Submit Search
Upload
Quality Improvement Tools for Business Processes
•
Download as PPT, PDF
•
0 likes
•
0 views
AI-enhanced title
C
cfisicaster
Follow
Newbold_estadistica_universitaria
Read less
Read more
Education
Report
Share
Report
Share
1 of 62
Download now
Recommended
Chapter 18
Chapter 18
Aneel Raza
quality_and_statistical_process_control.ppt
quality_and_statistical_process_control.ppt
HassanHani5
Statistical Process Control
Statistical Process Control
Nicola Mezzetti
Chapter 20 Lecture Notes
Chapter 20 Lecture Notes
Matthew L Levy
Quality and statistical process control ppt @ bec doms
Quality and statistical process control ppt @ bec doms
Babasab Patil
Operations Management VTU BE Mechanical 2015 Solved paper
Operations Management VTU BE Mechanical 2015 Solved paper
Somashekar S.M
process monitoring (statistical process control)
process monitoring (statistical process control)
Bindutesh Saner
Statistical Applications in Quality and Productivity Management
Statistical Applications in Quality and Productivity Management
Yesica Adicondro
Recommended
Chapter 18
Chapter 18
Aneel Raza
quality_and_statistical_process_control.ppt
quality_and_statistical_process_control.ppt
HassanHani5
Statistical Process Control
Statistical Process Control
Nicola Mezzetti
Chapter 20 Lecture Notes
Chapter 20 Lecture Notes
Matthew L Levy
Quality and statistical process control ppt @ bec doms
Quality and statistical process control ppt @ bec doms
Babasab Patil
Operations Management VTU BE Mechanical 2015 Solved paper
Operations Management VTU BE Mechanical 2015 Solved paper
Somashekar S.M
process monitoring (statistical process control)
process monitoring (statistical process control)
Bindutesh Saner
Statistical Applications in Quality and Productivity Management
Statistical Applications in Quality and Productivity Management
Yesica Adicondro
Quality management techniques
Quality management techniques
selinasimpson0401
C O N T R O L L P R E S E N T A T I O N
C O N T R O L L P R E S E N T A T I O N
وديع المخلافي
Statistical quality control presentation
Statistical quality control presentation
Suchitra Sahu
Engineering Data Analysis-ProfCharlton
Engineering Data Analysis-ProfCharlton
CharltonInao1
Seven Basic Quality Control Tools أدوات ضبط الجودة السبعة
Seven Basic Quality Control Tools أدوات ضبط الجودة السبعة
Mohamed Khaled
Quality management principle
Quality management principle
selinasimpson2501
Ch3. Demand Forecasting.ppt
Ch3. Demand Forecasting.ppt
MohammadYousefBaniMu
Chap17 statistical applications on management
Chap17 statistical applications on management
Uni Azza Aunillah
Newbold_chap03.ppt
Newbold_chap03.ppt
cfisicaster
Quality management service
Quality management service
selinasimpson321
Seven Quality Tools.pptx
Seven Quality Tools.pptx
Vijayarani Kasinadar
Purpose of quality management system
Purpose of quality management system
selinasimpson1801
Basic Analytics Module for Sponsors
Basic Analytics Module for Sponsors
Dee Daley
Chap07
Chap07
Marouane Zouzhi
Chap07
Chap07
Marouane Zouzhi
Lesson 6 measures of central tendency
Lesson 6 measures of central tendency
nurun2010
Service quality management system
Service quality management system
selinasimpson361
Qms quality management systems
Qms quality management systems
selinasimpson371
7 qc tools
7 qc tools
kmsonam
7 qc tools
7 qc tools
gurjeetdhillon
slidesWaveRegular.pdf
slidesWaveRegular.pdf
cfisicaster
WavesNotesAnswers.pdf
WavesNotesAnswers.pdf
cfisicaster
More Related Content
Similar to Quality Improvement Tools for Business Processes
