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**Chapter 18: Statistical Quality Control**

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Learning Objectives LO1 Explain the meaning of quality in business, compare the approaches to quality improvement by various quality gurus and movements, and compare different approaches to controlling the quality of a product, including benchmarking, just-in-time inventory systems, Six Sigma, lean manufacturing, reengineering, failure mode and effects analysis, poka-yoke, and quality circles. LO2 Compare various tools that identify, categorize, and solve problems in the quality improvement process, including flowcharts, Pareto analysis, cause-and-effect diagrams, control charts, check sheets, histograms, and scatter charts. LO3 Measure variation among manufactured items using various control charts, including x charts, R charts, p charts, and c charts.

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Quality There are as many definitions of quality as people and products A view generally held is that Quality is achieved when a product delivers what is stipulated for in its specifications Crosby: “quality is conformance to requirements”. When a producer delivers what has been specified in the product description, as agreed upon by both buyer and seller Feigenbaum defines quality as something that is customer determined not management or design determined: “quality is a customer determination” David A. Garvin claims that there are there are at least five types of quality LO1

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**Garvin’s Five Dimensions of Quality**

Transcendent quality: Claims that the product has an “innate excellence” Product quality: refers to perceivable qualitative attributes as well as quantifiable characteristics of the product: quality is measurable User quality: quality is determined by the consumer Manufacturing quality: quality is measured by the manufacturer's ability to target the product specifications with little variability Value Quality: Answers the question did the consumer get his or her money’s worth? Cost benefit analysis applies. LO1

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**Quality Control Quality control (quality assurance) is**

the collection of strategies, techniques, and actions taken by an organization to assure themselves that they are producing a quality product Two approaches to quality control After-process quality control: involves inspecting the attributes of a finished product to determine whether the product is acceptable, is in need of rework, or is to be rejected and scrapped. reporting of the number of defects per time period screening defective products from consumers In-process quality control techniques: measure product attributes at various intervals throughout the manufacturing process in an effort to pinpoint problem areas. LO1

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**The Deming Chain Reaction**

Deming gives a cause and effect explanation of the impact of TQM embodied in the concept of quality control as generating a chain reaction through the company The Deming chain reaction begins with improving quality, which reduces cost, because of less reworking, fewer mistakes, fewer delays and better use of machinery time and materials. From the reduction in cost resulting from getting it right the first time follows an improvement in productivity Because productivity = Output / Input As productivity improves a company is more able to capture the market with better quality and lower prices. LO1

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**Total Quality Management (TQM): Deming’s Fourteen Points (1-7)**

1. Create constancy of purpose for improvement of product and service 2. Adopt a new philosophy. 3. Cease dependence on mass inspection. 4. End the practice of awarding business on price tag alone. 5. Improve constantly and forever the system of production and service. 6. Institute training. 7. Institute leadership. LO1

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**Total Quality Management (TQM): Deming’s Fourteen Points (8-14)**

8. Drive out fear. 9. Break down barriers between staff areas. 10. Eliminate slogans. 11. Eliminate numerical quotas. 12. Remove barriers to pride of workmanship. 13. Institute a vigorous program of education and retraining. 14. Take action to accomplish the transformation. LO1

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SIX SIGMA Six Sigma is a quality movement methodology, and a measurement. This movement is very actively adhered to worldwide in the manufacturing and services sectors. It provides a methodology for evaluating the capability of a process to perform defect-free, where a defect is defined as anything that results in customer dissatisfaction Sigma is customer focused. It keeps in mind both internal and external customers LO1

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SIX SIGMA It has the potential to achieve exponential quality improvement through the reduction of variation in system processes Six –sigma system contains a formalized problem-solving approach called DMAIC process: define, measure analyze, improve, and control. This requires highly coordinated teamwork LO1

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**Seven Important Quality Concepts**

Benchmarking Benchmarking examine and emulate the best practices and techniques used in the industry a positive, proactive process to make changes that will effect superior performance Just-In-Time Inventory Systems necessary parts for production arrive “just in time” reduced holding costs, personnel, and space needed for inventory no extra raw materials or inventory of parts for production are stored Reengineering complete redesign of the core business process in a company LO1

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**Seven Important Quality Concepts**

