# STATISTICAL QUALITY CONTROL (SQC)

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Statistical Quality Control 1 SQC consists of two major areas: STATISTICAL QUALITY CONTOL (SQC) - Acceptance Sampling - Process Control or Control Charts Both of these statistical techniques may be applied to two kinds of data. 1. Attribute Data: when the quality characteristic being investigated is noted by either its presence or absence and then classified as Defective or Non-Defective. Example: Conforming or non-conforming Pass or fail Good or bad 2. Variable Data: The characteristics are actually measured and can take on a value along a continuous scale. Example: Length, Weight Sometimes variable data can be transformed into attribute data. For example, the specifications required for a shaft diameter (X) is 2" plus or minus 0.01". If X falls within 1.99" and 2.01", then the shaft diameter is conforming to specifications and hence is classified as good. If X < 1.99" or X > 2.01", then the shaft diameter is not conforming to specifications and hence classified as bad. Thus, attribute data does not have information of how much good or how much bad? which the variable data would have, because it would record the exact measurements of each shaft. We will first study Acceptance Sampling.

2 2 Statistical Quality Control Acceptance Sampling: Inspection provides a means for monitoring quality. For example, inspection may be performed on incoming raw material, to decide whether to keep it or return it to the vendor if the quality level is not what was agreed on. Similarly, inspection can also be done on finished goods before deciding whether to make the shipment to the customer or not. However, performing 100% inspection is generally not economical or practical, therefore, sampling is used instead. Acceptance Sampling is therefore a method used to make a decision as to whether to accept or to reject lots based on inspection of sample(s). The objective is not to control or estimate the quality of lots, only to pass a judgment on lots. Using sampling rather than 100% inspection of the lots brings some risks both to the consumer and to the producer, which are called the consumer's and the producer's risks, respectively. We encounter making decisions on sampling in our daily affairs. Example: LOT (N) SAMPLE (n) STATISTICAL Inference is made on the quality of the lot by inspecting only the small sample drawn from the lot.

3 Statistical Quality Control 3 There are several Acceptance Sampling Plans: - Single Sampling (Inference made on the basis of only one sample) - Double Sampling (Inference made on the basis of one or two samples) - Sequential Sampling (Additional samples are drawn until an inference can be made) etc. We will do Single Sampling plans only in this course. Single Sampling Plans A Single Sampling plan is characterized by n (the sample size) which is drawn from the lot and inspected for defects. The number of defects (d) found are checked against c (the acceptance number) and the procedure works as follows (clearly, d = 0, 1, 2, n): Example: Suppose n=100 and c=3, which means that if the number of defectives in the sample (d) is equal to 0, 1, 2, or 3, then the lot will be accepted, and if d is 4 or more, then the lot will be rejected.

4 4 Statistical Quality Control As mentioned earlier, inherent in a sampling plan are producer s and consumer s risk. These risks can be depicted by the following table: Lot is Good Decision Accept No Error eject Error (Producer s isk) Bad Error (Consumer s isk) No Error Formally, these risks are written as: where α : The producer's risk, is the probability that a lot with AQL will be rejected. β : The consumer's risk, is the probability that a lot with LTPD will be accepted. Acceptable Quality Level (AQL) = The quality level acceptable to the consumer Lot Tolerance Percent Defective (LTPD) = The level of "poor' quality that the consumer is willing to tolerate only a small percentage of the time. In general, both the producer and the consumer want to minimize their risks. The choice of a well designed sampling plan can help both the producer and the consumer maintain their respective risks at acceptable levels to both. For example, α = 5% for AQL of 0.02 and β = 10% for LTPD of 0.08.

5 Statistical Quality Control 5 Keeping c constant: What is the effect on producer s risk? What is the effect on consumer s risk? Keeping n constant: What is the effect on producer s risk? What is the effect on consumer s risk?