Quality management techniques
Quality management techniques
selinasimpson0401
C O N T R O L L P R E S E N T A T I O N
C O N T R O L L P R E S E N T A T I O N
وديع المخلافي
Statistical quality control presentation
Statistical quality control presentation
Suchitra Sahu
Engineering Data Analysis-ProfCharlton
Engineering Data Analysis-ProfCharlton
CharltonInao1
Seven Basic Quality Control Tools أدوات ضبط الجودة السبعة
Seven Basic Quality Control Tools أدوات ضبط الجودة السبعة
Mohamed Khaled
Quality management principle
Quality management principle
selinasimpson2501
Ch3. Demand Forecasting.ppt
Ch3. Demand Forecasting.ppt
MohammadYousefBaniMu
Chap17 statistical applications on management
Chap17 statistical applications on management
Uni Azza Aunillah
Newbold_chap03.ppt
Newbold_chap03.ppt
cfisicaster
Quality management service
Quality management service
selinasimpson321
Seven Quality Tools.pptx
Seven Quality Tools.pptx
Vijayarani Kasinadar
Purpose of quality management system
Purpose of quality management system
selinasimpson1801
Basic Analytics Module for Sponsors
Basic Analytics Module for Sponsors
Dee Daley
Chap07
Chap07
Marouane Zouzhi
Chap07
Chap07
Marouane Zouzhi
Lesson 6 measures of central tendency
Lesson 6 measures of central tendency
nurun2010
Service quality management system
Service quality management system
selinasimpson361
Qms quality management systems
Qms quality management systems
selinasimpson371
7 qc tools
7 qc tools
kmsonam
7 qc tools
7 qc tools
gurjeetdhillon
Similar to Quality Improvement Tools for Business Processes
(20)
Quality management techniques
Quality management techniques
C O N T R O L L P R E S E N T A T I O N
C O N T R O L L P R E S E N T A T I O N
Statistical quality control presentation
Statistical quality control presentation
Engineering Data Analysis-ProfCharlton
Engineering Data Analysis-ProfCharlton
Seven Basic Quality Control Tools أدوات ضبط الجودة السبعة
Seven Basic Quality Control Tools أدوات ضبط الجودة السبعة
Quality management principle
Quality management principle
Ch3. Demand Forecasting.ppt
Ch3. Demand Forecasting.ppt
Chap17 statistical applications on management
Chap17 statistical applications on management
Newbold_chap03.ppt
Newbold_chap03.ppt
Quality management service
Quality management service
Seven Quality Tools.pptx
Seven Quality Tools.pptx
Purpose of quality management system
Purpose of quality management system
Basic Analytics Module for Sponsors
Basic Analytics Module for Sponsors
Chap07
Chap07
Chap07
Chap07
Lesson 6 measures of central tendency
Lesson 6 measures of central tendency
Service quality management system
Service quality management system
Qms quality management systems
Qms quality management systems
7 qc tools
7 qc tools
7 qc tools
7 qc tools
More from cfisicaster
slidesWaveRegular.pdf
slidesWaveRegular.pdf
cfisicaster
WavesNotesAnswers.pdf
WavesNotesAnswers.pdf
cfisicaster
WavesLoading.pdf
WavesLoading.pdf
cfisicaster
WavesTransformation.pdf
WavesTransformation.pdf
cfisicaster
WavesAppendix.pdf
WavesAppendix.pdf
cfisicaster
WavesLinear.pdf
WavesLinear.pdf
cfisicaster
WavesExamplesAnswers.pdf
WavesExamplesAnswers.pdf
cfisicaster
slidesWaveTransformation.pdf
slidesWaveTransformation.pdf
cfisicaster
WavesStatistics.pdf
WavesStatistics.pdf
cfisicaster
slidesWaveLoading.pdf
slidesWaveLoading.pdf
cfisicaster
WavesExamples.pdf
WavesExamples.pdf
cfisicaster
slidesWaveStatistics.pdf
slidesWaveStatistics.pdf
cfisicaster
WavesSchedule.pdf
WavesSchedule.pdf
cfisicaster
Richard I. Levine - Estadistica para administración (2009, Pearson Educación)...
