1 / 260

My Reading on ASQ CQA HB Part v Part 1

My Reading on ASQ CQA HB Part v Part 1

charliechong
Download Presentation

My Reading on ASQ CQA HB Part v Part 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. My Reading on ASQ CQA The Handbook ½ of Part V (VA-VC) My Pre-exam Self Study Notes, 14.7%. 29th September 2018 – 8th Oct 2018 Charlie Chong/ Fion Zhang

  2. Industrial Robotic Charlie Chong/ Fion Zhang

  3. The Magical Book of CQA Charlie Chong/ Fion Zhang

  4. 闭门练功 Charlie Chong/ Fion Zhang

  5. Charlie Chong/ Fion Zhang

  6. Fion Zhang at Heilongjiang 29th September 2018 Charlie Chong/ Fion Zhang

  7. ASQ Mission: The American Society for Quality advances individual, organizational, and community excellence worldwide through learning, quality improvement, and knowledge exchange. Charlie Chong/ Fion Zhang

  8. BOK Knowledge Percentage Score I. Auditing Fundamentals (30 Questions) II. Audit Process (60 Questions) III. Auditor Competencies (23 Questions) IV. Audit Program Management and Business Applications (15 Questions) V. Quality Tools and Techniques (22 Questions) 150 Questions 20% 40% 15.3% 10% 14.7% 100% https://asq.org/cert/resource/docs/cqa_bok.pdf Charlie Chong/ Fion Zhang

  9. Part V Quality Tools and Techniques [26 of the CQA Exam Questions or 14.7 percent] _____________________________________________________ Chapter 18 Basic Quality and Problem- Solving Tools/Part VA Chapter 19 Process Improvement Techniques/Part VB Chapter 20 Basic Statistics/Part VC Chapter 21 Process Variation/Part VD Chapter 22 Sampling Methods/Part VE Chapter 23 Change Control and Configuration Management/Part VF Chapter 24 Verification and Validation/Part VG Chapter 25 Risk Management Tools/Part VH Part V Charlie Chong/ Fion Zhang

  10. Auditors use many types of tools to plan and perform an audit, as well as to analyze and report audit results. An understanding of these tools and their application is essential for the performance of an effective audit since both auditors and auditees use various tools and techniques to define processes, identify and characterize problems, and report results. An auditor must have sufficient knowledge of these tools in order to determine whether the auditee is using them correctly and effectively. This section provides basic information on some of the most common tools, their use, and their limitations. For more in- depth information on the application of tools, readers should consult an appropriate textbook. Part V Charlie Chong/ Fion Zhang

  11. Chapter 18 Basic Quality and Problem- Solving Tools/Part VA __________________________________________________ Pareto Charts Pareto charts, also called Pareto diagrams or Pareto analysis, are based on the Pareto principle, which suggests that most effects come from relatively few causes. As shown in Figure 18.1, a Pareto chart consists of a series of bars in descending order. The bars with the highest incidence of failure, costs, or other occurrences are on the left side. The miscellaneous category, an exception, always appears at the far right, regardless of size. Pareto charts display, in order of importance, the contribution of each item to the total effect and the relative rank of the items. Pareto charts can be used to prioritize problems and to check performance of implemented solutions to problems. The Pareto chart can be a powerful management tool for focusing effort on the problems and solutions that have the greatest payback. Some organizations construct year- end Pareto diagrams and form corporate improvement teams in the areas determined to be in need of the greatest attention. Part VA Charlie Chong/ Fion Zhang