6 6 Statistical Quality Control The Theory Behind Process Control Let s now turn our attention to the second major area of SQC, namely Process Control or Control Charts, which directly affect the quality of a production or service process. Every production process has a natural variation. For example, a process making shafts is adjusted so that the shaft diameter will be 2". However, due to the natural variation in the manufacturing process, not every shaft coming off the production line will have a diameter of exactly 2". There will be some unexplained variation around the nominal value of 2". Therefore, some tolerance is built into the design of the product to allow for this natural (random) variation. However, if the process goes out of control, the variation may become more than that allowed by the design indicating the presence of variation that can be explained(e.g., defective raw material, untrained worker, etc.). In this case some action needs to be taken, the machine can be readjusted, replaced etc. The control charts show when the variation in the process is within the limits of the natural variation and when it goes out of control. Below are pictures that show various in-control and out-of-control situations for a process.

7 Statistical Quality Control 7 Even when the process is in control, we need to make sure that the mean of the process is in conformance with specifications as shown below.

8 8 Statistical Quality Control Continuous improvement in the process is possible by reducing the variation around the mean as shown below.

9 Statistical Quality Control 9 Charts Used with Variable Data: Control charts are of two types corresponding to the type of data that is used, namely variable or attribute data. We will study the popular control charts of both these types. X and -Charts (mean and range charts) are commonly used in dealing with variable data to monitor the quality of a manufacturing process. The reason that both the charts have to be used together is that both the mean and the variation (spread) have to be under control. ecall that the variable data consists of actual measurements (e.g., shaft lengths, weight of bags in lbs, etc.). Let us take an example of variable data that is pertinent for the acid content in a certain chemical product. The operator measured and recorded the acid content of a sample of 4 units at a time at regular intervals for at least 25 times. This variable data and the calculations performed with it are shown on the following table. Also, given are the variable control charts ( X and charts) for the data.

10 10 Statistical Quality Control The Control Limits (UCL = Upper Control Limit and LCL = Lower Control Limit with the mean of the data as the central line) for X and Charts are established as follows: X -Charts X = g i g X i UCL x = X + 3σ LCL = X 3σ x x x where: X = average of subgroup averages (the central line in the chart) X i = average of the ith subgroup g = number of subgroups σ x is further estimated using the range information (i.e., 3σ x = A 2 ); as such the control limit calculations are much simplified. The simplified control limits are as follows: UCL = X + x A2 LCL = X x A2 where A 2 is a factor available in tables for different sample sizes (see table below). -Charts: = g i g i UCL = + 3σ LCL = 3σ where = average of subgroup ranges (the central line in the chart) i = range if the ith subgroup g = number of subgroups Similarly, control limit calculations are much simplified and are: UCL = D4 LCL = D3 where D 3 and D 4 are factors available in tables for different sample sizes (see table below). Factors for Control Limits n A 2 D 4 D

11 Statistical Quality Control 11 Let us now calculate the control limits for the given data, starting first with the ange () chart. This is done first because the X chart requires in determining its control limits. Therefore, naturally we need to first check if the chart is under control and use that in the control limits of the X chart. -Chart: n = = X = A 2 = D 3 = D 4 = UCL = D 4 LCL = D 3 = = Does the chart show that the process is under control? Yes or No and why? X -Chart: UCL = X + A 2 LCL = X - A 2 = = Does the X chart show that the process is under control? Yes or No and why?

12 12 Statistical Quality Control Another Example: The St. Patrick's Hospital is starting a quality improvement project on the time to admit a patient using X and Charts. Determine the limits for the X and charts and check to see if there are any out-of-control points. Subgroup Number OBSEVATION X 1 X 2 X 3 X Subgroup Number OBSEVATION X 1 X 2 X 3 X n = = X = A 2 = D 3 = D 4 = -Chart: UCL = D 4 LCL = D 3 = = Does the chart show that the process is under control? Yes or No and why? X -Chart: UCL = X + A 2 LCL = X - A 2 = = Does the X chart show that the process is under control? Yes or No and why?

