Premium Essay

Percentiles of Range Chart : Pareto Distribution

In:

Submitted By Bhaskarprasad22
Words 1949
Pages 8
International Journal of Advances in Applied Sciences (IJAAS)
Vol. 2, No. 3, September 2013, pp. 141~144
ISSN: 2252-8814



141

Percentiles of Range: Pareto Type Model
R. Subba Rao1, G. Prasad2, R. R. L. Kantam3
1

Shri Vishnu Engineering College for Women, Bhimavaram - 534202, A.P., India
2
Aditya Degree College, Rajahmundry – 533103, A.P., India
3
Acharya Nagarjuna University, Guntur - 522510, A.P., India

Article Info

ABSTRACT

Article history:

Statistical quality control relates heavily on the goodness of control chart limits. The more accurate those limits are, the more likely are to detect whether a process is in control. Various procedures have been developed to compute good control limits. This paper proposes construction of Range chart by considering a Pareto distribution of IV kind. The cumulative distribution function of sample range from their distribution is derived. The percentiles of the distribution of range are worked out and are used to construct the control limits. The performance of the control chart is compared with that of gamma based control chart. Interval estimation for the scale parameter is also worked out.

Received Nov 11, 2012
Revised Mar 17, 2013
Accepted Mar 28, 2013
Keyword:
Order Statistics
Distribution of Range
Interval estimation
Percentiles
Control limits

Copyright © 2013 Institute of Advanced Engineering and Science.
All rights reserved.

Corresponding Author:
R. Subba Rao,
Shri Vishnu Engineering College for Women,
Bhimavaram - 534202,
A.P., India.
Email: rsr_vishnu@rediffmail.com

1.

INTRODUCTION
Industrial statisticians are accustomed to monitoring the stability of the process output through the maintenance of control charts. Use of these control charts assumes that the process output is normally distributed or that appeal to the central limit theorem is

Similar Documents

Premium Essay

Business

...1 - 14 to answer parts (a),(b),(c). That is, for each of the survey questions indicate which are a) categorical b) numerical-continuous or c) numerical-discrete. Try to provide some indication as to why it is that type. (0.5 points) Group work 3. From the file PS1_S14_Absent.xlsx in Laulima Resources Problem Sets PS1, create a Summary table, Pie chart, Bar chart, and Pareto chart for the Rate variable using PHStat – One-Way Tables and Charts. Copy and paste the table and charts into your word document and answer the following questions: (a) From the table which is the least frequent absenteeism rate? (b) From the Bar chart which two absenteeism rates are the most frequent? (c) From the pie chart what is percent of absenteeism rate high? (d) From the Pareto chart the two most frequent two absenteeism rates contribute what percentage together? (1 point) How-to: Click on Add-Ins - PHSTAT - Descriptive Statistics and choose One Way Tables and Charts. Check Raw Categorical data. Click in the Raw Data Cell Range window and then highlight the entire column labeled Rate. Choose the pie, bar charts since you will need all these at some point. PHStat puts the table on 1 sheet and the graphs on another, but you can change the location of the graphs by right clicking on the graph and choosing ‘Move’ and put it in the same...

Words: 907 - Pages: 4

Premium Essay

Business

...1 - 14 to answer parts (a),(b),(c). That is, for each of the survey questions indicate which are a) categorical b) numerical-continuous or c) numerical-discrete. Try to provide some indication as to why it is that type. (0.5 points) Group work 3. From the file PS1_S14_Absent.xlsx in Laulima Resources Problem Sets PS1, create a Summary table, Pie chart, Bar chart, and Pareto chart for the Rate variable using PHStat – One-Way Tables and Charts. Copy and paste the table and charts into your word document and answer the following questions: (a) From the table which is the least frequent absenteeism rate? (b) From the Bar chart which two absenteeism rates are the most frequent? (c) From the pie chart what is percent of absenteeism rate high? (d) From the Pareto chart the two most frequent two absenteeism rates contribute what percentage together? (1 point) How-to: Click on Add-Ins - PHSTAT - Descriptive Statistics and choose One Way Tables and Charts. Check Raw Categorical data. Click in the Raw Data Cell Range window and then highlight the entire column labeled Rate. Choose the pie, bar charts since you will need all these at some point. PHStat puts the table on 1 sheet and the graphs on another, but you can change the location of the graphs by right clicking on the graph and choosing ‘Move’ and put it in the same...