  12. Figure 18.1 SQM software example of a frequency Pareto analysis. Part VA 80% Defects Charlie Chong/ Fion Zhang

  13. Pareto Analysis- vital few and the trivial many. Pareto charts, also called Pareto diagrams or Pareto analysis, are based on the Pareto principle, which suggests that most effects come from relatively few causes. BREAKING DOWN 'Pareto Analysis' In 1906, Italian economist Vilfredo Pareto discovered that 80% of the land in Italy was owned by just 20% of the people in the country. He extended this research and found out that the disproportionate wealth distribution was also the same across all of Europe. The 80/20 rule was formally defined as the rule that the top 20% of a country‘s population accounts for an estimated 80% of the country‘s wealth or total income. Joseph Juran, a Romanian-American business theorist stumbled on Pareto‘s research work 40 years after it was published, and named the 80/20 rule Pareto‘s Principle of Unequal Distribution. Juran extended Pareto‘s Principle in business situations to understand whether the rule could be applied to problems faced by businesses. He observed that in quality control departments, most production defects resulted from a small percentage of the causes of all defects, a phenomenon which he described as ―the vital few and the trivial many.‖ Following the work of Pareto and Juran, the British NHS Institute for Innovation and Improvement provided that 80% of innovations comes from 20% of the staff; 80% of decisions made in meetings comes from 20% of the meeting time; 80% of your success comes from 20% of your efforts; 80% of complaints you make are from 20% of your services; etc. Read more: https://www.investopedia.com/terms/p/pareto-analysis.asp#ixzz5SU1aEH9H Part VA Charlie Chong/ Fion Zhang

  14. Cause-and-Effect Diagrams The cause-and-effect diagram (C-E diagram) is a visual method for analyzing causal factors for a given effect in order to determine their relationship. The C-E diagram, one of the most widely used quality tools, is also called an Ishikawa diagram (after its inventor) or a fishbone diagram (because of its shape). Basic characteristics of the C-E diagram include the following:  It represents the factors that might contribute to an observed condition or effect  It clearly shows interrelationships among possible causal factors  The interrelationships shown are usually based on known data C-E diagrams are an effective way to generate and organize the causes of observed events or conditions since they display causal information in a structured way. C-E diagrams consist of a description of the effect written in the head of the fish and the causes of the effect identified in the major bones of the body. These main branches typically include four or more of the following six influences but may be specifically tailored as needed: 1. People (worker) 2. Equipment (machine) 3. Method 4. Material 5. Environment 6. Measurement Figure 18.2 is a C-E diagram that identifies all the program elements that should be in place to prevent design output errors. Part VA Charlie Chong/ Fion Zhang

  15. Part VA Cause-and-Effect Diagrams Charlie Chong/ Fion Zhang

  16. Figure 18.2 Cause-and-effect diagram. These main branches typically include four or more of the following six influences but may be specifically tailored as needed: 1. People (worker) 2. Equipment (machine) 3. Method 4. Material 5. Environment 6. Measurement Part VA Charlie Chong/ Fion Zhang

  17. Figure 18.2 Cause-and-effect diagram. These main branches typically include four or more of the following six influences but may be specifically tailored as needed: 1. People (worker) 2. Equipment (machine) 3. Method 4. Material 5. Environment 6. Measurement Part VA Charlie Chong/ Fion Zhang

  18. Part VA These main branches typically include four or more of the following six influences but may be specifically tailored as needed: 1. People (worker) 2. Equipment (machine) 3. Method 4. Material 5. Environment 6. Measurement Charlie Chong/ Fion Zhang