Richard I. Levine - Estadistica para administración (2009, Pearson Educación)...
cfisicaster
Mario F. Triola - Estadística (2006, Pearson_Educación) - libgen.li.pdf
Mario F. Triola - Estadística (2006, Pearson_Educación) - libgen.li.pdf
cfisicaster
David R. Anderson - Estadistica para administracion y economia (2010) - libge...
David R. Anderson - Estadistica para administracion y economia (2010) - libge...
cfisicaster
Richard I. Levin, David S. Rubin - Estadística para administradores (2004, Pe...
Richard I. Levin, David S. Rubin - Estadística para administradores (2004, Pe...
cfisicaster
N. Schlager - Study Materials for MIT Course [8.02T] - Electricity and Magnet...
N. Schlager - Study Materials for MIT Course [8.02T] - Electricity and Magnet...
cfisicaster
Teruo Matsushita - Electricity and Magnetism_ New Formulation by Introduction...
Teruo Matsushita - Electricity and Magnetism_ New Formulation by Introduction...
cfisicaster
Fisica2.pdf
Fisica2.pdf
cfisicaster
More from cfisicaster
(20)
slidesWaveRegular.pdf
slidesWaveRegular.pdf
WavesNotesAnswers.pdf
WavesNotesAnswers.pdf
WavesLoading.pdf
WavesLoading.pdf
WavesTransformation.pdf
WavesTransformation.pdf
WavesAppendix.pdf
WavesAppendix.pdf
WavesLinear.pdf
WavesLinear.pdf
WavesExamplesAnswers.pdf
WavesExamplesAnswers.pdf
slidesWaveTransformation.pdf
slidesWaveTransformation.pdf
WavesStatistics.pdf
WavesStatistics.pdf
slidesWaveLoading.pdf
slidesWaveLoading.pdf
WavesExamples.pdf
WavesExamples.pdf
slidesWaveStatistics.pdf
slidesWaveStatistics.pdf
WavesSchedule.pdf
WavesSchedule.pdf
Richard I. Levine - Estadistica para administración (2009, Pearson Educación)...
Richard I. Levine - Estadistica para administración (2009, Pearson Educación)...
Mario F. Triola - Estadística (2006, Pearson_Educación) - libgen.li.pdf
Mario F. Triola - Estadística (2006, Pearson_Educación) - libgen.li.pdf
David R. Anderson - Estadistica para administracion y economia (2010) - libge...
David R. Anderson - Estadistica para administracion y economia (2010) - libge...
Richard I. Levin, David S. Rubin - Estadística para administradores (2004, Pe...
Richard I. Levin, David S. Rubin - Estadística para administradores (2004, Pe...
N. Schlager - Study Materials for MIT Course [8.02T] - Electricity and Magnet...
N. Schlager - Study Materials for MIT Course [8.02T] - Electricity and Magnet...
Teruo Matsushita - Electricity and Magnetism_ New Formulation by Introduction...
Teruo Matsushita - Electricity and Magnetism_ New Formulation by Introduction...
