Chapter 18:Statistical Quality

Control

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.

• 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

Quality

LO1

1. Transcendent quality: Claims that the product has an “innate excellence”

2. Product quality: refers to perceivable qualitative attributes as well as quantifiable characteristics of the product: quality is measurable

3. User quality: quality is determined by the consumer4. Manufacturing quality: quality is measured by the

manufacturer's ability to target the product specifications with little variability

5. Value Quality: Answers the question did the consumer get his or her money’s worth? Cost benefit analysis applies.

Garvin’s Five Dimensions of Quality

LO1

• 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.

Quality Control

LO1

• 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.

The Deming Chain Reaction

LO1

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.

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

LO1

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.

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

LO1

• 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

SIX SIGMA

LO1

• 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

SIX SIGMA

LO1

• 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

Seven Important Quality Concepts

LO1

• 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

Seven Important Quality Concepts

LO1

• 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

Process Analysis and Tools Used

LO2

• 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

Process Analysis and Tools Used

• 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.

Use of Flow Charts in Process Analysis

LO2

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

Start/Stop Symbol

Flow line Symbol

LO2

Flowchart of Loan Process At a Bank

LO2

• 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

Pareto Charts : Figure 18.3

LO2

Pareto Chart of Medication Errors

LO2

• 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

Cause-and Effect Analysis

LO2

• 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

The Electric Motor Problem

LO2

Pareto Charts for the Electric Motor Problem: Figure 18.4

LO2

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

LO2

• 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.

Check Sheets or Checklists

LO2

• 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.

Check Sheets or Checklists

LO2

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

• 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).

Scatter Charts or Scatter Diagrams

LO2

• 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 .

Scatter Charts or Scatter Diagrams

LO2

• 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.

Control Charts

LO3

• Control charts for measurements– charts– R charts

• Control charts for compliance items– P charts– c charts

Types of Control Charts

LO3

• 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).

Chart X

LO3

• 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.

Chart X

LO3

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.

Control ChartX

LO3

Control Chart: FormulasX

LO3

Data for Demonstration Problem 18.1: Samples 1 - 10

1 2 3 4 5 6 7 8 9 105.13 4.96 5.21 5.02 5.12 4.98 4.99 4.96 4.96 5.034.92 4.98 4.87 5.09 5.08 5.02 5.00 5.01 5.00 4.995.01 4.95 5.02 4.99 5.09 4.97 5.00 5.02 4.91 4.964.88 4.96 5.08 5.02 5.13 4.99 5.02 5.05 4.87 5.145.05 5.01 5.12 5.03 5.06 4.98 5.01 5.04 4.96 5.114.97 4.89 5.04 5.01 5.13 4.99 5.01 5.02 5.01 5.04

4.9933 4.9583 5.0567 5.0267 5.1017 4.9883 5.0050 5.0167 4.9517 5.04500.25 0.12 0.34 0.10 0.07 0.05 0.03 0.09 0.14 0.18

XR

LO3

Data for Demonstration Problem 18.1: Samples 11 - 20

11 12 13 14 15 16 17 18 19 204.91 4.97 5.09 4.96 4.99 5.01 5.05 4.96 4.90 5.044.93 4.91 4.96 4.99 4.97 5.04 4.97 4.93 4.85 5.035.04 5.02 5.05 4.82 5.01 5.09 5.04 4.97 5.02 4.975.00 4.93 5.12 5.03 4.98 5.07 5.03 5.01 5.01 4.994.90 4.95 5.06 5.00 4.96 5.12 5.09 4.98 4.88 5.054.82 4.96 5.01 4.96 5.02 5.13 5.01 4.92 4.86 5.06

4.9333 4.9567 5.0483 4.9600 4.9883 5.0767 5.0317 4.9617 4.9200 5.02330.22 0.11 0.16 0.21 0.06 0.12 0.12 0.09 0.17 0.09

XR

Demonstration Problem 18.1:Control Chart Computations

LO3

Determine the value of A2 by using ni = 6 (size of the sample) from Table A.15, giving A2 = 0.483.