  19. Fishbone Diagram Background Fishbone Diagrams (also known as Ishikawa Diagrams) are can be used to answer the following questions that commonly arise in problem solving: What are the potential root causes of a problem? What category of process inputs represents the greatest source of variability in the process output? Dr. Kaoru Ishikawa developed the "Fishbone Diagram" at the University of Tokyo in 1943. Hence the Fishbone Diagram is frequently referred to as an "Ishikawa Diagram". Another name for this diagram is the "Cause & Effect" or CE diagram. As illustrated below, a completed Fishbone diagram includes a central "spine" and several branches reminiscent of a fish skeleton. This diagram is used in process improvement methods to identify all of the contributing root causes likely to be causing a problem. The Fishbone chart is an initial step in the screening process. After identifying potential root cause(s), further testing will be necessary to confirm the true root cause(s). This methodology can be used on any type of problem, and can be tailored by the user to fit the circumstances. Using the Ishikawa approach to identifying the root cause(s) of a problem provides several benefits to process improvement teams:  Constructing a Fishbone Diagram is straightforward and easy to learn.  The Fishbone Diagram can incorporate metrics but is primarily a visual tool for organizing critical thinking.  By Involving the workforce in problem resolution the preparation of the fishbone diagram provides an education to the whole team.  Using the Ishikawa method to explore root causes and record them helps organize the discussion to stay focused on the current issues.  It promotes "System Thinking" through visual linkages.  It also helps prioritize further analysis and corrective actions. Part VA https://www.moresteam.com/toolbox/fishbone-diagram.cfm Charlie Chong/ Fion Zhang

  20. How to Get Started This tool is most effective when used in a team or group setting. 1. To create a Fishbone Diagram, you can use any of a variety of materials. In a group setting you can use a white board, butcher-block paper, or a flip chart to get started. You may also want to use "Post-It" notes to list possible causes but have the ability to re-arrange the notes as the diagram develops. 2. Write the problem to be solved (the EFFECT) as descriptively as possible on one side of the work space, then draw the "backbone of the fish", as shown below. The example we have chosen to illustrate is "Missed Free Throws" (an acquaintance of ours just lost an outdoor three-on-three basketball tournament due to missed free throws). 3. The next step is to decide how to categorize the causes. There are two basic methods: A) by function, or B) by process sequence. The most frequent approach is to categorize by function. In manufacturing settings the categories are often: Machine, Method, Materials, Measurement, People, and Environment. In service settings, Machine and Method are often replaced by Policies (high level decision rules), and Procedures (specific tasks). In this case, we will use the manufacturing functions as a starting point, less Measurement because there was no variability experienced from measurements (its easy to see if the ball goes through the basket). Part VA https://www.moresteam.com/toolbox/fishbone-diagram.cfm Charlie Chong/ Fion Zhang

  21. You can see that this is not enough detail to identify specific root causes. There are usually many contributors to a problem, so an effective Fishbone Diagram will have many potential causes listed in categories and sub-categories. The detailed sub-categories can be generated from either or both of two sources: 1. Brainstorming by group/team members based on prior experiences. 2. Data collected from check sheets or other sources. A closely related Cause & Effect analytical tool is the "5-Why" approach, which states: "Discovery of the true root cause requires answering the question 'Why?' at least 5 times". See the 5-Why feature of the Toolbox. Additional root causes are added to the fishbone diagram below: Part VA 4. https://www.moresteam.com/toolbox/fishbone-diagram.cfm Charlie Chong/ Fion Zhang

  22. Cont.….The following chart has the top five primary root cause contributors highlighted in gold. The note "MC" (for Mathematical Correlation) attached to air pressure indicates that strong correlation has been established through statistical analysis of data (the lower the air pressure, the less bounce off the rim). If you have ever tried to shoot baskets at a street fair or carnival to win a prize, you know that the operator always over-inflates the ball to lower your chances. Pick any system that works for you - you could circle instead of highlighting. The priority numbers can carry over to a corrective action matrix to help organize and track improvement actions. The tutorial provided below that shows how to make and use a Fishbone Diagram using EngineRoom. Part VA 5. The usefulness of a Fishbone Diagram is dependent upon the level of development - moving past symptoms to the true root cause, and quantifying the relationship between the Primary Root Causes and the Effect. You can take the analysis to a deeper level by using Regression Analysis to quantify correlation, and Designed Experiments to quantify causation. As you identify the primary contributors, and hopefully quantify correlation, add that information to your chart, either directly or with foot notes. 5. 6. https://www.moresteam.com/toolbox/fishbone-diagram.cfm Charlie Chong/ Fion Zhang

