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Unit 3

Unit 3. Statistical Process Control. SEVEN QUALITY CONTROL TOOLS. (or) OLD SEVEN TOOLS. Dr.Kaoru Ishikawa, Professor at Tokyo University & Father of Q C in Japan. CAUSE ANALYSIS TOOLS are Cause and Effect diagram, Pareto analysis & Scatter diagram .

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Unit 3

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  1. Unit 3 Statistical Process Control

  2. SEVEN QUALITY CONTROL TOOLS (or) OLD SEVEN TOOLS

  3. Dr.Kaoru Ishikawa, Professor at Tokyo University & Father of Q C in Japan. • CAUSE ANALYSIS TOOLS are Cause and Effect diagram, Pareto analysis & Scatter diagram. • EVALUATION AND DECISION MAKING TOOLS are decision matrix and multivoting

  4. DATA COLLECTION AND ANALYSIS TOOLS are check sheet, control charts, DOE, scatter diagram, stratification, histogram, survey. • IDEA CREATION TOOLS are Brainstorming, Benchmarking, Affinity diagram, Normal group technique. • PROJECT PLANNING AND IMPLEMENTATIONTOOLS are Gantt chart and PDCA Cycle.

  5. Cause-and-effect diagram (also called Ishikawa or fishbone chart ) DESCRIPTION • The fishbone diagram identifies many possible causes for an effect or problem. It can be used to structure a brainstorming session. It immediately sorts ideas into useful categories. WHEN TO USE • When identifying possible causes for a problem. • Especially when a team’s thinking tends to fall into ruts

  6. PROCEDURE • MATERISLS REQUIRED:Flipchart (or) White Board, Marking Pens. • Agree on a problem statement (effect). Write it at the center right of the flipchart or whiteboard. Draw a box around it and draw a horizontal arrow running to it. • Brainstorm the major categories of causes of the problem. If this is difficult use generic headings: • Methods • Machines (equipment) • People (manpower) • Materials • Measurement • Environment

  7. Write the categories of causes as branches from the main arrow. • Brainstorm all the possible causes of the problem. Ask: “Why does this happen?” As each idea is given, the facilitator writes it as a branch from the appropriate category. Causes can be written in several places if they relate to several categories. • Again ask “why does this happen?” about each cause. Write sub-causes branching off the causes. Continue to ask “Why?” and generate deeper levels of causes. Layers of branches indicate causal relationships. • When the group runs out of ideas, focus attention to places on the chart where ideas are few.

  8. Example • This fishbone diagram was drawn by a manufacturing team to try to understand the source of periodic iron contamination. The team used the six generic headings to prompt ideas. Layers of branches show thorough thinking about the causes of the problem.

  9. For example, under the heading “Machines,” the idea “materials of construction” shows four kinds of equipment and then several specific machine numbers. • Note that some ideas appear in two different places. “Calibration” shows up under “Methods” as a factor in the analytical procedure, and also under “Measurement” as a cause of lab error. “Iron tools” can be considered a “Methods” problem when taking samples or a “Manpower” problem with maintenance personnel

  10. CHECK SHEET (or) DEFECT CONCENTRATION DIAGRAM DESCRIPTION • A check sheet is a structured, prepared form for collecting and analyzing data. This is a generic tool that can be adapted for a wide variety of purposes

  11. WHEN TO USE • When data can be observed and collected repeatedly by the same person or at the same location. • When collecting data on the frequency or patterns of events, problems, defects, defect location, defect causes, etc. • When collecting data from a production process.

  12. PROCEDURE • Decide what event or problem will be observed. Develop operational definitions. • Decide when data will be collected and for how long. • Design the form. Set it up so that data can be recorded simply by making check marks or Xs or similar symbols and so that data do not have to be recopied for analysis. • Label all spaces on the form. • Test the check sheet for a short trial period to be sure it collects the appropriate data and is easy to use. • Each time the targeted event or problem occurs, record data on the check sheet.