13 Statistical Quality Control 13 Charts Used with Attribute Data P-Chart, also known as the fraction or percent defective chart, is commonly used in dealing with attribute data to monitor the quality of a manufacturing process. The mean percent defective ( p ) is the central line. The upper and lower control limits are constructed as follows: The mean proportion defective ( p ): The standard deviation of p: p = Total Number of Defectives Total Number Inspected p( 1 p) σ p = n where n = sample size. Control Limits are: UCL = p + Z σ p LCL = p Z σ p or UCL = p + Z p( 1 p) n LCL = p Z p( 1 p) n Usually the Z value is equal to 3 (as was used in the X and charts), since the variations within three standard deviations are considered as natural variations. However, the choice of the value of Z depends on the environment in which the chart is being used, and on managerial judgment.

14 14 Statistical Quality Control Example: A computer manufacturer collects data from the final test of its product starting from the end of January and all through February. Each day a sample of 2000 items are inspected and the number of items in the sample that do not conform to specifications is recorded. The data is shown below: Subgroup Number Number Percent Subgroup Number Number Percent Number Inspected Defective Defective Number Inspected Defective Defective (day) (day) n = p = σ p = UCL = LCL =

### Learning Objectives. Understand how to select the correct control chart for an application. Know how to fill out and maintain a control chart.

CONTROL CHARTS Learning Objectives Understand how to select the correct control chart for an application. Know how to fill out and maintain a control chart. Know how to interpret a control chart to determine

### Managerial Statistics Module 10

Title : STATISTICAL PROCESS CONTROL (SPC) Period : 4 hours I. Objectives At the end of the lesson, students are expected to: 1. define statistical process control 2. describe the fundamentals of SPC and

### Attributes Acceptance Sampling Understanding How it Works

Attributes Acceptance Sampling Understanding How it Works Dan O Leary CBE, CQE, CRE, CSSBB, CIRM, LLC 603-209-0600 OmbuEnterprises@msn.com Copyright 2008, 2009 by, LLC Acceptance Sampling 1 Instructor

### STATISTICAL REASON FOR THE 1.5σ SHIFT Davis R. Bothe

STATISTICAL REASON FOR THE 1.5σ SHIFT Davis R. Bothe INTRODUCTION Motorola Inc. introduced its 6σ quality initiative to the world in the 1980s. Almost since that time quality practitioners have questioned

### Confidence Intervals for Cp

Chapter 296 Confidence Intervals for Cp Introduction This routine calculates the sample size needed to obtain a specified width of a Cp confidence interval at a stated confidence level. Cp is a process

### STATISTICAL METHODS FOR QUALITY CONTROL

statistics STATISTICAL METHODS FOR QUALITY CONTROL CONTENTS STATISTICS IN PRACTICE: DOW CHEMICAL U.S.A. 1 STATISTICAL PROCESS CONTROL Control Charts x Chart: Process Mean and Standard Deviation Known x

### Control CHAPTER OUTLINE LEARNING OBJECTIVES

Quality Control 16Statistical CHAPTER OUTLINE 16-1 QUALITY IMPROVEMENT AND STATISTICS 16-2 STATISTICAL QUALITY CONTROL 16-3 STATISTICAL PROCESS CONTROL 16-4 INTRODUCTION TO CONTROL CHARTS 16-4.1 Basic

### Quality control: Meaning, process control, SQC control charts, single, double and sequential sampling, Introduction to TQM.

Unit 4 Notes By Neha Chhabra Quality control: Meaning, process control, SQC control charts, single, double and sequential sampling, Introduction to TQM. QUALITY CONTROL DEFINITION OF QUALITY: The meaning

### Applied Reliability ------------------------------------------------------------------------------------------------------------ Applied Reliability

Applied Reliability Techniques for Reliability Analysis with Applied Reliability Tools (ART) (an EXCEL Add-In) and JMP Software AM216 Class 6 Notes Santa Clara University Copyright David C. Trindade, Ph.

### 6.4 Normal Distribution

Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under

### DISCRETE MODEL DATA IN STATISTICAL PROCESS CONTROL. Ester Gutiérrez Moya 1. Keywords: Quality control, Statistical process control, Geometric chart.