  23. Categorize The Causes by Functions Part VA Manufacturing Services People People Machine Policy Methods Procedures Materials Materials Measurement Measurement Environment Environment https://www.moresteam.com/toolbox/fishbone-diagram.cfm Charlie Chong/ Fion Zhang

  24. Flowcharts and Process Mapping Process maps and flowcharts are used to depict the steps or activities in a process or system that produces some output. Flowcharts are specific tools for depicting sequential activities and typically use standard symbols in their creation. Flowcharts and process maps are effective means for understanding procedures and overall processes and are used by auditees to help define how work is performed. Flowcharts are especially helpful in understanding processes that are complicated or that appear to be in a state of disorder. Auditors may also use flowcharts to help understand both production and service processes during audit preparation. A flowchart may be used to describe an existing system or process or to design a new one. It can be used to:  Develop a common understanding of an overall process, system, and sequence of operations  Identify inspection and checkpoints that result in a decision  Identify personnel (by job title) performing specific steps  Identify potential problem areas, bottlenecks, unnecessary steps or loops, and rework loops  Discover opportunities for changes and improvements  Guide activities for identifying problems, theorizing about root causes, developing potential corrective actions and solutions, and achieving continuous improvement Flowcharting usually follows a sequence from top to bottom and left to right, with arrowheads used to indicate the direction of the activity sequence. Common symbols often used for quality applications are shown in Figure 18.3. However, there are many other types of symbols used in flowcharting, such as ANSI Y15.3, Operation and Flow Process Charts (see Figures 18.4–18.8). Templates and computer software, both of which are easy to use and fairly inexpensive, are available for making flowcharts. Part VA Charlie Chong/ Fion Zhang

  25. The implementation of a process- based QMS (such as ISO 9001:2008) and the use of process auditing techniques have made charting an important auditing tool. In the book How to Audit the Process- Based QMS, the authors state, ―Many auditors find it useful to draw a flowchart of the operations about to be audited. What processes are performed and what are the linkages? This also helps to define the interfaces where information and other resources come into and flow out of the audited area.‖ They continue by stating, ―To make maximum use of the process approach to auditing, the work papers should reflect the flow of activities to be audited.‖ In the book The Process Auditing Techniques Guide, the author explains, ―The primary tool of process auditing is creating a process flow diagram [PFD] or flowchart. Charting the process steps [sequential activities] is an effective method for describing the process. For auditing purposes, process flow diagrams should be used to identify sequential process steps [activities] and kept as simple or as reasonable as possible.‖ Another variation of a flowchart is a process map. Process maps are very good tools that show inputs, outputs, and area or department responsibilities along a timeline. The complexity of process maps can vary, but for auditing, simplicity is the key. Part VA Charlie Chong/ Fion Zhang

  26. Process maps are very good tools that show inputs, outputs, and area or department responsibilities along a timeline. The complexity of process maps can vary, but for auditing, simplicity is the key. Part VA Charlie Chong/ Fion Zhang

  27. Process maps are very good tools that show inputs, outputs, and area or department responsibilities along a timeline. The complexity of process maps can vary, but for auditing, simplicity is the key. Part VA Charlie Chong/ Fion Zhang

  28. Process Flow Diagram PFD. Part VA Charlie Chong/ Fion Zhang

  29. Part VA Charlie Chong/ Fion Zhang

  30. Figure 18.3 Common flowchart symbols. Part VA Charlie Chong/ Fion Zhang

  31. Figure 18.4 Activity sequence flowchart. Part VA Charlie Chong/ Fion Zhang

  32. Figure 18.5 Top-down flowchart. A top-down diagram shows the breakdown of a system to its lowest manageable levels. They are used in structured programming to arrange program modules into a tree. Each module is represented by a box, which contains the module's name. The tree structure visualizes the relationships between modules. Part VA https://www.edrawsoft.com/topdowndiagram.php Charlie Chong/ Fion Zhang