Fisica2.pdf
Fisica2.pdf
Recently uploaded
Employee wellbeing at the workplace.pptx
Employee wellbeing at the workplace.pptx
NirmalaLoungPoorunde1
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
EduSkills OECD
Solving Puzzles Benefits Everyone (English).pptx
Solving Puzzles Benefits Everyone (English).pptx
OH TEIK BIN
Crayon Activity Handout For the Crayon A
Crayon Activity Handout For the Crayon A
UnboundStockton
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Celine George
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
Chameera Dedduwage
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
Sayali Powar
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impact
dawncurless
Concept of Vouching. B.Com(Hons) /B.Compdf
Concept of Vouching. B.Com(Hons) /B.Compdf
UmakantAnnand
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communication
nomboosow
Mastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory Inspection
SafetyChain Software
microwave assisted reaction. General introduction
microwave assisted reaction. General introduction
Maksud Ahmed
MENTAL STATUS EXAMINATION format.docx
MENTAL STATUS EXAMINATION format.docx
PoojaSen20
Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝
Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝
9953056974 Low Rate Call Girls In Saket, Delhi NCR
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)
eniolaolutunde
_Math 4-Q4 Week 5.pptx Steps in Collecting Data
_Math 4-Q4 Week 5.pptx Steps in Collecting Data
JhengPantaleon
Enzyme, Pharmaceutical Aids, Miscellaneous Last Part of Chapter no 5th.pdf
Enzyme, Pharmaceutical Aids, Miscellaneous Last Part of Chapter no 5th.pdf
Sumit Tiwari
KSHARA STURA .pptx---KSHARA KARMA THERAPY (CAUSTIC THERAPY)————IMP.OF KSHARA ...
KSHARA STURA .pptx---KSHARA KARMA THERAPY (CAUSTIC THERAPY)————IMP.OF KSHARA ...
M56BOOKSTORE PRODUCT/SERVICE
call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️
call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️
9953056974 Low Rate Call Girls In Saket, Delhi NCR
Separation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and Actinides
FatimaKhan178732
Recently uploaded
(20)
Employee wellbeing at the workplace.pptx
Employee wellbeing at the workplace.pptx
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Solving Puzzles Benefits Everyone (English).pptx
Solving Puzzles Benefits Everyone (English).pptx
Crayon Activity Handout For the Crayon A
Crayon Activity Handout For the Crayon A
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impact
Concept of Vouching. B.Com(Hons) /B.Compdf
Concept of Vouching. B.Com(Hons) /B.Compdf
Interactive Powerpoint_How to Master effective communication
Interactive Powerpoint_How to Master effective communication
Mastering the Unannounced Regulatory Inspection
Mastering the Unannounced Regulatory Inspection
microwave assisted reaction. General introduction
microwave assisted reaction. General introduction
MENTAL STATUS EXAMINATION format.docx
MENTAL STATUS EXAMINATION format.docx
Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝
Model Call Girl in Bikash Puri Delhi reach out to us at 🔝9953056974🔝
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)
_Math 4-Q4 Week 5.pptx Steps in Collecting Data
_Math 4-Q4 Week 5.pptx Steps in Collecting Data
Enzyme, Pharmaceutical Aids, Miscellaneous Last Part of Chapter no 5th.pdf
Enzyme, Pharmaceutical Aids, Miscellaneous Last Part of Chapter no 5th.pdf
KSHARA STURA .pptx---KSHARA KARMA THERAPY (CAUSTIC THERAPY)————IMP.OF KSHARA ...
KSHARA STURA .pptx---KSHARA KARMA THERAPY (CAUSTIC THERAPY)————IMP.OF KSHARA ...
call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️
call girls in Kamla Market (DELHI) 🔝 >༒9953330565🔝 genuine Escort Service 🔝✔️✔️
Separation of Lanthanides/ Lanthanides and Actinides
Separation of Lanthanides/ Lanthanides and Actinides
Quality Improvement Tools for Business Processes
1.