Failure Mode and Effects Analysis systematic approach to identify the effects of a potential product or process failure and includes methodology for eliminating or reducing the chance of a failure occurring Poka-Yoke Use of devices, methods and inspections to avoid machine error or simple human error. Quality Circles and Six Sigma Teams Total quality approach that measures the capacity of a process to perform defect -free work Team Building employee groups take on managerial responsibilities quality circle teams from the same department meet regularly to discuss quality issues LO1

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**Process Analysis and Tools Used**

A process is a series of actions, changes or functions that bring about a result: involve the assembly or development of an output from a given input. Meaningful systems add value to the inputs as part of the process LO2

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**Process Analysis and Tools Used**

Tools Used in Process Analysis Flowcharts - schematic representation of all the activities and interactions that occur in a process or a meaningful system Check sheets or check lists Pareto Analysis -quantitative tallying of the number and types of defects that occur with a product Pareto Chart - ranked vertical bar chart with most frequently occurring on the left Fishbone Diagram - display of potential cause-and-effect relationships Control Charts - graphical method for evaluating whether a process is or is not in a “state of statistical control” Histogram Scatter charts or scatter diagrams

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**Use of Flow Charts in Process Analysis**

A flow chart is a schematic representation of all the activities and interactions that occur in a process. It includes decision points, activities, input/output, start/stop, and a flow line. Once the process has been mapped by a procedure or procedures such as the Flow chart, procedures for identifying bottlenecks and problem causes can begin. This takes us to the Pareto chart and cause and effect diagram such as the fishbone chart. LO2

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Flowchart Symbols Input/Output Symbol: Represents an input to the process or an output from it Processing Symbol: represents an activity Decision Symbol: points to where decisions are being made Flow line Symbol Start/Stop Symbol LO2

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**Flowchart of Loan Process At a Bank**

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Pareto Charts : Figure 18.3 Pareto Charts are vertical bar charts that display the most common types of defects that occur with a product or service, ranked in order of occurrence from left to right Figure 18.3 on the next slide is a Pareto chart depicting various potential sources of medication error in a hospital. The Pareto chart shows the most frequent types of defects but it does not indicate or identify the causes. The fishbone or Ishikawa diagram can be used to assist in the identification of cause-and-effect LO2

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**Pareto Chart of Medication Errors**

LO2

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**Cause-and Effect Analysis**

The fishbone was developed Kaoru Ishikawa in the 1940s as a way to display possible causes of a problem and the interrelationships among the causes . The causes can be uncovered through brainstorming, investigating, surveys, and other information gathering techniques. The diagram is in the shape of the skeleton of a fish: the head represents the problem to be resolved; possible causes are represented by the ribs/bone attached too both sides of the main bone or spine. Sub-causes can be included along each fish bone LO2

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**The Electric Motor Problem**

Suppose official at a company producing the electric motor want to construct a fish bone diagram to display the poor wiring problem it has discovered it has Figure 18.4 is a Pareto diagram showing the frequency of number of defects in the functioning of the motor> Poor wiring is the most frequent problem Figure 18.5 is a presentation of the fishbone diagram showing possible causes of the problem LO2

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**Pareto Charts for the Electric Motor Problem: Figure 18.4**

LO2

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**Cause-and-Effect Diagram for Electric Motor Problem: Figure 18.5**

LO2

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**Check Sheets or Checklists**

Most check sheets are simple forms consisting of multiple categories and columns for recording tallies and are used for collecting data in a logical format and helping to organize data by category. Check sheets are simple to use, and the convert data into useful information, and frequently the results can be interpreted on the form without additional processing. LO2

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**Check Sheets or Checklists**

Very useful in tracking problems and causes of problems and the provision of hard evidence. One of the tool fundamental tools used in constructing a Pareto diagram, cause-and-effect diagrams, histograms and frequency distributions. Checklists are central to the activity of gathering, organizing and summarizing data. LO2

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**Check Sheet Showing Why Patients Do Not Consume Meal Within an Hour**

Note that a Check Sheet not only indicates the cause as “Patient asleep”, “Patient out of room”, and “Nursing not available”, but the times during which the problem is worse. LO2

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**Scatter Charts or Scatter Diagrams**

Quite frequently the implementation of quality improvement techniques and in root-cause analysis, it is important to explore the relationship between two numerical variables. One graphical mechanism for examining the relationship between two variable is the scatter chart. Assist in determining if there is a relationship and if so the direction of that relationship (Positive or Negative). LO2

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**Scatter Charts or Scatter Diagrams**

