Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Business Statistics, 4e by Ken Black Chapter 18 Statistical Quality Control

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Understand the concepts of quality, quality control, and total quality management. Understand the importance of statistical quality control in total quality management. Learn about process analysis and some process analysis tools, including Pareto charts, fishbone diagrams, and control chars. Learn how to construct charts, R charts, P charts, and c charts. Understand the theory and application of acceptance sampling. Learning Objectives X

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Quality Quality is when a product delivers what is stipulated for in its specifications Crosby: “quality is conformance to requirements” Feigenbaum: “quality is a customer determination”

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Garvin’s Five Dimensions of Quality Transcendent quality: “innate excellence” Product quality: quality is measurable User quality: quality is determined by the consumer Manufacturing quality: quality is measured by the manufacturer's ability to target the product specifications with little variability Value Quality: did the consumer get his or her money’s worth?

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Quality Control Quality control is the collection of strategies, techniques, and actions taken by an organization to assure themselves that they are producing a quality product. After-process quality control involves inspecting the attributes of a finished product to determine whether the product is acceptable, is in need of rework, or is to be rejected and scrapped. –reporting of the number of defects per time period –screening defective products from consumers In-process quality control techniques measure product attributes at various intervals throughout the manufacturing process in an effort to pinpoint problem areas.

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Deming’s Fourteen Points 1.Create constancy of purpose fro improvement of product and service. 2.Adopt a new philosophy. 3.Cease dependence on mass inspection. 4.End the practice of awarding business on price tag alone. 5.Improve constantly and forever the system of production and service. 6.Institute training. 7.Institute leadership. 8Drive out fear. 9.Break down barriers between staff areas. 10.Eliminate slogans. 11.Eliminate numerical quotas. 12.Remove barriers to pride of workmanship. 13.Institute a vigorous program of education and retraining. 14.Take action to accomplish the transformation.

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Important Quality Concepts Benchmarking –examine and emulate the best practices and techniques used in the industry –a positive, proactive process to make changes that will effect superior performance Just-In-Time Inventory Systems –necessary parts for production arrive “just in time” –reduced holding costs, personnel, and space needed for inventory Reengineering –complete redesign of the core business process in a company Six sigma –Total quality approach that measures the capacity of a process to perform defect -free work Team Building: –employee groups take on managerial responsibilities –quality circle

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Process Analysis A process is a series of actions, changes or functions that bring about a result. Flowcharts - schematic representation of all the activities and interactions that occur in a process Pareto Analysis -quantitative tallying of the number and types of defects that occur with a product Pareto Chart - ranked vertical bar chart with most frequently occurring on the left Fishbone Diagram - display of potential cause-and- effect relationships Control Charts - graphical method for evaluating whether a process is or is not in a “state of statistical control”

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Flowchart Symbols Input/Output Symbol Processing Symbol Decision Symbol Start/Stop Symbol Flow line Symbol

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Pareto Chart Poor Wiring Short in Coil Defective Plug Other Frequency 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Cause-and-Effect Diagram Raw MaterialsEquipment WorkersMethodology Poor Wiring Wiring Scheme Pland Layout Maintenance Tools Out-of-Adjustment Out-of-Date Vendor Transportation Inventory Training Attitude Absenteeism

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Control Chart Sample Number Sample Mean UCL LCL Centerline X

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Types of Control Charts Control charts for measurements – charts –R charts Control charts for compliance items –P charts –c charts X

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Control Chart Monitor process location (center) 1.Decide on the quality to be measured. 2.Determine a sample size. 3.Gather 20 to 30 samples. 4.Compute the sample average for each sample. 5.Compute the sample range for each sample. 6.Determine the average sample mean for all samples. 7.Determine the average sample range (or sample standard deviation) for all samples. 8Using the size of the samples, determine the value of A 2 or A 3. 9.Compute the UCL and the LCLX

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Control Chart: FormulasX

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Data for Demonstration Problem 18.1: Samples X R

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Data for Demonstration Problem 18.1: Samples X R

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.1: Control Chart Computations

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Sigma level: Bearing Diameter UCL = Average = LCL = Control Chart: Bearing Diameter Mean Demonstration Problem 18.1: Control ChartX

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons R Chart Monitor process variation 1.Decide on the quality to be measured. 2.Determine a sample size. 3.Gather 20 to 30 samples. 4.Compute the sample range for each sample. 5.Determine the average sample mean for all samples. 6.Using the size of the samples, determine the values of D 3 and D 4. 7.Compute the UCL and the LCL Monitor process variation 1.Decide on the quality to be measured. 2.Determine a sample size. 3.Gather 20 to 30 samples. 4.Compute the sample range for each sample. 5.Determine the average sample mean for all samples. 6.Using the size of the samples, determine the values of D 3 and D 4. 7.Compute the UCL and the LCL

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons R Chart Formulas

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.2: R Control Chart

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons P Charts Monitor proportion in noncompliance 1.Decide on the quality to be measured. 2.Determine a sample size. 3.Gather 20 to 30 samples. 4.Compute the sample proportion for each sample. 5.Determine the average sample proportion for all samples. 6.Compute the UCL and the LCL

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons P Chart Formulas

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.3: Twenty Samples of Bond Paper Samplen Number Out of ComplianceSamplen Number Out of Compliance