Chap 18-1 Statistics for
Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 18 Introduction to Quality Statistics for Business and Economics 6th Edition
2.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-2 Chapter Goals After completing this chapter, you should be able to: Describe the importance of statistical quality control for process improvement Define common and assignable causes of variation Explain process variability and the theory of control charts Construct and interpret control charts for the mean and standard deviation Obtain and explain measures of process capability Construct and interpret control charts for number of occurrences
3.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-3 The Importance of Quality Primary focus is on process improvement Data is needed to monitor the process and to insure the process is stable with minimum variance Most variation in a process is due to the system, not the individual Focus on prevention of errors, not detection Identify and correct sources of variation Higher quality costs less Increased productivity increased sales higher profit
4.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-4 Variation A system is a number of components that are logically or physically linked to accomplish some purpose A process is a set of activities operating on a system to transform inputs to outputs From input to output, managers use statistical tools to monitor and improve the process Goal is to reduce process variation
5.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-5 Sources of Variation Common causes of variation also called random or uncontrollable causes of variation causes that are random in occurrence and are inherent in all processes management, not the workers, are responsible for these causes Assignable causes of variation also called special causes of variation the result of external sources outside the system these causes can and must be detected, and corrective action must be taken to remove them from the process failing to do so will increase variation and lower quality
6.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-6 Process Variation Variation is natural; inherent in the world around us No two products or service experiences are exactly the same With a fine enough gauge, all things can be seen to differ Total Process Variation Common Cause Variation Assignable Cause Variation = +
7.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-7 Total Process Variation Total Process Variation Common Cause Variation Assignable Cause Variation = + People Machines Materials Methods Measurement Environment Variation is often due to differences in:
8.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-8 Common Cause Variation Common cause variation naturally occurring and expected the result of normal variation in materials, tools, machines, operators, and the environment Total Process Variation Common Cause Variation Assignable Cause Variation = +
9.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-9 Special Cause Variation Special cause variation abnormal or unexpected variation has an assignable cause variation beyond what is considered inherent to the process Total Process Variation Common Cause Variation Assignable Cause Variation = +
10.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-10 Stable Process A process is stable (in-control) if all assignable causes are removed variation results only from common causes
11.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-11 Control Charts The behavior of a process can be monitored over time Sampling and statistical analysis are used Control charts are used to monitor variation in a measured value from a process Control charts indicate when changes in data are due to assignable or common causes
12.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-12 Overview Process Capability Tools for Quality Improvement Control Charts X-chart for the mean s-chart for the standard deviation P-chart for proportions c-chart for number of occurrences
13.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-13 X-chart and s-chart Used for measured numeric data from a process Start with at least 20 subgroups of observed values Subgroups usually contain 3 to 6 observations each For the process to be in control, both the s-chart and the X-chart must be in control
14.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-14 Preliminaries Consider K samples of n observations each Data is collected over time from a measurable characteristic of the output of a production process The sample means (denoted xi for i = 1, 2, . . ., K) can be graphed on an X-chart The average of these sample means is the overall mean of the sample observations K 1 i i/K x x
15.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-15 Preliminaries The sample standard deviations (denoted si for i = 1, 2, . . . ,K) can be graphed on an s-chart The average sample standard deviation is The process standard deviation, σ, is the standard deviation of the population from which the samples were drawn, and it must be estimated from sample data /K s s K 1 i i (continued)
16.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-16 Example: Subgroups Sample measurements: Subgroup measures Subgroup number Individual measurements (subgroup size = 4) Mean, x Std. Dev., s 1 2 3 … 15 12 17 … 17 16 21 … 15 9 18 … 11 15 20 … 14.5 13.0 19.0 … 2.517 3.162 1.826 … Average subgroup mean = Average subgroup std. dev. = s x
17.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-17 Estimate of Process Standard Deviation Based on s An estimate of process standard deviation is Where s is the average sample standard deviation c4 is a control chart factor which depends on the sample size, n Control chart factors are found in Table 18.1 or in Appendix 13 If the population distribution is normal, this estimator is unbiased 4 /c s σ ˆ
18.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-18 Factors for Control Charts n c4 A3 B3 B4 2 .789 2.66 0 3.27 3 .886 1.95 0 2.57 4 .921 1.63 0 2.27 5 .940 1.43 0 2.09 6 .952 1.29 0.03 1.97 7 .959 1.18 0.12 1.88 8 .965 1.10 0.18 1.82 9 .969 1.03 0.24 1.76 10 .973 0.98 0.28 1.72 Selected control chart factors (Table 18.1)
19.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-19 Process Average Control Charts and Control Limits UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations UCL LCL +3σ -3σ time A control chart is a time plot of the sequence of sample outcomes Included is a center line, an upper control limit (UCL) and a lower control limit (LCL)
20.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-20 Control Charts and Control Limits s A x ) n /(c s 3 x n / σ 3 x Deviations Standard 3 Average Process 3 4 ˆ The 3-standard-deviation control limits are estimated for an X-chart as follows: (continued) Where the value of is given in Table 18.1 or in Appendix 13 n c 3 A 4 3
21.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-21 X-Chart The X-chart is a time plot of the sequence of sample means The center line is The lower control limit is The upper control limit is s A x LCL 3 X x CLX s A x UCL 3 X
22.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-22 X-Chart Example You are the manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For seven days, you collect data on five deliveries per day. Is the process mean in control?