VI Congreso de Ingeniería de Organización Gijón, 8 y 9 de septiembre 005 DISCRETE MODEL DATA IN STATISTICAL PROCESS CONTROL Ester Gutiérrez Moya Dpto. Organización Industrial y Gestión de Empresas. Escuela

### THE PROCESS CAPABILITY ANALYSIS - A TOOL FOR PROCESS PERFORMANCE MEASURES AND METRICS - A CASE STUDY

International Journal for Quality Research 8(3) 399-416 ISSN 1800-6450 Yerriswamy Wooluru 1 Swamy D.R. P. Nagesh THE PROCESS CAPABILITY ANALYSIS - A TOOL FOR PROCESS PERFORMANCE MEASURES AND METRICS -

### The normal approximation to the binomial

The normal approximation to the binomial In order for a continuous distribution (like the normal) to be used to approximate a discrete one (like the binomial), a continuity correction should be used. There

### Process Quality. BIZ2121-04 Production & Operations Management. Sung Joo Bae, Assistant Professor. Yonsei University School of Business

BIZ2121-04 Production & Operations Management Process Quality Sung Joo Bae, Assistant Professor Yonsei University School of Business Disclaimer: Many slides in this presentation file are from the copyrighted

### Statistical Quality Control

Statistical Quality Control CHAPTER 6 Before studying this chapter you should know or, if necessary, review 1. Quality as a competitive priority, Chapter 2, page 00. 2. Total quality management (TQM) concepts,

### Gage Studies for Continuous Data

1 Gage Studies for Continuous Data Objectives Determine the adequacy of measurement systems. Calculate statistics to assess the linearity and bias of a measurement system. 1-1 Contents Contents Examples

### Unit 22: Sampling Distributions

Unit 22: Sampling Distributions Summary of Video If we know an entire population, then we can compute population parameters such as the population mean or standard deviation. However, we generally don

### Control Charts for Variables. Control Chart for X and R

Control Charts for Variables X-R, X-S charts, non-random patterns, process capability estimation. 1 Control Chart for X and R Often, there are two things that might go wrong in a process; its mean or its

### MEANING & SIGNIFICANCE OF STATISTICAL PROCESS CONTROL [SPC] Presented by, JAYA VARATHAN B SANKARAN S SARAVANAN J THANGAVEL S

MEANING & SIGNIFICANCE OF STATISTICAL PROCESS CONTROL [SPC] Presented by, JAYA VARATHAN B SANKARAN S SARAVANAN J THANGAVEL S PRESENTATION OUTLINE History Of SPC Meaning &Significance Of SPC SPC in TQM

### SOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions

SOLUTIONS: 4.1 Probability Distributions and 4.2 Binomial Distributions 1. The following table contains a probability distribution for a random variable X. a. Find the expected value (mean) of X. x 1 2

### Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing 1) Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures

### Statistical Process Control OPRE 6364 1

Statistical Process Control OPRE 6364 1 Statistical QA Approaches Statistical process control (SPC) Monitors production process to prevent poor quality Acceptance sampling Inspects random sample of product

### Two-Sample T-Tests Assuming Equal Variance (Enter Means)

Chapter 4 Two-Sample T-Tests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when the variances of

### Two-Sample T-Tests Allowing Unequal Variance (Enter Difference)

Chapter 45 Two-Sample T-Tests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when no assumption

### Use and interpretation of statistical quality control charts

International Journal for Quality in Health Care 1998; Volume 10, Number I: pp. 69-73 Methodology matters VIII 'Methodology Matters' is a series of intermittently appearing articles on methodology. Suggestions

### SAMPLE SIZE CONSIDERATIONS

SAMPLE SIZE CONSIDERATIONS Learning Objectives Understand the critical role having the right sample size has on an analysis or study. Know how to determine the correct sample size for a specific study.