Words: 907 - Pages: 4

Premium Essay

The Correct Answers for Bus 308 Quizzes

...Answers Possibly for week 1 Quiz in BUS 308 The correct answer for each question is indicated by a . | ------------------------------------------------- Top of Form | 1 CORRECT | | A random sample is selected so that on each selection from the population every unit remaining in the population has an equal chance of being chosen. | | | A) | True | | | B) | False | | | | | | | | 2 INCORRECT | | Any characteristic of a population unit is called a(n): | | | A) | measurement. | | | B) | sample. | | | C) | observation. | | | D) | variable. | | | | | | | | 3 INCORRECT | | An example of a qualitative variable is the mileage of a car. | | | A) | True | | | B) | False | | | | | | | | 4 INCORRECT | | A list of all of the units in a population is called a: | | | A) | census. | | | B) | frame. | | | C) | sample. | | | D) | variable. | | | | | | | | 5 CORRECT | | Which of the following is a quantitative variable? | | | A) | The make of a TV | | | B) | A person's gender | | | C) | The mileage of a car | | | D) | Whether a person is a college graduate | | | E) | Whether a person has a charge account | | | | | | | | 6 INCORRECT | | Measurements from a population are called: | | | A) | statistics. | | | B) | observations. | | | C) | variables. | | | D) | inferences. | | | | | | | | 7 INCORRECT |...

Words: 1902 - Pages: 8

Premium Essay

Statistics Summary

...the number of observations in the data set that fall into a particular class. The class relative frequency is the class frequency divided by the total number of observations in the data set; that is, class relative frequency = (class frequency) / n. The class percentage is the class relative frequency multiplied by 100; that is, class percentage = (class relative frequency) x 100. Summary of Graphical Descriptive Methods for Qualitative Data Bar Graph: The categories (classes) of the qualitative variable are represented by bars, where the height of each bar is either the class frequency, the class relative frequency, or the class percentage. Pie Chart: The categories (classes) of the qualitative variable are represented by slices of a pie (circle). The size of each slice is proportional to the class relative frequency. Pareto Diagram: A bar graph with the categories (classes) of the qualitative variable (i.e. the bars) arranged by height in descending order from left to right. Summary of Graphical Descriptive Methods for Quantitative Data Dot Plot: The numerical value of each quantitative measurement in the data set is represented by a dot on a horizontal scale. When data values repeat, the dots are placed above one another vertically. Stem-and-Leaf Display: The numerical value of the quantitative variable is partitioned into a “stem” and a “leaf”. The possible stems are listed in order in a column. The leaf for each quantitative measurement in the data set is placed...

Words: 2367 - Pages: 10

Free Essay

Six Sigma

...Control Charts and Introduction to Six Sigma Session 12: Control Charts and Introduction to Six Sigma concepts Control Charts and Introduction to Six Sigma Control Charts - Topics of Discussion – – – – – Control Chart History Control Limits Individuals and Moving Range Charts X-bar and R Charts Subgrouping Control Charts and Introduction to Six Sigma Typical Process Metrics • • • • • • • • • Cycle times Lead times Productivity Schedule variance Budget variance Employee satisfaction Customer satisfaction Safety incidents System users (# hits) • • • • • • • • • Days sales outstanding Customer service calls Request for quotes Proposal development Attrition/retention Bid win rate Transactional defects Sales orders Revenue dollars What are some metrics associated with your projects? What are some metrics associated with your projects? Control Charts and Introduction to Six Sigma Control Charts – “While every process displays Variation, some processes display controlled variation, while other processes display uncontrolled variation” (Walter Shewhart). – Controlled Variation is characterised by a stable and consistent pattern of variation over time. Associated with Common Causes. – Process A shows controlled variation. X-Bar Chart for Process A X-Bar Chart for Process A UCL=77.20 UCL=77.20 75 X a C a fo P ce B -B r h rt r ro ss 8 0 U L 7 .2 C= 7 7 Sample Mean 7 0 X= 0 8 7 .9 L L 6 .7 C= 4 0 6 0 5 0 Special Causes 0 5 1...