23.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-23 X-Chart Example: Subgroup Data Day Subgroup Size Subgroup Mean Subgroup Std. Dev. 1 2 3 4 5 6 7 5 5 5 5 5 5 5 5.32 6.59 4.89 5.70 4.07 7.34 6.79 1.85 2.27 1.28 1.99 2.61 2.84 2.22 These are the xi values for the 7 subgroups These are the si values for the 7 subgroups
24.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-24 X-Chart Control Limits Solution 5.813 7 6.79 6.59 5.32 K x x i 2.151 7 2.22 2.27 1.85 K s s i 2.737 51) (1.43)(2.1 5.813 ) s ( A x LCL 8.889 51) (1.43)(2.1 5.813 ) s ( A x UCL 3 X 3 X A3 = 1.43 is from Appendix 13
25.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-25 X-Chart Control Chart Solution UCL = 8.889 LCL = 2.737 0 2 4 6 8 1 2 3 4 5 6 7 Minutes Day x = 5.813 _ _ Conclusion: Process mean is in statistical control
26.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-26 s-Chart The s-chart is a time plot of the sequence of sample standard deviations The center line on the s-chart is The lower control limit (for three-standard error limits) is The upper control limit is Where the control chart constants B3 and B4 are found in Table 18.1 or Appendix 13 s B LCL 3 s s CL s B UCL 4 s
27.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-27 s-Chart Control Limits Solution 5.813 7 6.79 6.59 5.32 K x x i 2.151 7 2.22 2.27 1.85 K s s i 0 (0)(2.151) s B LCL 4.496 51) (2.09)(2.1 s B UCL 3 s 4 s B4 and B3 are found in Appendix 13
28.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-28 s-Chart Control Chart Solution UCL = 4.496 0 2 4 1 2 3 4 5 6 7 Minutes Day LCL = 0 s = 2.151 _ Conclusion: Variation is in control
29.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-29 Process Average Control Chart Basics UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations UCL LCL +3σ -3σ Common Cause Variation: range of expected variability Special Cause Variation: Range of unexpected variability time
30.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-30 Process Average Process Variability UCL = Process Average + 3 Standard Deviations LCL = Process Average – 3 Standard Deviations UCL LCL ±3σ → 99.7% of process values should be in this range time Special Cause of Variation: A measurement this far from the process average is very unlikely if only expected variation is present
31.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-31 Using Control Charts Control Charts are used to check for process control H0: The process is in control i.e., variation is only due to common causes H1: The process is out of control i.e., assignable cause variation exists If the process is found to be out of control, steps should be taken to find and eliminate the assignable causes of variation
32.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-32 In-control Process A process is said to be in control when the control chart does not indicate any out-of-control condition Contains only common causes of variation If the common causes of variation is small, then control chart can be used to monitor the process If the variation due to common causes is too large, you need to alter the process
33.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-33 Process In Control Process in control: points are randomly distributed around the center line and all points are within the control limits UCL LCL time Process Average
34.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-34 Process Not in Control Out of control conditions: One or more points outside control limits 6 or more points in a row moving in the same direction either increasing or decreasing 9 or more points in a row on the same side of the center line