### Software Quality. Unit 2. Advanced techniques

Software Quality Unit 2. Advanced techniques Index 1. Statistical techniques: Statistical process control, variable control charts and control chart for attributes. 2. Advanced techniques: Quality function

### The normal approximation to the binomial

The normal approximation to the binomial The binomial probability function is not useful for calculating probabilities when the number of trials n is large, as it involves multiplying a potentially very

### Confidence Intervals for Cpk

Chapter 297 Confidence Intervals for Cpk Introduction This routine calculates the sample size needed to obtain a specified width of a Cpk confidence interval at a stated confidence level. Cpk is a process

### 10 CONTROL CHART CONTROL CHART

Module 10 CONTOL CHT CONTOL CHT 1 What is a Control Chart? control chart is a statistical tool used to distinguish between variation in a process resulting from common causes and variation resulting from

### Getting Started with Statistics. Out of Control! ID: 10137

Out of Control! ID: 10137 By Michele Patrick Time required 35 minutes Activity Overview In this activity, students make XY Line Plots and scatter plots to create run charts and control charts (types of

### Confidence Intervals for the Difference Between Two Means

Chapter 47 Confidence Intervals for the Difference Between Two Means Introduction This procedure calculates the sample size necessary to achieve a specified distance from the difference in sample means

### Chapter 7 Notes - Inference for Single Samples. You know already for a large sample, you can invoke the CLT so:

Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N(µ, ). Also for a large sample, you can replace an unknown σ by s. You know how to do a

### Math 251, Review Questions for Test 3 Rough Answers

Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,

### Simple Regression Theory II 2010 Samuel L. Baker

SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the

### CHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is.

Some Continuous Probability Distributions CHAPTER 6: Continuous Uniform Distribution: 6. Definition: The density function of the continuous random variable X on the interval [A, B] is B A A x B f(x; A,

### USE OF SHEWART CONTROL CHART TECHNIQUE IN MONITORING STUDENT PERFORMANCE

Bulgarian Journal of Science and Education Policy (BJSEP), Volume 8, Number 2, 2014 USE OF SHEWART CONTROL CHART TECHNIQUE IN MONITORING STUDENT PERFORMANCE A. A. AKINREFON, O. S. BALOGUN Modibbo Adama

### The Management and Control of Quality

The Management and Control of Quality JAMES R. EVANS University of Cincinnati WILLIAM M. LINDSAY Northern Kentucky University TfCHNISCHE HOCHSCHULE DARMSTADT Fochbcroic'n 1 G e 8o m t b i b I i o t h e

### Experimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test

Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely

### SAMPLE EXAMINATION. If you have any questions regarding this sample examination, please email cert@asq.org

SAMPLE EXAMINATION The purpose of the following sample examination is to provide an example of what is provided on exam day by ASQ, complete with the same instructions that are provided on exam day. The

### Confidence Intervals for One Standard Deviation Using Standard Deviation

Chapter 640 Confidence Intervals for One Standard Deviation Using Standard Deviation Introduction This routine calculates the sample size necessary to achieve a specified interval width or distance from

### Point and Interval Estimates

Point and Interval Estimates Suppose we want to estimate a parameter, such as p or µ, based on a finite sample of data. There are two main methods: 1. Point estimate: Summarize the sample by a single number

### Pearson's Correlation Tests

Chapter 800 Pearson's Correlation Tests Introduction The correlation coefficient, ρ (rho), is a popular statistic for describing the strength of the relationship between two variables. The correlation

### CHAPTER TWELVE TABLES, CHARTS, AND GRAPHS

TABLES, CHARTS, AND GRAPHS / 75 CHAPTER TWELVE TABLES, CHARTS, AND GRAPHS Tables, charts, and graphs are frequently used in statistics to visually communicate data. Such illustrations are also a frequent

### THE USE OF STATISTICAL PROCESS CONTROL IN PHARMACEUTICALS INDUSTRY

THE USE OF STATISTICAL PROCESS CONTROL IN PHARMACEUTICALS INDUSTRY Alexandru-Mihnea SPIRIDONICĂ 1 E-mail: aspiridonica@iota.ee.tuiasi.ro Abstract The use of statistical process control has gained a major

