Premium Essay

Percentiles of Range Chart : Pareto Distribution

In: Other Topics

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

Pareto Principle

...The Pareto principle is one of the important managerial tool that can be used to identify alternatives which are worthy of attention during decision making. (Grosfeld-Nir, Ronen & Kozlovsky, 2007). Named after an economist, Vilfredo Pareto, and also known as the 80/20 rule, he stated that, “20% of the population possesses 80% of the wealth” (Grosfeld-Nir et. al, 2007 para ii). Liebler and McConnell (2008) call it “a criterion for decision making” (p 155) which suggests that every persons need should be met possibly without causing loss to another person. It also means that when choosing from among alternatives, the ones rejected are due to the reduced merits to one or more groups. This suggests to me that a little portion (components) of a whole heightens the end product of whatever the thing is meant for. For example, 20% of employees help to achieve 80% of an organizational goal. That is, a little input of the few can help in finishing a greater part of a target provided no one is disregarded. An example is when a healthcare facility with so many departments invests more into a smaller department that spells out the organizations’ image giving it the permit to achieve goals successfully; the other departments are not left hanging and yet most of the goals required are reached. A funny but practical example in daily life activity is marriage. The little things that a spouse put into the marriage sparks it up with all the good things that comes with it. If a husband gives a......

Words: 348 - Pages: 2

Premium Essay

Chart

... local authorities, police and the voluntary sector. Our new way of operating reflects the overall direction of Government policy to: • Concentrate on outcomes not processes – results are what matter • Support local freedoms to pursue what works • Improve accountability and transparency through the system • Harness the efficiency and innovation of competition across public, private and third sector organisations including paying these providers by results • Reduce costs and become more efficient in all that we do Specifically, the Agency: • Specifies and commissions Offender Management services • Directly manages 120 public sector prisons (and a directly employed workforce of c48,000) • Contract manages 14 private sector prisons and a range of system-wide contracts (such as Prisoner Escort Service; Electronic Monitoring; Bail Accommodation Contract) • Contract manages 35 Probation Trusts and Third Sector Providers; and • Manages system-wide service delivery National Offender Management Service tel: 0300 047 6325 email: public.enquiries@noms.gsi.gov.uk print this document How NOMS Works introduction who we are key functions our structure Key Functions by commissioning by providing • Specifying, procuring and managing contracts • HM Prison Service • Services to all prisons • Deciding what needs to be done to deliver the sentences of the courts, protect the public and reduce reoffending, in custodial and community settings • Setting standards and specifications –......

Words: 3413 - Pages: 14

Premium Essay

Pareto Efficiency

...Markets, Organizations and the Role of Knowledge What is Pareto efficiency? Why do economists use this criterion for comparing alternative economic systems? An allocation of resources is Pareto efficient when there is no alternative that keeps all individuals at least as well off, but makes at least one person better off. One reason that economists use this criterion for comparing economic systems is that it is relatively uncontroverisial. Stronger criteria are likely to be met with more disagreement. What is a property right? What role do property rights play in a market economy? A property right is a socially-enforced right to select the uses of an economic good. A property right is private when it is assigned to a specific person. Property rights are alienable when they can be transferred (sold or given) to other individuals. Since owners bear the wealth effects of their actions, there are strong incentives to rearrange property rights in market transactions to increase efficiency and value. Many economists favor free trade between nations. They argue that free trade will increase total world output and make people of trading nations better off. Discuss how this argument relates to concepts presented in this chapter. Free trade allows countries to concentrate on producing goods and services for which they have a comparative advantage. This specialization increases the total production of goods in the global economy. Thus, each nation can be better off......

Words: 321 - Pages: 2

Premium Essay

Pareto Analysis

...Table of Contents 1.0 Introduction 2 1.1 Total Quality Management 2 1.2 Quality Improvement Strategy 2 1.3 Key Tools for Quality Improvement 2 1.4 Problem Statement 2 1.5 The main Objective 2 1.6 Specific Objectives 2 2.0 Literature Review 2 2.1 Pareto Analysis 2 3.0 Methodology 2 3.1 Data Collection 2 4.0 Results and Findings 2 5.0 Recommendations 2 5.1 Response 2 5.2 Limitations 2 5.3 Conclusion 2 References: 2 CHAPTER ONE 1.0 Introduction This paper aims at demonstrating the use of total quality management Pareto Analysis technique tool at Customs Department in Tanzania Revenue Authority to improve the process of clearing imported cargo through the Dar es salaam Port. One of the focal points in international trade is the country’s borders and the performance of customs and other border agencies, in particular their efficiency in clearing goods. In the modern business environment of just-in-time production and delivery it has become ever more important for traders to be guaranteed fast and predictable release of imported goods. 1.1 Total Quality Management TQM stands for Total Quality management. It is one of the most effective and least understood corporate strategies. It can affect every level, procedure and every person in a company. It is a most comprehensive process that can bring a company to the forefront of the global market. TQM has been defined in many ways by various authors. Some of them are......