35.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-35 Process Not in Control One or more points outside control limits UCL LCL Nine or more points in a row on one side of the center line UCL LCL Six or more points moving in the same direction UCL LCL Process Average Process Average Process Average
36.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-36 Out-of-control Processes When the control chart indicates an out-of- control condition (a point outside the control limits or exhibiting trend, for example) Contains both common causes of variation and assignable causes of variation The assignable causes of variation must be identified If detrimental to the quality, assignable causes of variation must be removed If increases quality, assignable causes must be incorporated into the process design
37.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-37 Process Capability Process capability is the ability of a process to consistently meet specified customer-driven requirements Specification limits are set by management (in response to customers’ expectations or process needs, for example) The upper tolerance limit (U) is the largest value that can be obtained and still conform to customers’ expectations The lower tolerance limit (L) is the smallest value that is still conforming
38.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-38 Capability Indices A process capability index is an aggregate measure of a process’s ability to meet specification limits The larger the value, the more capable a process is of meeting requirements
39.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-39 Measures of Process Capability Process capability is judged by the extent to which lies between the tolerance limits L and U Cp Capability Index Appropriate when the sample data are centered between the tolerance limits, i.e. The index is A satisfactory value of this index is usually taken to be one that is at least 1.33 (i.e., the natural rate of tolerance of the process should be no more than 75% of (U – L), the width of the range of acceptable values) σ 3 x ˆ σ 6 L U Cp ˆ U)/2 (L x
40.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-40 Measures of Process Capability Cpk Index Used when the sample data are not centered between the tolerance limits Allows for the fact that the process is operating closer to one tolerance limit than the other The Cpk index is A satisfactory value is at least 1.33 (continued) σ 3 L x , σ 3 x U Min Cpk ˆ ˆ
41.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-41 You are the manager of a 500-room hotel. You have instituted tolerance limits that luggage deliveries should be completed within ten minutes or less (U = 10, L = 0). For seven days, you collect data on five deliveries per day. You know from prior analysis that the process is in control. Is the process capable? Process Capability Example
42.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-42 Process Capability: Hotel Data Day Subgroup Size Subgroup Mean Subgroup Std. Dev. 1 2 3 4 5 6 7 5 5 5 5 5 5 5 5.32 6.59 4.89 5.70 4.07 7.34 6.79 1.85 2.27 1.28 1.99 2.61 2.84 2.22
43.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-43 Process Capability: Hotel Example Solution 0.610 0.847 , 0.610 Min 3(2.228) 0 5.813 , 3(2.228) 5.813 10 Min σ 3 L x , σ 3 x U Min Cpk ˆ ˆ 0.940 c 2.151 s 5.813 X 5 n 4 2.288 0.940 2.151 c s σ Estimate 4 ˆ The capability index for the luggage delivery process is less than 1. The upper specification limit is less than 3 standard deviations above the mean.