Words: 13809 - Pages: 56

Premium Essay

Statistics Cheat Sheet

...Statistic- is a number computed from a sample of data. It is characteristic of a sample. A summary measure that is computed from a sample to describe a characteristic. (Numerical summary of the population) (Ex. The proportion of females randomly selected from the registered voters of a county or the average time it takes for the first 5 students to complete an exam) Parameter- A characteristic (numerical summary) of the entire population. A number computed from the entire population usually unobservable. Subject- the entities that we measure in a study. Population- the collection of all subjects under study. Proportion- of the observations that fall in a certain category is the frequency (count) of observations in that category divided by the total number of observations. Proportion and percentages (aka relative frequencies) Probability- the chance that an even will occur. Sample- a subset of the population. Random Samples are most valid. Design- Plan for how the data will be collected. Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed. Sample Space- set of all possible outcomes for a random phenomenon Variables (COLUMNS)- characteristics or measurements on the subject. Event-subset of the sample space Description- summarizing the data that are obtained. Descriptive Statistics- methods for summarizing the data. Usually consists of bar graphs and...

Words: 12484 - Pages: 50

Premium Essay

The Six Sigma Handbook

...The Six Sigma Handbook Revised and Expanded A Complete Guide for Green Belts, Black Belts, and Managers at All Levels THOMAS PYZDEK McGraw-Hill New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2003 by The McGraw-HIll Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-141596-3 The material in this eBook also appears in the print version of this title: 0-07-141015-5. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. For more information, please contact George Hoare, Special Sales, at george_hoare@mcgraw-hill.com or (212) 904-4069. TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licensors reserve all...

Words: 236475 - Pages: 946

Premium Essay

Probability and Statistics for Finance

...Probability and Statistics for Finance The Frank J. Fabozzi Series Fixed Income Securities, Second Edition by Frank J. Fabozzi Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and James A. Abate Handbook of Global Fixed Income Calculations by Dragomir Krgin Managing a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. Fabozzi Real Options and Option-Embedded Securities by William T. Moore Capital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. Fabozzi The Exchange-Traded Funds Manual by Gary L. Gastineau Professional Perspectives on Fixed Income Portfolio Management, Volume 3 edited by Frank J. Fabozzi Investing in Emerging Fixed Income Markets edited by Frank J. Fabozzi and Efstathia Pilarinu Handbook of Alternative Assets by Mark J. P. Anson The Global Money Markets by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry The Handbook of Financial Instruments edited by Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis by Laurie S. Goodman and Frank J. Fabozzi Interest Rate, Term Structure, and Valuation Modeling edited by Frank J. Fabozzi Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J. Fabozzi The Theory and Practice of Investment Management edited by Frank J. Fabozzi and Harry M. Markowitz Foundations of Economic Value Added, Second Edition by James L. Grant Financial Management and Analysis, Second Edition...

Words: 176154 - Pages: 705

Free Essay

Industrial Engineering

...McGraw-Hill Create™ Review Copy for Instructor Espinoza. Not for distribution. Course BBE 4505 Omar Espinoza University Of Minnesota NATURAL RESOURCES McGraw-Hill Create™ Review Copy for Instructor Espinoza. Not for distribution. http://create.mcgraw-hill.com Copyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior written permission of the publisher. This McGraw-Hill Create text may include materials submitted to McGraw-Hill for publication by the instructor of this course. The instructor is solely responsible for the editorial content of such materials. Instructors retain copyright of these additional materials. ISBN-10: 1121789048 ISBN-13: 9781121789043 McGraw-Hill Create™ Review Copy for Instructor Espinoza. Not for distribution. Contents 1. Preface 1 2. Methods, Standards, and Work Design: Introduction 7 Problem-Solving Tools 27 3. Tex 29 4. Operation Analysis 79 5. Manual Work Design 133 6. Workplace, Equipment, and Tool Design 185 7. Work Environment Design 239 8. Design of Cognitive Work 281 9. Workplace and Systems Safety 327 10. Proposed Method Implementation 379 11. Time Study 413 12. Performance Rating and Allowances 447 13. Standard Data and Formulas 485 14. Predetermined Time Systems 507...