  33. Figure 18.5 Top-down flowchart. A top-down diagram shows the breakdown of a system to its lowest manageable levels. They are used in structured programming to arrange program modules into a tree. Each module is represented by a box, which contains the module's name. The tree structure visualizes the relationships between modules. Part VA https://www.edrawsoft.com/topdowndiagram.php Charlie Chong/ Fion Zhang

  34. Figure 18.6 Matrix flowchart. Deployment or Matrix Flowchart- A deployment flowchart maps out the process in terms of who is doing the steps. It is in the form of a matrix, showing the various participants and the flow of steps among these participants. It is chiefly useful in identifying who is providing inputs or services to whom, as well as areas where different people may be needlessly doing the same task. See the Deployment of Matrix Flowchart. Part VA https://www.edrawsoft.com/Flowchart-Definition.php Charlie Chong/ Fion Zhang

  35. Figure 18.7 Flow process worksheet. PFD Worksheets (Process Flow Diagrams) In RCM++, there are two kinds of process flow diagrams (PFDs): a graphical process flow diagram, which is a high level chart of a process; and a PFD worksheet, which integrates the chart into a worksheet that records more detailed information about what the product goes through in each step of the manufacturing or assembly process. This includes the processing of individual components, transportation of materials, storage, etc. Also recorded are descriptions of the process and product characteristics that are affected in each step of the process, how these characteristics are controlled and what needs to be achieved at each step. For example, a process characteristic may be the temperature range for wax that will be sprayed onto the finished vehicle and a product characteristic may be the required wax thickness. Part VA Charlie Chong/ Fion Zhang

  36. Flow process worksheet. Part VA Charlie Chong/ Fion Zhang

  37. Figure 18.8 A process map. Process mapping is used to visually demonstrate all the steps and decisions in a particular process. A process map or flowchart describes the flow of materials and information, displays the tasks associated with a process, shows the decisions that need to be made along the chain and shows the essential relationships between the process steps. Part VA https://www.lucidchart.com/pages/process-mapping/how-to-make-a-process-map Charlie Chong/ Fion Zhang

  38. Figure 18.8 A process map. Process mapping is used to visually demonstrate all the steps and decisions in a particular process. A process map or flowchart describes the flow of materials and information, displays the tasks associated with a process, shows the decisions that need to be made along the chain and shows the essential relationships between the process steps. Part VA Charlie Chong/ Fion Zhang

  39. Statistical Process Control (SPC) Charts Many companies use statistical process control (SPC) techniques as part of a continuing improvement effort. Auditors need to be knowledgeable about the methods and application of control charts in order to determine the adequacy of their use and evaluate the results achieved. Auditors need this knowledge for observation purposes, but they are not required to plot control charts as part of the audit process. Control charts, also called process control charts or run charts, are tools used in SPC. SPC recognizes that some random variation always exists in a process and that the goal is to control distribution rather than individual dimensions. Operators and quality control technicians use SPC to determine when to adjust a process and when to leave it alone. The ability to operate to a tight tolerance without producing defects can be a major business advantage. Control charts can tell an organization when a process is good enough so that resources can be directed to more pressing needs. A control chart, such as the one shown in Figure 18.9, is used to distinguish variations in a process over time. Variations can be attributed to either special or common causes.  Common-cause variations repeat randomly within predictable limits and can include chance causes, random causes, system causes, and inherent causes.  Special-cause variations indicate that some factors affecting the process need to be identified, investigated, and brought under control. Such causes include assignable causes, local causes, and specific causes. Control charts use operating data to establish limits within which future observations are expected to remain if the process remains unaffected by special causes. Part VA Charlie Chong/ Fion Zhang

