important parameter to describe a set of data is spread or dispersion. Measures of Central Tendency Measures of central tendency represent different ways of describing the central value of a collection of data. Three of these measures will be addressed here: mean, mode, and median. What Does It Mean? The mean is the arithmetic average of all the data points in the dataset. Median The median is the middlemost point in the data set. Mode Mode is the most frequently occurring data point in the data set. The mean is the total of all data values divided by the number of data points. The arithmetic mean is the most widely used measure of central tendency. Advantages of Using the Mean It is the centre of gravity of the data. It makes use of all of the data. No sorting is needed. The disadvantages of using the mean extreme data values may distort the picture. It can be time consuming.

The mean may not be the actual value of any data points. The mode is the most frequently occurring number in a data set. No advantages to using the mode of no calculations or sorting are necessary. It is not influenced by extreme values. It is an actual value. It can be detected visually in distribution plots. Disadvantages to using the mode The data may not have a mode or may have more than one mode. Median The median is the middle value when the data is arranged in either ascending or descending order. For an even set of data, the median is the average of the middle two values. The advantages of using the median provide an idea of where most data is located. Little calculation requires insensitivity to extreme values. The disadvantage of using the median is that the data must be sorted and organized. Extreme values may be important. Two medians cannot be averaged to obtain a combined distribution. The median will have more variation between samples than the average in a given figure.

You would see a comparison of central tendency in a normal and skewed distribution. For normal distribution, mean = median equals mode. Furthermore, the normal distribution curve is a bell-shaped curve. The area under the curve is equal to one and the curve is symmetrical. For a skewed distribution, the mean mode and median are not equal. Measures of dispersion Other than central tendency, the other important parameter to describe the set of data is spread or dispersion. Three main measures of dispersion will be reviewed: range, variance, and standard deviation. Range The range of a set of data is the difference between the largest and smallest values. Variance The variance Sigma squared or F squared is equal to the sum of the squared deviations from the mean divided by the sample size. Standard Deviation: The standard deviation is the square root of the variance. The standard deviation is also the average distance of all data points from the mean of the data set.

Normal Distribution introduces The Normal Distribution was developed by astronomer Carl Gauss and is widely used in distribution and statistics. where, given the population knowledge, we need to predict the sample behavior. It comes close to fitting the actual frequency distribution of many phenomena. Human characteristics such as weights, heights, and IQs Physical process outputs such as yields As seen in the diagram, there are a few critical characteristics of normal distribution. It's a probability distribution illustrated asN, that is, mu or sigma. Simply put, a probability distribution is a theoretical frequency distribution. The frequency of values around the mean is higher than at values away from the mean. continuous and symmetrical tails. Asymptotic to the x-axis bell shape, the total area under the normal curve equals one. This is a very important figure that indicates the area under the curve for various sigma values. Area under one sigma equals 68 26%; area under two sigma equals 95 46%; area under three sigma equals 9973%; area under four sigma equals 99 99 73%; and area under six sigma equals 99 99 8%. graphical Analysis Graphical analysis includes box plots, stem and leaf plots, scatter diagrams, runcharts, histograms, and normal probability plots.

Here are some examples of graphical summary charts and normal probability plots. We will be studying each of them in detail. Let us now understand how to draw an abox plot, stem and leaf plot, scatter diagram,run charts, and histogram using minitab scatter A scatter diagram is a graphic display of many XY coordinate data points which represent the relationship between two different variables. It is also referred to as a correlation chart. For example, temperature changes cause contraction and expansion of many materials. Both time and temperature in a kiln will affect the amount of moisture retained in wood. Examples of such relationships on the job are abundant. Knowledge of the nature of these relationships can oftenprovide a clue to the solution to a problem. Scatter diagrams can help determine if a relationship exists and how to control the effect of the relationship on the process. In most cases, there is an independent variable and a dependent variable. Traditionally, the dependent variable is represented by the vertical axis and the independent variable is represented by the horizontal axis.

The ability to meet specifications in many processes is dependent upon controlling two interacting variables, and therefore, it is important to be able to control the effect one variable has on another. For instance, if the amount of heatapplied to plastic liners affects their durability,then control limits must be set to consistently apply the right amount of heat. Through the use of scatter diagrams, the proper temperature can be determined, ensuring a quality product. The dependent variable can be controlled if the relationship is understood. Correlation originates from the following a cause-effect relationship, a relationship between two or more causes, or a relationship between one cause and two or more other causes Not all scatter diagrams reveal a linear relationship.

The examples here definitely portray a relationship between the two variables, even though they do not necessarily produce a straight line. If a centre line can be fitted to the ascattered diagram, it will be possible to interpret it. To use scatter diagrams, one must be able to decide what factors will best control the process within the specifications as shown in the diagram. The first graph shows a strong positive correlation. The second one shows a strong negative correlation. The third one shows no correlation. The next one is possible positive, followed by possible negative and some other patterns at the end. Graphal Analysis Run or Trend Charts: The average human brain is not good at comparing more than a few numbers at a time. Therefore, a large amount of data is often difficult to analyse unless it is presented in some easily digested format. Data can be presented in either a summary that is isstatic or a time sequence that is dynamic fashion.Important elements of most processes can change over time.

These changes can be presented graphically by the use of control charts or by the use of run or trend charts for many business activities. Trend charts will show patterns that indicate whether a process is running normally or whether desirable or undesirable changes are occurring. It should be noted that normal convention has timeincreasing across the page from left to right and the measurement value increasing up the page depending upon the process management values can be good if they go up or down the page or remain as close as possible to some target value. Consider the following examples run Same value Plot A runchart having seven or more points with the same value in sequence indicates a bias in the process. A Clustering Plot Such a plot has a lot of datapoints next to each other on one side of the median and the same way on the other side of the median over time and indicates a periodic shift in the processaverage due to lot to lot or setup variability. also known as "too few runs." Such a plot has an absence of points near the centre line with a sequence of 14 or more points in a row alternating up and down. indicates a bias or systematic sampling from different sources or processes. also known as a "cycle" or "too many runs." Plot oscillation Plot: Such a plot has data points constantly fluctuating up and down rapidly around the median and indicates that the process is not steady or stable.

Such a plot has a sequence of seven or more data points continuously increasing or decreasing and indicates a gradual increase or decreasing trend in the data. Measurement Methods Such a plot has a sequence of eight or more points on the same side of the median and indicates a gradual shift in the process. Graphical Analysis Descriptive or enumerative research Enumerative data is data that can be counted, for example,the classification of things or the classification of people into intervals of income, age, or health. A census is an enumerative collection and study. Thechi square, binomial and Poisson distributions are useful tools for tests of hypotheses conducted on enumerative data. Demming in 1075 defined the contrast between enumeration and analysis. Enumerative Study: A study in which action will be taken on the universe. Analytical Study: A study in which action will be taken on a process to improve performance in the future. Numerical descriptive measures create a mental picture of a set of data.

The measures calculated from the asample are called statistics. When these measures describe an apopulation, they are called parameters. Table 526 shows examples of statistics and parameters for the mean and standard deviation. These two important measures are called central tendency and dispersion. Summary of Analytical and Enumerative Studies Analytical studies start with a hypothesis made about population parameters. A sample statistic is then used to test the hypothesis and either reject or fail to reject it at a stated level of confidence. One is then able to make inferences about the population summary process. Definition In this session, you learn about the following What are the basic statistics? What are descriptive statistics? What is the normal distribution and normality? What are the different graphical analyses?

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