Demonstration Problem 18.1:Control Chart Computations

LO3

Demonstration Problem 18.1: Control ChartX

Sigma level: 3

2019

1817

1615

1413

1211

109

87

65

43

21

Bearing Diameter

UCL = 5.0679

Average = 5.0022

LCL = 4.9364

Control Chart: Bearing Diameter

Mean

5.10963

5.05590

5.00217

4.94844

4.89471

LO3

Monitor process variation

1. Decide on the quality to be measured.

2. Determine a sample size.

3. Gather 20 to 30 samples.

4. Compute the sample range, R, for each sample.

5. Determine the average sample range for all samples.

6. Using the size of the samples, determine the values of D3 and D4 in Table A.15.

7. Construct the centreline, , compute the UCL and LCL.

R Chart

LO3

R Chart Formulas

LO3

Demonstration Problem 18.2: R Control Chart

LO3

Demonstration Problem 18.2: R Control Chart

Control Chart: Bearing Diameter

Sigma level: 3

2019

1817

1615

1413

1211

109

87

65

43

21

Range

.4

.3

.2

.1

0.0

Bearing Diameter

UCL = .2725

Average = .1360

LCL = .0000

LO3

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.

P Charts

LO3

P Chart Formulas

LO3

Demonstration Problem 18.3: Twenty Samples of Bond Paper

Sample n

Number Out of

Compliance Sample n

Number Out of

Compliance1 50 4 11 50 22 50 3 12 50 63 50 1 13 50 04 50 0 14 50 25 50 5 15 50 16 50 2 16 50 67 50 3 17 50 28 50 1 18 50 39 50 4 19 50 1

10 50 2 20 50 5

LO3

Demonstration Problem 18.3: Preliminary Calculations

Sample n nnon Sample n nnon

1 50 4 0.08 11 50 2 0.042 50 3 0.06 12 50 6 0.123 50 1 0.02 13 50 0 0.004 50 0 0.00 14 50 2 0.045 50 5 0.10 15 50 1 0.026 50 2 0.04 16 50 6 0.127 50 3 0.06 17 50 2 0.048 50 1 0.02 18 50 3 0.069 50 4 0.08 19 50 1 0.02

10 50 2 0.04 20 50 5 0.10

pp

Demonstration Problem 18.3:Centerline, UCL, and LCL Computations

LO3

Demonstration Problem 18.3:P Control Chart

LO3

Demonstration Problem 18.3:Minitab P Control Chart

Sample

Pro

port

ion

2018161412108642

0.16

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

_P=0.053

UCL=0.1480

LCL=0

P Chart of Out of Compliance

LO3

Monitor number of non-conformances per item

1. Decide on non-conformances to be evaluated.2. Determine the number of items to be studied (at least 25).3. Gather items or units.4. Determine the value of c for each item by summing the

number of non-conformances in the item.5. Calculate the value of 6. Determine the centreline, the UCL, and the LCL

c Charts

LO3

c Chart Formulas

LO3

Demonstration Problem 18.4:Number of Nonconformities in Oil Gauges

LO3

Demonstration Problem 18.4:c Chart Calculations

LO3

Demonstration Problem 18.4: c Chart

LO3

Demonstration Problem 18.4: Minitab c Chart

Sample

Sam

ple

Count

24222018161412108642

7

6

5

4

3

2

1

0

_C=2

UCL=6.243

LCL=0

C Chart of Number of Nonconformances

LO3

• 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

Rationale for Interpretation of Control Charts

LO3

• 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

Rationale for Interpretation of Control Charts

LO3

• 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

Rationale for Interpretation of Control Charts

LO3

1. Points are above the UCL and/or below the LCL.2. 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.

3. A trend of six or more consecutive points (increasing or decreasing) is present.

4. Two out of three consecutive values are in the outer one third.

5. Four out of five consecutive values are in the outer two thirds.

6. The centreline shifts from chart to chart.

Control Chart Abnormalities

LO3

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

Examples of Control Chart With Problems

LO3

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

LO3

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

LO3

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

LO3

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

LO3

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

LO3

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

Causes of Abnormalities Revealed by Control Charts

LO3

• 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.

Warning

LO3

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