  13. EXAMPLE • The figure below shows a check sheet used to collect data on telephone interruptions. The tick marks were added as data was collected over several weeks.

  14. Histogram • Histogram:The most commonly used graph for showing frequency distributions, or how often each different value in a set of data occurs

  15. WHEN TO USE • The data are numerical values. • To see the shape of the data’s distribution, especially when determining whether the output of a process is distributed approximately normally. • Analyzing whether a process can meet the customer’s requirements. • Analyzing what the output from a supplier’s process looks like. • Whether a process change has occurred from one time period to another. • To determine whether the outputs of two or more processes are different. • To communicate the distribution of data quickly and easily to others.

  16. Histogram Shapes and Meaning • Normal. A common pattern is the bell-shaped curve known as the “normal distribution.” In a normal distribution, points are as likely to occur on one side of the average as on the other.

  17. Skewed. The skewed distribution is asymmetrical because a natural limit prevents outcomes on one side. The distribution’s peak is off center toward the limit and a tail stretches away from it. • These distributions are called right- or left-skewed according to the direction of the tail.

  18. Double-peaked or bimodal. The bimodal distribution looks like the back of a two-humped camel. The outcomes of two processes with different distributions are combined in one set of data. A two-shift operation might be bimodal.

  19. Plateau. The plateau might be called a “multimodal distribution.” Several processes with normal distributions are combined.Because there are many peaks close together, the top of the distribution resembles a plateau.

  20. Dog food. The dog food distribution is missing something—results near the average. If a customer receives this kind of distribution, someone else is receiving a heart cut, and the customer is left with the “dog food,” the odds and ends left over after the master’s meal

  21. Pareto Chart (or)Pareto diagram (or) Pareto analysis • A Pareto chart is a bar graph. The lengths of the bars represent frequency or cost (time or money), and are arranged with longest bars on the left and the shortest to the right.

  22. When to Use • When analyzing data about the frequency of problems or causes in a process. • When there are many problems or causes and you want to focus on the most significant. • When analyzing broad causes by looking at their specific components. • When communicating with others about your data.

  23. The Pareto 80 / 20 rule 80 % of the problems are produced by 20 % of the causes. PARETO DIAGRAM To identify the ‘VITAL FEW FROM TRIVIAL MANY’ and to concentrate on the vital few for improvement. A Pareto diagram indicates which problem we should solve first in eliminating defects and improving the operation.

  24. Scatter Diagram (or) Scatter plot (or)X–Y graph • The scatter diagram graphs pairs of numerical data, with one variable on each axis, to look for a relationship between them. If the variables are correlated, the points will fall along a line or curve. The better the correlation, the tighter the points will hug the line.

  25. When to Use • When you have paired numerical data. • When your dependent variable may have multiple values for each value of your independent variable. • When trying to determine whether the two variables are related, such as when trying to identify potential root causes of problems. • After brainstorming causes and effects using a fishbone diagram, to determine objectively whether a particular cause and effect are related.

  26. Stratification (or) Flowchart (or) Run chart • Stratification is a technique used in combination with other data analysis tools. When data from a variety of sources or categories have been lumped together, the meaning of the data can be impossible to see

  27. When to Use • Before collecting data. • When data come from several sources or conditions, such as shifts, days of the week, suppliers or population groups. • When data analysis may require separating different sources or conditions.

  28. The ZZ-400 manufacturing team drew a scatter diagram to test whether product purity and iron contamination were related, but the plot did not demonstrate a relationship. Then a team member realized that the data came from three different reactors. The team member redrew the diagram, using a different symbol for each reactor’s data

  29. Benefit from stratification. • Always consider before collecting data whether stratification might be needed during analysis. Plan to collect stratification information. After the data are collected it might be too late. • On your graph or chart, include a legend that identifies the marks or colors used.

