To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 17-1 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter 17 Statistical Quality Control Mr.Mosab I. Tabash

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 17-2 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Learning Objectives Students will be able to: 1.Define the quality of a product or service. 2.Develop four types of control charts 3.Understand the basic theoretical underpinnings of statistical quality control, including the central limit theorem. 4.Know whether a process is in control.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 17-3 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter Outline 17.1 Introduction 17.2 Defining Quality and TQM 17.3 Statistical Process Control 17.4 Control Charts for Variables 17.5 Control Charts for Attributes

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 17-4 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Introduction Quality is a major issue in today’s organizations. Quality control (QC), or quality management, tactics are used throughout the organization to assure deliverance of quality products or services. Statistical process control (SPC) uses statistical and probability tools to help control processes and produce consistent goods and services. Total quality management (TQM) refers to a quality emphasis that encompasses the entire organization.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 17-5 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ  “Quality is the degree to which a specific product conforms to a design or specification.”  “Quality is the totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs.”  “Quality is fitness for use.”  “Quality is defined by the customer; customers want products and services that, throughout their lives, meet customers’ needs and expectations at a cost that represents value.”  “Even though quality cannot be defined, you know what it is.” Definitions of Quality

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 17-6 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ  Statistical technique used to ensure process is making product to standard. It can also monitor, measure, and correct quality problems.  Control charts are graphs that show upper and lower limits for the process we want to control. Thus, SPC involves taking samples of the process output and plotting the averages on a control chart. Statistical Process Control (SPC)

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 17-7 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ All processes are subject to variability.  Natural causes: Random variations that are uncontrollable and exist in processes that are statistically ‘in control.’  Assignable causes: Correctable problems that are not random and can be controlled. oExamples: machine wear, unskilled workers, poor material. The objective of control charts is to identify assignable causes and prevent them from reoccurring. Statistical Process Control (SPC) (continued)

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 17-8 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Produce Good Provide Service Stop Process Yes No Assign. Causes? Take Sample Inspect Sample Find Out Why Create Control Chart Start Statistical Process Control Steps

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 17-9 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Control Chart Patterns Upper control chart limit Target Lower control chart limit Normal behavior.One point out above. Investigate for cause. One point out below. Investigate for cause.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Control Chart Patterns (continued) Upper control chart limit Target Lower control chart limit Two points near upper control. Investigate for cause. Two points near lower control. Investigate for cause. Run of 5 points above central line. Investigate for cause.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Control Chart Patterns (continued) Upper control limit Target Lower control limit Run of 5 points below central line. Investigate for cause. Trends in either Direction. Investigate for cause of progressive change. Erratic behavior. Investigate.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Control Chart Types Control Charts R Chart Variables Charts Attributes Charts X Chart P C Continuous Numerical Data Categorical or Discrete Numerical Data

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Control Chart Types (continued) AttributesVariables Defect characteristics. Characteristics that you measure, e.g., weight, length. Classify products as either ‘good’ or ‘bad,’ or count # defects, e.g., radio works or not May be in whole or in fractional numbers. Categorical or discrete random variables. Continuous random variables p chart / c chartX chart / R chart

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Control Charts for Variables - CLT The central limit theorem (CLT) says that the distribution of sample means will follow a normal distribution as the sample size grows large. µ = µ and δ = δ n x - x - x

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Sampling Distribution of Sample Means 99.7% of all x fall within ± 3  x 95.5% of all x fall within ± 2  x

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Control Charts for Variables X charts measure the central tendency of a process and indicate whether changes have occurred. R charts values indicate that a gain or loss in uniformity has occurred. _ X charts and R charts are used together to monitor variables. -

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Steps to Follow in Using X and R Charts 1. Collect samples of n = 4, or n = 5 from a stable process. Compute the mean and range of each sample. 2. Compute the overall means. Set appropriate control limits - usually at 99.7 level. Calculate upper and lower control limits. If process not stable, use desired mean instead of sample mean. 3. Graph the sample means and ranges on their respective control charts. Look to see if any fall outside acceptable limits. __

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Investigate points or patterns that indicate the process is out of control. Try to assign causes for the variation, then resume the process. 5. Collect additional samples. If necessary, re-validate the control limits using the new data. Steps to Follow in Using X and R Charts (continued) __

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Setting Control Limits for the X Chart Sample Range at Time i # of Samples Sample Mean at Time i From Table Control Limits

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Setting Control Limits for the R Chart Sample Range at Time i # Samples From Table

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Table Factors for Control Chart Limits

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Super Cola Example: x and R Chart Super Cola bottles soft drinks labeled “net weight 16 ounces.” Several batches of 5 bottles each revealed the following: Construct a X and R chart for the data _ Each batch has 5 bottles of cola Batch Number Batch Average Batch Range

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Step 1: Collected 20 samples with 5 bottles in each. Compute the mean and range of each batch. The data are given on the previous slide. Super Cola Example: x and R Chart

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Step 2: Compute the overall means and range (x, R), calculate the upper and lower control limits at the 99.7%: Mean = ounces Range = 0.25 ounces For X chart UCL = (0.577)(0.25) = LCL = – (0.577)(0.25) = For R Chart UCL = (2.114)(0.25) =.5285 LCL = (0)(0.25) = 0 Super Cola Example: x and R Chart ____

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Step 3: Graph the sample means and determine if they fall outside the acceptable limits. Super Cola Example: x and R Chart

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Step 4: Investigate points or patterns that indicate the process is out of control. Are there any points we should investigate?? Super Cola Example: x and R Chart

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Step 5: Collect additional data and revalidate the control limits using the new data. This is particularly important for Super Cola because the original control limits were obtained from ‘unstable’ data. Super Cola Example: x and R Chart

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Control Charts for Attributes p charts measure the percent defective in a sample and are used to control attributes that typically follow the binomial distribution. c charts measure the count of the number defective and are used to control the number of defects per unit. The Poisson distribution is its basis. For example:  % of mortalities per month versus # of mortalities per month.  % of typed pages with mistakes vs. # of mistakes per page.  % of hamburgers without pickles per shift vs. # of missing pickles per shift.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Setting Control Limits for p Chart # Defective items in sample i Size of sample i z = 2 for 95.5% limits; z = 3 for 99.7% limits n pp zpUCL n pp zp P P )1( )1(    

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ ARCO p Chart Example Data entry clerks at ARCO key in thousands of insurance records each day. One hundred records were obtained from 20 clerks and checked for accuracy. Sample Number No. of errors % defective p = 0.04

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ ARCO p Chart Example (continued) n pp zpUCL n pp zp P P )1( )1(     = (.04)(.96) 100 = 0.04 – 3 (.04)(.96) 100 So, UCL = 0.10 LCL = 0 … cannot have a negative percent defective

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ ARCO’s p Chart Example (continued) What can you say about the accuracy of ARCO’s clerks???

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Setting Control Limits for c Chart z = 2 for 95.5% limits; z = 3 for 99.7% limits UCL = c + z c LCL = c – z c Where c = average of all of the samples

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Red Top Cab c Chart Example Red Top Cab Company is interested in studying the number of complaints it receives about the poor cab driver behavior. For nine days the manager recorded the total number of calls he received. c = 6 complaints per day DayComplaints UCL = ( 6 ) = LCL = 6 – 3 ( 6 ) = 0 … cannot have negative mistakes.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Red Top Cab Company c Chart Example (continued) After the control chart was posted prominently, the number of complaints dropped to an average of 3 per day. Can you explain why this may have occurred???