In using the method one has to be constantly aware of the existence of spurious relationships. Given the techniques we are using, variables may appear to be related. But this does not mean that one variable is causing the other to change or “drives” the other variable. The relationship observed may be due to chance or a result of other factors acting through one of the variable of interest . LO2

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Control Charts A control chart is a graphical method for evaluating whether a process is or is not in a state of statistical control. Control charts are used mainly to monitor product variation. The charts enable operators, technicians, managers to see when a process gets out of control, search for and to make an immediate correction of the problem. This prompt action improves quality and increases productivity: the Deming Chain Reaction principle at work. Process charts assist management in measuring, recording, and studying variations in the product or service, so that out of control conditions can be identified and corrected. LO3

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**Types of Control Charts**

Control charts for measurements charts R charts Control charts for compliance items P charts c charts LO3

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Chart The chart is a graphic of simple means computed for a series of small random samples over a period of time. The means are average measurements of some product characteristic. These sample means are plotted on a graph that contains a centreline, an upper control line (UCL) and a lower control line (LCL). LO3

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Chart For large samples the Empirical rule hold and UCL and LCL can be plotted at 3 standard deviations of the means below the process mean; and UCL 3 standard deviations of the means above the process mean. But when sample sizes are small an approximation of 3 standard deviation of means is used. These can be obtained from tables given in A.15 of the text. LO3

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Control Chart Monitor process location (center) 1. Decide on the quality to be measured. 2. Determine a sample size. 3. Gather 20 to 30 samples. 4. Compute the sample average for each sample. 5. Compute the sample range for each sample. 6. Determine the average sample mean for all samples. 7. Determine the average sample range (or sample standard deviation) for all samples. 8. Using the size of the samples, determine the value of A2 or A3. 9. Compute the UCL and the LCL. LO3

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**Control Chart: Formulas**

LO3

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**Data for Demonstration Problem 18.1: Samples 1 - 10**

2 3 4 5 6 7 8 9 10 5.13 4.96 5.21 5.02 5.12 4.98 4.99 5.03 4.92 4.87 5.09 5.08 5.00 5.01 4.95 4.97 4.91 4.88 5.05 5.14 5.06 5.04 5.11 4.89 4.9933 4.9583 5.0567 5.0267 5.1017 4.9883 5.0050 5.0167 4.9517 5.0450 0.25 0.12 0.34 0.10 0.07 0.05 0.03 0.09 0.14 0.18 X R LO3

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**Data for Demonstration Problem 18.1: Samples 11 - 20**

12 13 14 15 16 17 18 19 20 4.91 4.97 5.09 4.96 4.99 5.01 5.05 4.90 5.04 4.93 4.85 5.03 5.02 4.82 5.00 5.12 4.98 5.07 4.95 5.06 4.88 5.13 4.92 4.86 4.9333 4.9567 5.0483 4.9600 4.9883 5.0767 5.0317 4.9617 4.9200 5.0233 0.22 0.11 0.16 0.21 0.06 0.12 0.09 0.17 X R

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**Demonstration Problem 18.1: Control Chart Computations**

Determine the value of A2 by using ni = 6 (size of the sample) from Table A.15, giving A2 = LO3

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**Demonstration Problem 18.1: Control Chart Computations**

LO3

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**Demonstration Problem 18.1: Control Chart**

Sigma level: 3 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Bearing Diameter UCL = Average = LCL = Control Chart: Bearing Diameter Mean LO3

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**R Chart Monitor process variation**

Decide on the quality to be measured. Determine a sample size. Gather 20 to 30 samples. Compute the sample range, R, for each sample. Determine the average sample range for all samples. Using the size of the samples, determine the values of D3 and D4 in Table A.15. Construct the centreline, , compute the UCL and LCL. LO3

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R Chart Formulas LO3

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**Demonstration Problem 18.2: R Control Chart**

LO3

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**Demonstration Problem 18.2: R Control Chart**

Control Chart: Bearing Diameter Sigma level: 3 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Range .4 .3 .2 .1 0.0 Bearing Diameter UCL = .2725 Average = .1360 LCL = .0000 LO3

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P Charts Monitor proportion in noncompliance 1. Decide on the quality to be measured. 2. Determine a sample size. 3. Gather 20 to 30 samples. 4. Compute the sample proportion for each sample. 5. Compute the average proportion. 6. Determine the centreline, the UCL, and the LCL. LO3