  30. Statistical Process Control

  31. What is a process? A process can be described as a transformation of set of inputs into desired outputs. Inputs PROCESS Outputs

  32. Types of Measures • Measures where the metric is composed of a classification in one of two (or more) categories is called Attribute data. _ Good/Bad • Yes/No • Measures where the metric consists of a number which indicates a precise value is called Variable data. • Time • Miles/Hr

  33. A sample is just a subset of all possible values sample population • Since the sample does not contain all the possible values, there is some uncertainty about the population. Hence any statistics, such as mean and standard deviation, are just estimates of the true population parameters. Population Vs. Sample (Certainty Vs. Uncertainty)

  34. WHY STATISTICS?THE ROLE OF STATISTICS ……… Statistics is the art of collecting, classifying, presenting, interpreting and analyzing numerical data, as well as making conclusions about the system from which the data was obtained.

  35. Descriptive Statistics Descriptive Statistics is the branch of statistics which most people are familiar. It characterizes and summarizes the most prominent features of a given set of data (means, medians, standard deviations, percentiles, graphs, tables and charts.

  36. Inferential Statistics Inferential Statistics is the branch of statistics that deals with drawing conclusions about a population based on information obtained from a sample drawn from that population.

  37. ORDERED DATA SET The mean is simply the average value of the data. -5 -3 -1 å x - 2 -1 i mean = x = = = - . 17 n 12 0 0 n=12 0 0 0 1 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 4 å Mean x = - 2 i WHAT IS THE MEAN?

  38. If we rank order (descending or ascending) the data set ,we find the value half way (50%) through the data points and is called the median value. ORDERED DATA SET -5 -3 -1 50% of data points -1 0 0 Median 0 0 0 1 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 4 Median Value WHAT IS THE MEDIAN?

  39. If we rank order (descending or ascending) the data set We find that a single value occurs more often than any other. This is called the mode. ORDERED DATA SET -5 -3 . -1 -1 0 0 Mode Mode 0 0 0 1 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 4 WHAT IS THE MODE?

  40. ORDERED DATA SET The range is a very common metric . To calculate the range simply subtract the minimum value in the sample from the maximum value. -5 -3 -1 -1 Range = x - x = 4 - ( - 5 ) = 9 0 MIN MAX 0 Range 0 0 0 1 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 4 Range Min Max WHAT IS THE RANGE?

  41. The variance (s2) is a very robust metric . The standard deviation(s) is the square root of the variance and is the most commonly used measure of dispersion. å X - 2 i -.17 X = = = 12 n X - X DATA SET i -5 -5-(-.17)=-4.83 -3-(-.17)=-2.83 -1-(-.17)=-.83 -1-(-.17)=-.83 0-(-.17)=.17 0-(-.17)=.17 0-(-.17)=.17 0-(-.17)=.17 0-(-.17)=.17 1-(-.17)=1.17 3-(-.17)=3.17 4-(-.17)=4.17 (-4.83)2=23.32 (-2.83)2=8.01 (-.83)2=.69 (-.83)2=.69 (.17)2=.03 (.17)2=.03 (.17)2=.03 (.17)2=.03 (.17)2=.03 (1.17)2=1.37 (3.17)2=10.05 (4.17)2=17.39 61.67 -3 ( ) -1 å 2 X - X 61 . 67 -1 i 2 s = = = 5 . 6 0 n - 1 12 - 1 0 0 0 0 1 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 4 WHAT IS THE VARIANCE/STANDARD DEVIATION?

  42. Statistical Process Control (SPC) • Measures performance of a process • Uses mathematics (i.e., statistics) • Involves collecting, organizing, & interpreting data • Objective: Regulate product quality • Used to • Control the process as products are produced • Inspect samples of finished products

  43. CONTROL CHART Functions of a Process Control System are • To signal the presence of assignable causes of variation • To give evidence if a process is operating in a state of statistical control

  44. CONTROL CHART Essential features of a control chart Upper Control Limit Central Line VariableValues Lower Control Limit Time

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