  40. Figure 18.9 Control chart. Part VA Charlie Chong/ Fion Zhang

  41. Statistical Process Control (SPC) Charts Variations can be attributed to either special or common causes.  Common-cause variations repeat randomly within predictable limits and can include - chance causes, - random causes, - system causes, and - inherent causes.  Special-cause variations indicate that some factors affecting the process need to be identified, investigated, and brought under control. Such causes include - assignable causes, - local causes, and - specific causes. Part VA Charlie Chong/ Fion Zhang

  42. Control charts can monitor the aim and variability, and thereby continually check the stability of a process. This check of stability in turn ensures that the statistical distribution of the product characteristic is consistent with quality requirements. Control charts are commonly used to: 1. Attain a state of statistical control 2. Monitor a process 3. Determine process capability The type of control chart used in a specific situation depends on the type of data being measured or counted. Part VA Charlie Chong/ Fion Zhang

  43. Variable Data Variable data, also called continuous data or measurement data, are collected from measurements of the items being evaluated. For example, the measurement of physical characteristics such as time, length, weight, pressure, or volume through inspection, testing, or measuring equipment constitutes variable data collection. Variable data can be measured and plotted on a continuous scale and are often expressed as fractions or decimals. The X (average) chart and the R (range) chart are the most common types of control charts for variable data. The X chart illustrates the average measurement of samples taken over time. The R chart illustrates the range of the measurements of the samples taken. For these charts to be accurate, it is critical that individual items composing the sample are pulled from the same basic production process. That is, the samples should be drawn around the same time, from the same machine, from the same raw material source, and so on.8 These charts are often used in conjunction with one another to jointly record the mean and range of samples taken from the process at fairly regular intervals. Figure 18.10 shows an X and R chart. Part VA Charlie Chong/ Fion Zhang

  44. Figure 18.10 X and R chart example. Part VA http://asq.org/learn-about-quality/tools-templates.html Charlie Chong/ Fion Zhang

  45. ? and R chart In statistical quality control, the X and R chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. The chart is advantageous in the following situations:  The sample size is relatively small (say, n ≤ 10, X and s charts are typically used for larger sample sizes)  The sample size is constant  Humans must perform the calculations for the chart The "chart" actually consists of a pair of charts: One to monitor the process standard deviation (as approximated by the sample moving range) and another to monitor the process mean, as is done with the X and s and individuals control charts. The X and R chart plots the mean value for the quality characteristic across all units in the sample, X ?, plus the range of the quality characteristic across all units in the sample as follows: R = xmax– xmin. The normal distribution is the basis for the charts and requires the following assumptions:  The quality characteristic to be monitored is adequately modeled by a normally distributed random variable;  The parameters μ (mu- mean or expectation of the distribution) and σ (sigma- the standard deviation) for the random variable are the same for each unit and each unit is independent of its predecessors or successors;  The inspection procedure is same for each sample and is carried out consistently from sample to sample. As with X and s and individuals control charts, the X chart is only valid if the within-sample variability is constant. Thus, the R chart is examined before the X chart; if the R chart indicates the sample variability is in statistical control, then the X is examined to determine if the sample mean is also in statistical control. If on the other hand, the sample variability is not in statistical control, then the entire process is judged to be not in statistical control regardless of what the X chart indicates. Part VA https://en.wikipedia.org/wiki/X%CC%85_and_R_chart Charlie Chong/ Fion Zhang

  46. R chart Centre Line: R = UCL = D4R LCL = D3R Plot Statistic, Ri = max(xij) – min(xij) Part VA m i=1 max xij−min(xij) m https://en.wikipedia.org/wiki/X%CC%85_and_R_chart Charlie Chong/ Fion Zhang

  47. ? chart Centre Line: ?=1 Part VA ? ? ?=1 ?? ??? ? = UCL/LCL = ? ± A2R ? ?=1 ??? Plot Statistic, ?? = ? https://en.wikipedia.org/wiki/X%CC%85_and_R_chart Charlie Chong/ Fion Zhang