### Individual Moving Range (I-MR) Charts. The Swiss Army Knife of Process Charts

Individual Moving Range (I-MR) Charts The Swiss Army Knife of Process Charts SPC Selection Process Choose Appropriate Control Chart ATTRIBUTE type of data CONTINUOUS DEFECTS type of attribute data DEFECTIVES

### Characteristics of Binomial Distributions

Lesson2 Characteristics of Binomial Distributions In the last lesson, you constructed several binomial distributions, observed their shapes, and estimated their means and standard deviations. In Investigation

### Common Tools for Displaying and Communicating Data for Process Improvement

Common Tools for Displaying and Communicating Data for Process Improvement Packet includes: Tool Use Page # Box and Whisker Plot Check Sheet Control Chart Histogram Pareto Diagram Run Chart Scatter Plot

### Binomial Distribution Problems. Binomial Distribution SOLUTIONS. Poisson Distribution Problems

1 Binomial Distribution Problems (1) A company owns 400 laptops. Each laptop has an 8% probability of not working. You randomly select 20 laptops for your salespeople. (a) What is the likelihood that 5

### Selecting SPC Software for Batch and Specialty Chemicals Processing

WHITE PAPER Selecting SPC Software for Batch and Specialty Chemicals Processing Statistical Process Control (SPC) is a necessary part of modern chemical processing. The software chosen to collect quality

### Constructing and Interpreting Confidence Intervals

Constructing and Interpreting Confidence Intervals Confidence Intervals In this power point, you will learn: Why confidence intervals are important in evaluation research How to interpret a confidence

### Statistical estimation using confidence intervals

0894PP_ch06 15/3/02 11:02 am Page 135 6 Statistical estimation using confidence intervals In Chapter 2, the concept of the central nature and variability of data and the methods by which these two phenomena

### δ Charts for Short Run Statistical Process Control

50 Received April 1992 Revised July 1993 δ Charts for Short Run Statistical Process Control Victor E. Sower Sam Houston State University, Texas, USA, Jaideep G. Motwani Grand Valley State University, Michigan,

### Figure 1: Working area of the plastic injection moulding company. Figure 2: Production volume, quantity of defected parts, and DPPM

1. Title : BLACK DOT DEFECT REDUCTION IN PLASTIC INJECTION MOULDING PROCESS 2. Student Name: Mr. Itthiwat Rattanabunditsakun / ID: 557 12290 21 Advisor Name: Assoc. Prof. Parames Chutima, Ph.D. 3. Problem

### Control Charts and Data Integration

Control Charts and Data Integration The acceptance chart and other control alternatives. Examples on SPC applications 1 Modified Charts If C pk >> 1 we set control limits so that the fraction non-conf.

### Introduction to Analysis of Variance (ANOVA) Limitations of the t-test

Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA Limitations of the t-test Although the t-test is commonly used, it has limitations Can only

### Quality and Quality Control

1 Quality and Quality Control INSPECTION Inspection is the most common method of attaining standardisation, uniformity and quality of workmanship. It is the cost art of controlling the product quality

### Point Biserial Correlation Tests

Chapter 807 Point Biserial Correlation Tests Introduction The point biserial correlation coefficient (ρ in this chapter) is the product-moment correlation calculated between a continuous random variable

### Assessing Measurement System Variation

Assessing Measurement System Variation Example 1: Fuel Injector Nozzle Diameters Problem A manufacturer of fuel injector nozzles installs a new digital measuring system. Investigators want to determine

### Normal and Binomial. Distributions

Normal and Binomial Distributions Library, Teaching and Learning 14 By now, you know about averages means in particular and are familiar with words like data, standard deviation, variance, probability,

### NCSS Statistical Software

Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the

### Implementing SPC for Wet Processes

Implementing SPC for Wet Processes Yvonne Welz Atotech Deutschland GmbH, Berlin, Germany Statistical process control is rare for wet processes, yet OEMs demand quality systems for processes as well as

### Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving

Section 7 Algebraic Manipulations and Solving Part 1 Expressions, Equations, and Inequalities: Simplifying and Solving Before launching into the mathematics, let s take a moment to talk about the words

### A Study of Process Variability of the Injection Molding of Plastics Parts Using Statistical Process Control (SPC)

Paper ID #7829 A Study of Process Variability of the Injection Molding of Plastics Parts Using Statistical Process Control (SPC) Dr. Rex C Kanu, Ball State University Dr. Rex Kanu is the coordinator of

### HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

### Chapter 2. Hypothesis testing in one population

Chapter 2. Hypothesis testing in one population Contents Introduction, the null and alternative hypotheses Hypothesis testing process Type I and Type II errors, power Test statistic, level of significance

### Week 4: Standard Error and Confidence Intervals

Health Sciences M.Sc. Programme Applied Biostatistics Week 4: Standard Error and Confidence Intervals Sampling Most research data come from subjects we think of as samples drawn from a larger population.

### Measurement and Metrics Fundamentals. SE 350 Software Process & Product Quality

Measurement and Metrics Fundamentals Lecture Objectives Provide some basic concepts of metrics Quality attribute metrics and measurements Reliability, validity, error Correlation and causation Discuss

### The Seven Basic Tools. QUALITY CONTROL TOOLS (The Seven Basic Tools) What are check sheets? CHECK SHEET. Illustration (Painting defects)

QUALITY CONTROL TOOLS (The Seven Basic Tools) Dr. Ömer Yağız Department of Business Administration Eastern Mediterranean University TRNC The Seven Basic Tools The seven basic tools are: Check sheet Flow

### MBA 611 STATISTICS AND QUANTITATIVE METHODS

MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain

### Enhancing Student Understanding of Control Charts Using a Dice Activity

Enhancing Student Understanding of Control Charts Using a Dice Activity by Martin P. Jones, Ph.D. MartinJones@missouristate.edu Department of Industrial Management Missouri State University Rita S. Hawkins,

### Introduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses

Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the

### Unit 23: Control Charts

Unit 23: Control Charts Summary of Video Statistical inference is a powerful tool. Using relatively small amounts of sample data we can figure out something about the larger population as a whole. Many

### 3.4 Statistical inference for 2 populations based on two samples

3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted

### Practice Problems for Homework #6. Normal distribution and Central Limit Theorem.

Practice Problems for Homework #6. Normal distribution and Central Limit Theorem. 1. Read Section 3.4.6 about the Normal distribution and Section 4.7 about the Central Limit Theorem. 2. Solve the practice

### 12.5: CHI-SQUARE GOODNESS OF FIT TESTS

125: Chi-Square Goodness of Fit Tests CD12-1 125: CHI-SQUARE GOODNESS OF FIT TESTS In this section, the χ 2 distribution is used for testing the goodness of fit of a set of data to a specific probability

### CALCULATIONS & STATISTICS

CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents

### International Journal of Pure and Applied Sciences and Technology

Int. J. Pure Appl. Sci. Techl., 15(1) (2013), pp. 20-30 International Journal of Pure and Applied Sciences and Techlogy ISSN 2229-6107 Available online at www.ijopaasat.in Research Paper Statistical Quality

### Joint Exam 1/P Sample Exam 1

Joint Exam 1/P Sample Exam 1 Take this practice exam under strict exam conditions: Set a timer for 3 hours; Do not stop the timer for restroom breaks; Do not look at your notes. If you believe a question

### Chapter 4. Probability and Probability Distributions

Chapter 4. robability and robability Distributions Importance of Knowing robability To know whether a sample is not identical to the population from which it was selected, it is necessary to assess the

### HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

### START Selected Topics in Assurance

START Selected Topics in Assurance Related Technologies Table of Contents Introduction Some Essential Concepts Some QC Charts Summary For Further Study About the Author Other START Sheets Available Introduction