44.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-44 p-Chart Control chart for proportions Is an attribute chart Shows proportion of defective or nonconforming items Example -- Computer chips: Count the number of defective chips and divide by total chips inspected Chip is either defective or not defective Finding a defective chip can be classified a “success”
45.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-45 p-Chart Used with equal or unequal sample sizes (subgroups) over time Unequal sizes should not differ by more than ±25% from average sample sizes Easier to develop with equal sample sizes Should have large sample size so that the average number of nonconforming items per sample is at least five or six (continued)
46.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-46 Creating a p-Chart Calculate subgroup proportions Graph subgroup proportions Compute average of subgroup proportions Compute the upper and lower control limits Add centerline and control limits to graph
47.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-47 p-Chart Example Subgroup number, i Sample size Number of successes Sample Proportion, pi 1 2 3 … 150 150 150 15 12 17 … .1000 .0800 .1133 … Average sample proportions = p
48.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-48 Average of Sample Proportions The average of sample proportions = p where: pi = sample proportion for subgroup i K = number of subgroups of size n If equal sample sizes: K p p K 1 i i
49.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-49 Computing Control Limits The upper and lower control limits for a p-chart are The standard deviation for the subgroup proportions is UCL = Average Proportion + 3 Standard Deviations LCL = Average Proportion – 3 Standard Deviations n ) p )(1 p ( σp ˆ
50.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-50 Computing Control Limits The upper and lower control limits for the p-chart are (continued) n ) p (1 p 3 p UCL n ) p (1 p 3 p LCL p p Proportions are never negative, so if the calculated lower control limit is negative, set LCL = 0
51.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-51 p-Chart Example You are the manager of a 500-room hotel. You want to achieve the highest level of service. For seven days, you collect data on the readiness of 200 rooms. Is the process in control?
52.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-52 p Chart Example: Hotel Data # Not Day # Rooms Ready Proportion 1 200 16 0.080 2 200 7 0.035 3 200 21 0.105 4 200 17 0.085 5 200 25 0.125 6 200 19 0.095 7 200 16 0.080
53.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-53 p Chart Control Limits Solution .0864 7 .080 .035 .080 K p p K 1 i i .1460 200 .0864) .0864(1 3 .0864 n ) p (1 p 3 p UCL .0268 200 .0864) .0864(1 3 .0864 n ) p (1 p 3 p LCL p p
54.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-54 p = .0864 p Chart Control Chart Solution UCL = .1460 LCL = .0268 0.00 0.05 0.10 0.15 1 2 3 4 5 6 7 P Day Individual points are distributed around p without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of management. _ _
55.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-55 c-Chart Control chart for number of defects per item Also a type of attribute chart Shows total number of nonconforming items per unit examples: number of flaws per pane of glass number of errors per page of code Assume that the size of each sampling unit remains constant
56.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-56 Mean and Standard Deviation for a c-Chart The sample mean number of occurrences is K c c i The standard deviation for a c-chart is c σc ˆ where: ci = number of successes per item K = number of items sampled
57.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-57 c-Chart Center and Control Limits c 3 c UCL c 3 c LCL c c The control limits for a c-chart are c CLc The center line for a c-chart is The number of occurrences can never be negative, so if the calculated lower control limit is negative, set LCL = 0
58.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-58 Process Control Determine process control for p-chars and c-charts using the same rules as for X and s-charts Out of control conditions: One or more points outside control limits Six or more points moving in the same direction Nine or more points in a row on one side of the center line
59.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-59 c-Chart Example A weaving machine makes cloth in a standard width. Random samples of 10 meters of cloth are examined for flaws. Is the process in control? Sample number 1 2 3 4 5 6 7 Flaws found 2 1 3 0 5 1 0
60.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-60 Constructing the c-Chart The mean and standard deviation are: 1.7143 7 0 1 5 0 3 1 2 K c c i 1.3093 1.7143 c 2.214 3(1.3093) 1.7143 c 3 c LCL 5.642 3(1.3093) 1.7143 c 3 c UCL The control limits are: Note: LCL < 0 so set LCL = 0
61.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-61 The completed c-Chart The process is in control. Individual points are distributed around the center line without any pattern. Any improvement in the process must come from reduction in common-cause variation UCL = 5.642 LCL = 0 Sample number 1 2 3 4 5 6 7 c = 1.714 6 5 4 3 2 1 0
62.
Statistics for Business
and Economics, 6e © 2007 Pearson Education, Inc. Chap 18-62 Chapter Summary Reviewed the concept of statistical quality control Discussed the theory of control charts Common cause variation vs. special cause variation Constructed and interpreted X and s-charts Obtained and interpreted process capability measures Constructed and interpreted p-charts Constructed and interpreted c-charts
Download now