Words: 294686 - Pages: 1179

Premium Essay

Saswork

...© Orangetree Business Solutions Private Limited, 2012 No part of this book should be referenced or copied without the prior permission of the company. A FEW WORDS TO THE STUDENTS Analytics is becoming a popular tool for managerial decision making. It‘s still not so widespread in countries like India, but in the west it has become a standard practice. Previously studying analytics involved an in depth knowledge of statistics and programming languages. But widespread availability of statistical package software has changed the reality to some extent. Now more emphasis is given on the application of the techniques to solve the business problems. So there is a need to understand the meaning of the statistical procedures. This book has been written to cater that need. In this book, all the necessary concepts have been explained keeping the business problem in mind. Also, to remove the apathy for statistics, use of mathematical expressions have been limited. That doesn‘t imply that we don‘t have to study the mathematics part. The intention is to put the substance over matter. As the students get accustomed to these statistical concepts, they can go for further investigations using various mathematical and statistical techniques. A list of suggested books and links have been given in the appendix. This book is directly related to the instructor‘s presentation. So it is highly advised that students should go through this material at the end of each class. As for general ...

Words: 24975 - Pages: 100

Premium Essay

Super Man

...CD-ROM Included! “John Walkenbach’s writing style makes the difficult seem easy in this book that can be used as a reference or read cover to cover. You won’t find a more comprehensive book on Excel 2010 than this!” —Dick Kusleika, Microsoft MVP, DailyDoseOfExcel.com • Searchable PDF of the book • Understand functions, charts, worksheets, and workbooks System Requirements: See the CD Appendix in the book for details and complete system requirements. • Master “what-if” analysis, Goal Seeking, external database files, and pivot tables • Develop custom functions, program with VBA, and create UserForms • Try new slice-and-dice tools to dynamically filter your data Preview how your copied text will look www.wiley.com/compbooks Spot trends in your data with Sparklines John Walkenbach aka “Mr. Spreadsheet” is the principal of J-Walk and Associates, Inc. and a Microsoft Excel MVP. He is a leading authority on spreadsheet software and the creator of the award-winning Power Utility Pak. John has written more than 50 books, as well as articles and reviews for publications including PC World, InfoWorld, and Windows. He also maintains the popular Spreadsheet Page at spreadsheetpage.com. ® • All the examples and workbook files used in the book Microsoft® Follow the examples in the book, chapter by chapter, using the bonus materials on the CD-ROM: Excel 2010 What’s on the CD-ROM? • Get up to speed on everything new in Excel 2010 ...

Words: 167105 - Pages: 669

Premium Essay

Exsm

...Dear nutrition student, Thank you for inquiring about my RD/DTR study guide. And yes, there is no catch, the study guide is COMPLETELY FREE! All I ask for is some feedback. So feel free to shoot me any questions/comments! A little background: This study guide is the culmination of years of my own research. And after careful thought, I put into the study guide what I feel are the most important concepts you need to know for the RD/DTR exam. If you notice, I spent much time teaching you in detail the concepts you need to know, not just “spitting” you questions with little or no explanation. I believe this is important. I know you might be thinking “oh, how am I going to absorb and learn all this material?” I say, just read and answer the questions at your own pace. Simply test yourself and of course take some breaks along the way. Just take it one concept at a time. After you have mastered one concept, then move on to the next. I know if you study whole-heartedly what I have outlined in this study guide, you are sure to pass! GOOD LUCK! YOU CAN DO IT! ϑ Your nutrition friend, -Jonathan Brown, B.S, DTR THE “NO FLUFF” RD/DTR STUDY GUIDE *Updated as of July 2011 The “NO FLUFF” RD/DTR STUDY GUIDE Tips for taking the RD/DTR exam 1. PERIODICALLY CHECK THE CLOCK TO MAKE SURE YOU’RE GOOD ON TIME! If you wish, get a basic digital watch with a timer for...