### Six Sigma Project Charter

rev 2 Six Sigma Project Charter Name of project: Decreasing percent of transferred out calls by 50% Green belt: Submitted by: Joy May e-mail: joy@purdue.edu Date submitted: May 2, 202 I. Project Selection

### CHAPTER 13. Control Charts

13.1 Introduction 1 CHAPTER 13 Control Charts This chapter discusses a set of methods for monitoring process characteristics over time called control charts and places these tools in the wider perspective

### Elaboration of Scrum Burndown Charts.

. Combining Control and Burndown Charts and Related Elements Discussion Document By Mark Crowther, Empirical Pragmatic Tester Introduction When following the Scrum approach a tool frequently used is the

### Week 3&4: Z tables and the Sampling Distribution of X

Week 3&4: Z tables and the Sampling Distribution of X 2 / 36 The Standard Normal Distribution, or Z Distribution, is the distribution of a random variable, Z N(0, 1 2 ). The distribution of any other normal

### Introduction to Hypothesis Testing OPRE 6301

Introduction to Hypothesis Testing OPRE 6301 Motivation... The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about

### Products reliability assessment using Monte-Carlo simulation

Products reliability assessment using Monte-Carlo simulation Dumitrascu Adela-Eliza and Duicu Simona Abstract Product reliability is a critical part of total product quality. Reliability is a measure of

### Confidence Intervals for Exponential Reliability

Chapter 408 Confidence Intervals for Exponential Reliability Introduction This routine calculates the number of events needed to obtain a specified width of a confidence interval for the reliability (proportion

### 1 Variation control in the context of software engineering involves controlling variation in the

1 Variation control in the context of software engineering involves controlling variation in the A) process applied B) resources expended C) product quality attributes D) all of the above 2 There is no

### Math 319 Problem Set #3 Solution 21 February 2002

Math 319 Problem Set #3 Solution 21 February 2002 1. ( 2.1, problem 15) Find integers a 1, a 2, a 3, a 4, a 5 such that every integer x satisfies at least one of the congruences x a 1 (mod 2), x a 2 (mod

### AC 2012-4265: PROMOTING AWARENESS IN MANUFACTURING STU- DENTS OF

AC 2012-4265: PROMOTING AWARENESS IN MANUFACTURING STU- DENTS OF Dr. Merwan B. Mehta, East Carolina University Merwan Mehta, Ph.D., is Associate Professor at East Carolina University, Greenville, N.C.,

### Non-Parametric Tests (I)

Lecture 5: Non-Parametric Tests (I) KimHuat LIM lim@stats.ox.ac.uk http://www.stats.ox.ac.uk/~lim/teaching.html Slide 1 5.1 Outline (i) Overview of Distribution-Free Tests (ii) Median Test for Two Independent

### Lesson 20. Probability and Cumulative Distribution Functions

Lesson 20 Probability and Cumulative Distribution Functions Recall If p(x) is a density function for some characteristic of a population, then Recall If p(x) is a density function for some characteristic

### SIMULATION STUDIES IN STATISTICS WHAT IS A SIMULATION STUDY, AND WHY DO ONE? What is a (Monte Carlo) simulation study, and why do one?

SIMULATION STUDIES IN STATISTICS WHAT IS A SIMULATION STUDY, AND WHY DO ONE? What is a (Monte Carlo) simulation study, and why do one? Simulations for properties of estimators Simulations for properties

### 46.2. Quality Control. Introduction. Prerequisites. Learning Outcomes

Quality Control 46.2 Introduction Quality control via the use of statistical methods is a very large area of study in its own right and is central to success in modern industry with its emphasis on reducing

### Instruction Manual for SPC for MS Excel V3.0

Frequency Business Process Improvement 281-304-9504 20314 Lakeland Falls www.spcforexcel.com Cypress, TX 77433 Instruction Manual for SPC for MS Excel V3.0 35 30 25 LSL=60 Nominal=70 Capability Analysis