Words: 2111 - Pages: 9

Premium Essay

Pareto Law

...Pareto’s Law The law of the vital few and the trivial many In 1906, Italian economist Vilfredo Pareto created a mathematical formula to describe the unequal distribution of wealth in his country, observing that twenty percent of the people owned eighty percent of the wealth. 80% of Output comes from 20% of Input 80% of Results generates from 20% of Effort 80% of Consequences results from 20% of Causes What It Means The 80/20 Rule means that in anything a few (20 percent) are vital and many(80 percent) are trivial. In Pareto's case it meant 20 percent of the people owned 80 percent of the wealth. Project Managers know that 20 percent of the work (the first 10 percent and the last 10 percent) consume 80 percent of your time and resources. You can apply the 80/20 Rule to almost anything, from the science of management to the physical world. You know 20 percent of your stock takes up 80 percent of your warehouse space and that 80 percent of your stock comes from 20 percent of your suppliers. Also 80 percent of your sales will come from 20 percent of your sales staff. 20 percent of your staff will cause 80 percent of your problems, but another 20 percent of your staff will provide 80 percent of your production. It works both ways. How It Can Help You The value of the Pareto Principle for a manager is that it reminds you to focus on the 20 percent that matters. Of the things you do during your day, only 20 percent really matter. Those 20 percent produce 80......

Words: 372 - Pages: 2

Premium Essay

Annotated Sampling and Distribution

...Distributions, Sampling and Estimation Our main objective in this section is to learn how to estimate some important characteristics of random variables using data. We will concentrate on estimating the mean from a normal distribution, and the proportion of success in a binomial distribution. To talk about estimation, we first need to know something about distributions and sampling. Most data used for decision making exhibit variation. We are interested in drawing conclusions from such data. Probability and statistics give us the necessary tools. We will again make use of the concept of a random variable. We have reviewed discrete random variables already. Before moving on, we need to review continuous random variables. Continuous random variables take on continuous or interval values (there are an infinite number of possibilities). If you are measuring, the distribution of the result will almost always be continuous. For example, the width of an extruded bar is a continuous random variable. The distribution of a continuous random variable is represented by a continuous curve (called the probability density function (pdf) and often denoted f(y)). The height of the curve does not represent probabilities; instead, the area under the curve between two points tells us about the probability. As a result, the probability that a continuous random variable is exactly equal to a single value is 0 (there is no area under a......

Words: 2939 - Pages: 12

Premium Essay

Normal Distribution

...C H A P T E R 6 The Normal Distribution Objectives After completing this chapter, you should be able to Outline Introduction 6–1 Normal Distributions 1 2 3 4 5 6 7 Identify distributions as symmetric or skewed. Identify the properties of a normal distribution. Find the area under the standard normal distribution, given various z values. Find probabilities for a normally distributed variable by transforming it into a standard normal variable. Find specific data values for given percentages, using the standard normal distribution. Use the central limit theorem to solve problems involving sample means for large samples. Use the normal approximation to compute probabilities for a binomial variable. 6–2 Applications of the Normal Distribution 6–3 The Central Limit Theorem 6–4 The Normal Approximation to the Binomial Distribution Summary 6–1 300 Chapter 6 The Normal Distribution Statistics Today What Is Normal? Medical researchers have determined so-called normal intervals for a person’s blood pressure, cholesterol, triglycerides, and the like. For example, the normal range of systolic blood pressure is 110 to 140. The normal interval for a person’s triglycerides is from 30 to 200 milligrams per deciliter (mg/dl). By measuring these variables, a physician can determine if a patient’s vital statistics are within the normal interval or if some type of treatment is needed to correct a condition and avoid future illnesses. The question then is,...