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P Chart Formulas LO3

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**Demonstration Problem 18.3: Twenty Samples of Bond Paper**

Number Out of Compliance 1 50 4 11 2 3 12 6 13 14 5 15 16 7 17 8 18 9 19 10 20 LO3

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**Demonstration Problem 18.3: Preliminary Calculations**

Sample n nnon 1 50 4 0.08 11 2 0.04 3 0.06 12 6 0.12 0.02 13 0.00 14 5 0.10 15 16 7 17 8 18 9 19 10 20 p

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**Demonstration Problem 18.3: Centerline, UCL, and LCL Computations**

LO3

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**Demonstration Problem 18.3: P Control Chart**

LO3

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**Demonstration Problem 18.3: Minitab P Control Chart**

LO3

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**c Charts Monitor number of non-conformances per item**

Decide on non-conformances to be evaluated. Determine the number of items to be studied (at least 25). Gather items or units. Determine the value of c for each item by summing the number of non-conformances in the item. Calculate the value of Determine the centreline, the UCL, and the LCL LO3

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c Chart Formulas LO3

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**Demonstration Problem 18.4: Number of Nonconformities in Oil Gauges**

LO3

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**Demonstration Problem 18.4: c Chart Calculations**

LO3

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**Demonstration Problem 18.4: c Chart**

LO3

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**Demonstration Problem 18.4: Minitab c Chart**

LO3

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**Rationale for Interpretation of Control Charts**

Control outer limits (UCL and LCL) are established at three standard deviations above and below the centreline . According to the Empirical rule approximately 99.7% of all values should be within three standard deviations of the mean of the statistic If the system is in control virtually no data points should be outside these limits Data points found outside these limits should be strongly considered as outliers and investigated to determine the cause LO3

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**Rationale for Interpretation of Control Charts**

Being in bounds is not a sufficient condition for determining whether the system is in control. A necessary condition is that the data points are also randomly scattered around the centreline Check to see if at any point in time a trend is emerging in the data: linear, cyclical or any other. These may signal a system problem LO3

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**Rationale for Interpretation of Control Charts**

Also, in accordance with the empirical rule 95% of all values should be within two standard deviations of the centreline. Make sure that fewer than 5% of all points fall in the outer one third of the region between the centreline and the outer control limits Also by Empirical rule make sure that fewer than 32% are in the outer two thirds of the control chart. If this is not the case the process should be also examined LO3

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**Control Chart Abnormalities**

Points are above the UCL and/or below the LCL. Eight or more consecutive points are above or below or below the centreline. Ten out of 11 points fall above or below the centerline. Twelve out of 14 points fall above or below the centerline. A trend of six or more consecutive points (increasing or decreasing) is present. Two out of three consecutive values are in the outer one third. Four out of five consecutive values are in the outer two thirds. The centreline shifts from chart to chart. LO3

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**Examples of Control Chart With Problems**

The following slides are examples of charts that illustrate the type of problems presented in the previous slide. LO3

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**Interpreting Control Charts: Chart (a) Points above UCL and/or below LCL**

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**Interpreting Control Charts Chart (b): 8 Consecutive Points on One Side of the Centreline**

LO3

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**Interpreting Control Charts: Chart (c): 6 or More Consecutive Increasing Points**

LO3

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**Interpreting Control Charts: Chart (d): 2 out of 3 Consecutive Points in Outer 1/3**

LO3

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**Interpreting Control Charts Chart (e): 4 Out of Five Consecutive Values Are in the Outer 2/3**

LO3

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**Causes of Abnormalities Revealed by Control Charts**

Changes in the physical environment Worker fatigue Worn tools Changes in operators or machines Maintenance Changes in worker skills Changes in materials Process modification LO3

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Warning Statistical process control persons should be aware that control chart abnormalities can arise because of measurement errors or incorrect calculations of control limits Need to exercise judgment so as not to over control the process by adjusting to every oddity on a control chart. LO3

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COPYRIGHT Copyright © 2014 John Wiley & Sons Canada, Ltd. All rights reserved. Reproduction or translation of this work beyond that permitted by Access Copyright (The Canadian Copyright Licensing Agency) is unlawful. Requests for further information should be addressed to the Permissions Department, John Wiley & Sons Canada, Ltd. The purchaser may make back-up copies for his or her own use only and not for distribution or resale. The author and the publisher assume no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained herein.

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