Words: 20721 - Pages: 83

Premium Essay

Healthcare

...APPENDIX Checklists A Checklist A-1 Reviewing a Budget 1. Is this budget static (not adjusted for volume) or flexible (adjusted for volume during the year)? 2. Are the figures designated as fixed or variable? 3. Is the budget for a defined unit of authority? 4. Are the line items within the budget all expenses (and revenues, if applicable) that are controllable by the manager? 5. Is the format of the budget comparable with that of previous periods so that several reports over time can be compared if so desired? 6. Are actual and budget for the same period? 7. Are the figures annualized? 8. Test one line-item calculation. Is the math for the dollar difference computed correctly? Is the percentage properly computed based on a percentage of the budget figure? 333 334 APPENDIX A Checklists Checklist A-2 Building a Budget 1. What is the proposed volume for the new budget period? 2. What is the appropriate inflow (revenues) and outflow (cost of services delivered) relationship? 3. What will the appropriate dollar cost be? (Note: this question requires a series of assumptions about the nature of the operation for the new budget period.) 3a. Forecast service-related workload. 3b. Forecast non–service-related workload. 3c. Forecast special project workload if applicable. 3d. Coordinate assumptions for proportionate share of interdepartmental projects. 4. Will additional resources be available? 5. Will this budget accomplish the appropriate managerial objectives for...

Words: 33826 - Pages: 136

Premium Essay

Project Mgmt

...Project Management Institute A GUIDE TO THE PROJECT MANAGEMENT BODY OF KNOWLEDGE (PMBOK® Guide)—Fourth Edition 30, 0HPEHU &RS\ ² 1RW IRU 5HSURGXFWLRQ RU 'LVWULEXWLRQ An American National Standard ANSI/PMI 99-001-2008 ISBN: 978-1-933890-51-7 Published by: Project Management Institute, Inc. 14 Campus Boulevard Newtown Square, Pennsylvania 19073-3299 USA. Phone: +610-356-4600 Fax: +610-356-4647 E-mail: customercare@pmi.org Internet: www.pmi.org ©2008 Project Management Institute, Inc. All rights reserved. “PMI”, the PMI logo, “PMP”, the PMP logo, “PMBOK”, “PgMP”, “Project Management Journal”, “PM Network”, and the PMI Today logo are registered marks of Project Management Institute, Inc. The Quarter Globe Design is a trademark of the Project Management Institute, Inc. For a comprehensive list of PMI marks, contact the PMI Legal Department. PMI Publications welcomes corrections and comments on its books. Please feel free to send comments on typographical, formatting, or other errors. Simply make a copy of the relevant page of the book, mark the error, and send it to: Book Editor, PMI Publications, 14 Campus Boulevard, Newtown Square, PA 19073-3299 USA. To inquire about discounts for resale or educational purposes, please contact the PMI Book Service Center. PMI Book Service Center P.O. Box 932683, Atlanta, GA 31193-2683 USA Phone: 1-866-276-4764 (within the U.S. or Canada) or +1-770-280-4129 (globally) Fax: +1-770-280-4113 E-mail: book.orders@pmi.org Printed in the...

Words: 148336 - Pages: 594

Premium Essay

Abcd

...Cameron.ffirs 10/11/05 1:46 PM Page iii Diagnosing and Changing Organizational Culture Based on the Competing Values Framework REVISED EDITION The Jossey-Bass Business & Management Series Cameron.ffirs 10/11/05 1:46 PM Page i Diagnosing and Changing Organizational Culture Cameron.ffirs 10/11/05 1:46 PM Page ii Kim S. Cameron Robert E. Quinn Cameron.ffirs 10/11/05 1:46 PM Page iii Diagnosing and Changing Organizational Culture Based on the Competing Values Framework REVISED EDITION The Jossey-Bass Business & Management Series Cameron.ffirs 10/11/05 1:46 PM Page iv Copyright © 2006 by John Wiley & Sons, Inc. All rights reserved. Published by Jossey-Bass A Wiley Imprint 989 Market Street, San Francisco, CA 94103-1741 www.josseybass.com No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600, or on the Web at www.copyright.com. Requests to the publisher for permission should be addressed to the Permissions Department...

Words: 72417 - Pages: 290