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.3: Preliminary Calculations Samplenn non Samplenn non  p  p

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 17.3: Centerline, UCL, and LCL Computations

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 17.3: P Control Chart Sample Number P =.053 UCL =.148 LCL = 0  p

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons c Charts Monitor number of nonconformances per item 1.Decide on nonconformances to be evaluated. 2.Determine the number of items to be studied (at least 25). 3.Gather items. 4.Determine the value of c for each item by summing the number of nonconformances in the item. 5.Determine the average number of nonconformances per item. 6.Determine the UCL and the LCL

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons c Chart Formulas

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.4: Number of Nonconformities in Oil Gauges Item Number Number of Nonconformities Item Number Number of Nonconformities

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.4: c Chart Calculations

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.4: c Chart Item Number c UCL = 6.2 LCL = 0 c = 2.0

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Interpreting Control Charts Points are above UCL and/or below LCL Eight or more consecutive points fall above or below the centerline. Ten out of 11 points fall above or below the centerline. Twelve out of 14 points fall above or below the centerline. A trend of 6 or more consecutive points (increasing or decreasing) is present Two out of 3 consecutive values are in the outer one-third. Four out 5 consecutive values are in the outer two-thirds. The centerline shifts from chart to chart.

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Interpreting Control Charts: Points above UCL and/or below LCL UCL LCL Centerline

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons I nterpreting Control Charts: 8 Consecutive Points on One Side of the Centerline UCL LCL Centerline

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Interpreting Control Charts: 7 Consecutive Increasing Points UCL LCL Centerline

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Interpreting Control Charts: 2 out of 3 Consecutive Points in Outer 1/3 UCL LCL Centerline

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Interpreting Control Charts: 4 out of 5 Consecutive Points in Outer 2/3 UCL LCL Centerline

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Acceptance Sampling Acceptance sampling is the inspection of a sample from a lot of goods to determine if the lot will be accepted or rejected. –N = the lot size –n = the sample size Single Sample Plan Double-Sample Plan Multiple-Sample Plan

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Rules for Sampling Plans Single Sample Plan Double Sample Plan

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Producer’s and Consumer’s Risk State of Nature Null TrueNull False Actions Fail to Reject Null Type II errorCorrect Decision-- Consumer’s Risk Reject NullType I error -- Producer’s Risk Correct Decision H 0 : the lot is of acceptable quality

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Bicycle Manufacturer Example N = 3,000 (Braces arrive at the manufacturer’s plant in lots of 3,000.) n = 15 (The bicycle manufacturer randomly selects a sample of 15 braces to inspect.) X is the number of nonconforming braces in the sample of 15. A 2% nonconformance rate is acceptable to the consumer (the bicycle manufacturer). If the lot contains 60 nonconforming braces, what is the probability that the consumer will reject the lot (producer’s risk)? If the lot contains 360 nonconforming braces, what is the probability that the consumer will not reject the lot (consumer’s risk)?

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. Bicycle Manufacturer Example: Sampling Plan

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. Bicycle Manufacturer Example: Analysis for 2% Nonconforming Braces   p PxPx                  Probability of accepting Probability of rejecting 9647 Producer’s Risk

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. Bicycle Manufacturer Example: Analysis for 12% Nonconforming Braces   p PxPx                  Probability of accepting Probability of rejecting Consumer’s Risk

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Bicycle Manufacturer Example: OC Curve for n = 15 and c = %10%20%30%40% Percent nonconforming Probability of acceptance 2%.9647 }.0353 Producer’s Risk.4476 Consumer’s Risk 12%.4476

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Bicycle Manufacturer Example: OC Curve for n = 15 and c = %10%20%30%40% Percent nonconforming Probability of acceptance 2%.74 12%.21

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.5

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.5

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons Demonstration Problem 18.5 n =20 c =2 pP(Accept) =BINOMDIST(B$2,B$1,A5,TRUE) 0.01=BINOMDIST(B$2,B$1,A6,TRUE) 0.02=BINOMDIST(B$2,B$1,A7,TRUE) 0.03=BINOMDIST(B$2,B$1,A8,TRUE) 0.04=BINOMDIST(B$2,B$1,A9,TRUE) 0.05=BINOMDIST(B$2,B$1,A10,TRUE) 0.06=BINOMDIST(B$2,B$1,A11,TRUE) 0.07=BINOMDIST(B$2,B$1,A12,TRUE) 0.08=BINOMDIST(B$2,B$1,A13,TRUE) 0.09=BINOMDIST(B$2,B$1,A14,TRUE) 0.1=BINOMDIST(B$2,B$1,A15,TRUE) 0.11=BINOMDIST(B$2,B$1,A16,TRUE) 0.12=BINOMDIST(B$2,B$1,A17,TRUE) 0.13=BINOMDIST(B$2,B$1,A18,TRUE) 0.14=BINOMDIST(B$2,B$1,A19,TRUE) 0.15=BINOMDIST(B$2,B$1,A20,TRUE) 0.16=BINOMDIST(B$2,B$1,A21,TRUE) 0.17=BINOMDIST(B$2,B$1,A22,TRUE) 0.18=BINOMDIST(B$2,B$1,A23,TRUE) 0.19=BINOMDIST(B$2,B$1,A24,TRUE) 0.2=BINOMDIST(B$2,B$1,A25,TRUE)