  48. Plotting ? and R chart An X -Bar and R-Chart is a type of statistical process control chart for use with continuous data collected in subgroups at set time intervals - usually between 3 to 5 pieces per subgroup. The Mean (X -Bar) of each subgroup is charted on the top graph and the Range (R) of the subgroup is charted on the bottom graph. Out of Control points or patterns can occur on either the X -bar or R chart. Like all control charts, an X -Bar and R-Chart is used to answer the following questions:  Is the process stable over time?  What is the effect of a process change on the output characteristics?  How will I know if the process becomes unstable, or the performance changes over time? When is it used?  Constructed throughout the DMAIC (Define, Measure, Analyze, Improve and Control) process, particularly in the Measure, Analyze and Control phases of the cycle.  Used to understand process behavior, evaluate different treatments or methods, and to control a process.  Recommended for subgroup sizes of 10 or less. If the subgroup size exceeds 10, the range chart is replaced by a chart of the subgroup standard deviation, or S chart. NOTE: It has been estimated that 98% of all processes can be effectively represented by using either the X mR charts or X -Bar & R charts. Part VA https://www.moresteam.com/university/workbook/wb_spcxbarandrintro.pdf Charlie Chong/ Fion Zhang

  49. How to Construct an X-Bar and R Control Chart To construct an X -Bar and R Chart, follow the process steps below. For subgroup sizes greater than 10, substitute the subgroup standard deviation (S) for range (R), and use constants for S from the table located after the instructional steps. 1. Record subgroup observations. 2. Calculate the average (X -Bar) and range (R) for each subgroup. ??? ?=1 ? 3. Calculate the average R value, or R-bar, and plot this value as the centerline on the R chart; R = m 45. Calculate the average ? value, or ? -bar, and plot this value as the centerline on the ? chart; ??? ?=1 ?=1 ?? Where: m is the number of subgroup, n is the size of subgroup (sampling size) 5. Plot the ?? and Ri values for each subgroup in time series. You can create a meaningful control chart from as few as 6-7 data points, although a larger sample size (20+ subgroups) will provide much more reliability. In most cases, control limits are not calculated until at least 20 subgroups of data are collected. Part VA ? ?? = , Ri = max(xij) – min(xij) m i=1 max xij−min(xij) ? ? ? = https://www.moresteam.com/university/workbook/wb_spcxbarandrintro.pdf Charlie Chong/ Fion Zhang

  50. 5. Based on the subgroup size, select the appropriate constant, called D4, and multiply by R-bar (R ) to determine the Upper Control Limit for the Range Chart. All constants are available from the reference table. If the subgroup size is between 7 and 10, select the appropriate constant, called D3, and multiply by R-bar to determine the Lower Control Limit for the Range Chart. There is no Lower Control Limit for the Range Chart if the subgroup size is 6 or less. UCL (R) = R x D4 Plot the Upper Control Limit on the R chart. LCL(R) = R x D3 Plot the Lower Control Limit on the R chart. 6. Calculate the X-bar Chart Upper Control Limit, or upper natural process limit, by multiplying R-bar by the appropriate A2 factor (based on subgroup size) and adding that value to the average (X -bar-bar). Calculate the X-bar Chart Lower Control Limit, or lower natural process limit, for the X -bar chart by multiplying R-bar by the appropriate A2 factor (based on subgroup size) and subtracting that value from the average (X -barbar). UCL(? -bar) = ? + (A2 x R ) LCL (? -bar) = ? - (A2 x R ) Plot the UCL/LCL on the ? -bar chart. 10.After constructing the control chart, follow the same rules to assess stability that are used on mR charts. Make sure to evaluate the stability of the Range Chart before drawing any conclusions about the Averages (? - Bar) Chart --- if the Range Chart is out of control, the control limits on the Averages Chart will be unreliable. Part VA https://www.moresteam.com/university/workbook/wb_spcxbarandrintro.pdf Charlie Chong/ Fion Zhang

More Related