Words: 18901 - Pages: 76

Free Essay

Pareto

...Pareto was born of an exiled noble Genoese[->0] family in 1848 in Paris, the centre of the popular revolutions of that year. His father, Raffaele Pareto (1812–1882), was an Italian civil engineer and Ligurian marchese who had left Italy much like Mazzini and other Italian nationalists.[3] His mother, Marie Metenier, was a French woman. Enthusiastic about the 1848 German revolution[->1], his parents named him Fritz Wilfried, which became Vilfredo Federico upon his family's move back to Italy in 1858.[4] In his childhood, Pareto lived in a middle-class environment, receiving a high standard of education. In 1869, he earned a doctor's degree in engineering from what is now the Polytechnic University of Turin[->2].[3] His dissertation was entitled "The Fundamental Principles of Equilibrium in Solid Bodies". His later interest in equilibrium analysis in economics[->3] and sociology[->4] can be traced back to this paper. From Civil engineer to liberal, and then to economist[edit[->5]] For some years after graduation, he worked as a civil engineer[->6], first for the state-owned Italian Railway Company and later in private industry. He was manager of the Iron Works of San Giovanni Valdarno and later general manager of Italian Iron Works.[3] He did not begin serious work in economics until his mid-forties. He started his career a fiery liberal[->7], besting the most ardent British liberals with his attacks on any form of government intervention in the free market[->8]. In 1886 he......

Words: 2396 - Pages: 10

Free Essay

Chart

...University of Phoenix Material Employment Laws Chart Complete the chart below using information from the weekly readings and additional research if necessary. | | |Court Case Influential to | | | | |Description and Requirement of Law |Establishment of Law |Importance of Law |Workplace Application | |Employment Law | | | | | | |Prohibits discrimination because of |Heart of Atlanta Motel Inc. v. United |Recognized that separate is not equal.|Prohibits employers from retaliation | |Civil Rights Act of 1964 |race, color, religion, sex, or |States 1964 | |against employees who exercise this | | |national origin. | | |right. | | |Prohibits discrimination because of |Amendment to the Civil Rights Act of |Gives all applicants an......

Words: 684 - Pages: 3

Premium Essay

Probability and Distributions

...the data that they are looking to collect. Memo To: Director, American Intellectual Union From: John C. Carter Date: 8/2/2014 Subject: Distribution and Probability of data collected Dear Sir: As we discussed in earlier meetings, the AIU is looking for research data to help provide clear and concise numbers that you will be able to use in your business. These numbers that will be included in this document will allow the AIU to make sound and responsible business decisions about the future of your company. Overview of the Data Set The data that was used in this report came from information collected by AIU. These data sets include: Gender, Age, Department, Position, Tenure, Job Satisfaction, Intrinsic, Extrinsic and Benefits. With this data we will be looking at job satisfaction and how it relates to the different data sets that are included. These data sets include some Quantitive data sets like; Gender, Age and Tenure and Intrinsic. They also include a set of Qualitative categories like Department, Position, Extrinsic and Benefits. Use of Statistics and Probability in the Real World Statistics and Probability are used in a wide variety of ways in the modern workplace. Being able to read and evaluate these types of charts and graphs are a key to being a highly skilled employee. These charts and graphs are used to measure the quality of products, job performance, and job satisfaction along with many more options. Being able to utilize this......

Words: 823 - Pages: 4

Free Essay

Control Charts

...manufacturing recycle paper box company. This study starts with reading the standard operation procedures and analyzing the process flow to get the whole idea on how to manufacture paper box. At the same time, observations at the production line were made to identify problem occurs in the production line. By using check sheet, the defect data from each station were collected and have been analyzed using Pareto Chart. From the chart, it is found that glue workstation shows the highest number of defects. Based on observation at the glue workstation, the existing method used to glue the box was inappropriate because the operator used a lot of glue. Then, by using cause and effect diagram, the root cause of the problem was identified and solutions to overcome the problem were proposed. There are three suggestions proposed to overcome this problem. Cost reduction for each solution was calculated and the best solution is using three hair drier to dry the sticky glue which produce only 6.4 defects in an hour with cost of RM 0.0224. Keywords: Industrial engineering tools, Check sheet, Pareto chart and Cause and effect diagram. 1. Introduction Survival of any industry in today’s environment especially manufacturing industry not only depends on response time but also quality of the product produced. In this respect, seven quality control tools can be utilized as a method or process to reduce the manufacturing costs, production time and increasing the production line productivity.......

Words: 2893 - Pages: 12

Premium Essay

Pareto Case Study

...Jody Kelly Case Study #2 This Pareto Diagram shows that the most dissatisfaction comes from the areas of making appointments and checking in/out. Waiting time, whether it is to see a physician, getting an appointment or getting through on the phone, is the biggest issue to be addressed. Improving upon waiting time will drastically improve patient dissatisfaction. Problem Area | Occurrences | | Length to wait to see Physician | 13 | | Ease of Getting Appt. | 12 | | Ease of Getting Through on Phone | 10 | | Convenience of Office Hours | 7 | | Courtesy and Helpfulness of Receptionist | 7 | | Friendliness of Receptionist | 5 | | Resposiveness to Phone Calls Related to Care | 5 | | Comfort of Waiting Area | 4 | | How Well Physician Listened | 3 | | Respect Shown By Physician | 2 | | Confidence in Physician's Ability | 1 | | Respect Shown by Nurses/asst. | 0 | | | | | The lengthy wait to see a physician is due to the fact that the doctors are sometimes late getting to the clinic due to surgeries, teaching at a medical school, and unexpected emergences. The ease of getting a convenient appointment is could be inhibited by the doctor’s busy and unpredicted schedules and also the lack of communication between receptionists and secretaries. The difficulty getting through on the phone is caused by a heavy load on the receptionists and the fact that they cannot relay messages to secretaries without adequate phone coverage which also......

Words: 678 - Pages: 3

Premium Essay

Pareto

...Pareto In general terms, Pareto coined the 80/20 rule whereby 20% of the issues cause 80% of your problems.  So the idea is to identify and focus your resources on the issues which are causing most of your problems. The Pareto bar chart will visually display from left to right a rank-order of which factors are most critical to be addressed. (Heldman, 2013, p.502) More specifically, a Pareto diagram displays “the magnitude of the change on the vertical axis and the root causes along the horizontal axis” (Kendrick, 2009, p.26).  In our text, examples are provided in which a Pareto chart represents magnitude in terms of “weeks impacted” along the vertical axis, and its relationship to scope, resource, and schedule.  Another Pareto diagram is narrowed to display how each specific subcategory relates to the magnitude of change. (Kendrick, 2009, p.35-36)  A “probability and impact matrix” combines the likelihood of occurrence with the impact that the event would have in order to determine the need for, and at what level of detail, a risk response plan is required.  A numbering system such as 1-5 could be used or something more simple such as low-medium-high.  How a “probability and impact matrix” is defined will vary by organization and should be developed during the planning stage. (Heldman, 2013, p.254) As is evident, tables and charts can be used to rank risk by schedule, scope, and budget.  These visual representations can be used to quickly identify areas of concern.  One......

Words: 772 - Pages: 4

Free Essay

750 Powerpoint Chart

...PowerPoint Charts & Diagrams CEO Pack ©Presentation-Process.com 750+ POWERPOINT CHARTS & DIAGRAMS CEO PACK Press Ctrl + F to find a particular term, and locate the folder and file name where you can find the specific diagram. A screenshot of all the diagrams are included to help you locate just what you need easily and quickly. Browsing through this set of creative diagrams can also inspire new ideas! CONTENTS (793 SLIDES + 156 ICONS = 949 ITEMS) Folder: Cause Effect diagram (38) ........................................................................................................................... 2 Folder: Circle diagram (21)...................................................................................................................................... 4 Folder: Consulting diagrams (83) ............................................................................................................................ 6 Folder: Extreme custom animation (15) ................................................................................................................ 10 Folder: PowerPoint 3D (51)................................................................................................................................... 11 Folder: PowerPoint charts (51) ............................................................................................................................. 14 Folder: PowerPoint concepts (84) ........................................

Words: 5723 - Pages: 23

Premium Essay

Chart

...Axia College Material Appendix B Ethical Theories Chart Complete the chart below using information from the weekly readings and additional research if necessary. Include APA formatted in-text citations when applicable and list all references at the bottom of the page. Ethical Theory | | | | | Utilitarianism | Deontological | Virtue ethics | | Definition | “Moral decisions require taking full advantage of the benefits as well as minimizing the damage to society. (Trevino & Nelson, 2007)”Or moral worth can determine only by the result outcome. One can only weight the morality of an action after knowing the consequences. | “Somebody who concentrates on carrying out what is “right” consistent with their own ethics as it’s as ideals. (Trevino & Nelson, 2007)” “So this approach judges the morality of someone action based on the action's adherence to a rule or rules, according to which the rightness of an action is determined by its consequences.” | This focuses more on the integrity of the moral actor than on the moral act itself.”“A concentration on virtue ethics, or honesty, deal mainly with an individual’s character, inspirations, as their objectives, in place of results or regulations, as their crucial factor of moral philosophy.” (Trevino & Nelson, 2007) | Ethical thinker associated with theory | Jeremy Bentham and John Stuart | Immanuel Kant | Plato and Aristotle | Decision-making process | “What action nets the......

Words: 498 - Pages: 2