Chapter 3 Statistical Process Control Operations Management - 6th Edition Roberta Russell & Bernard W. Taylor, III Copyright 2009 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Lecture Outline Basics of Statistical Process Control Control Charts Control Charts for Attributes Control Charts for Variables Control Chart Patterns Process Capability Copyright 2009 John Wiley & Sons, Inc. 3-2 Product launch activities: Revise periodically Customer Requirements Product Specifications Process Specifications Statistical Process Control: Measure & monitor quality Ongoing Activities Meets Specifications? Yes Conformance Quality No Fix process or inputs Basics of Statistical Process Control Statistical Process Control (SPC) monitoring production process to detect, correct, and prevent poor quality UCL Sample subset of items produced to use for inspection LCL Control Chart Is the process within statistical control limits? Copyright 2009 John Wiley & Sons, Inc. 3-4 Variation in a Transformation Process Inputs • Facilities • Equipment • Materials • Energy • Employees Transformation Process Outputs Goods & Services •Variation in inputs create variation in outputs •Variations in the transformation process create variation in outputs Basics of Statistical Process Control Types of Variation (1) 1. Random variation Also called common cause variation This type of variation is inherent in a process. Caused by usual variations in equipment, tooling, employee actions, facility environment, materials, measurement system, etc. If random variation is excessive, the goods or services will not meet quality standards. To reduce random variation, we must reduce variation in the inputs and the process Copyright 2009 John Wiley & Sons, Inc. 3-6 Basics of Statistical Process Control Types of Variation (2) 2. Non-random variation Also called special cause variation or assignable cause variation Caused by equipment out of adjustment, worn tooling, operator errors, poor training, defective materials, measurement errors, etc. The process is not behaving as it usually does. The cause can and should be identified and corrected. Copyright 2009 John Wiley & Sons, Inc. 3-7 Statistical Process Control (SPC) When is a process in control? A process is in control if it has no special cause variation. The process is consistent or predictable. SPC distinguishes between common cause and special cause variation Measure characteristics of goods or services that are important to customers Make a control chart for each characteristic The chart is used to determine whether the process is in control Specification Limits The target is the ideal value Example: if the amount of beverage in a bottle should be 16 ounces, the target is 16 ounces Specification limits are the acceptable range of values for a variable Example: the amount of beverage in a bottle must be at least 15.98 ounces and no more than 16.02 ounces. Range is 15.98 – 16.02 ounces. Lower specification limit = 15.98 ounces or LSPEC = 15.98 ounces Upper specification limit = 16.02 ounces or USPEC = 16.02 ounces Specifications and Conformance Quality A product which meets its specification has conformance quality. Capable process: a process which consistently produces products that have conformance quality. Must be in control and meet specifications Quality Measures Attributes and Variables Discrete measures Discrete means separate or distinct Good/bad, yes/no (p charts) - Does the product meet standards? Count of defects (c charts) – the count is a whole number Variables – continuous numerical measures Length, diameter, weight, height, time, speed, temperature, pressure - does not have to be a whole number Controlled with x-bar and R charts SPC Applied to Services (1) A service defect is a failure to meet customer requirements. Different customers have different requirements. Examples of attribute measures used in services Customer satisfaction surveys – provides customer perceptions Reports from mystery shoppers, based on standards Employee or supervisor inspects cleanliness, etc., according to standards Copyright 2009 John Wiley & Sons, Inc. 3-12 SPC Applied to Services (2) Examples of variable measures used in services Waiting time and service time On-time service delivery Accuracy Number of stockouts (retail and distribution) Percentage of lost luggage (airlines) Web site availability (online retailing or technical support) Copyright 2009 John Wiley & Sons, Inc. 3-13 SPC Applied to Services (3) Hospitals timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts Grocery stores waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors Airlines flight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance Copyright 2009 John Wiley & Sons, Inc. 3-14 SPC Applied to Services (4) Fast-food restaurants waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy Catalogue-order companies order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time Insurance companies billing accuracy, timeliness of claims processing, agent availability and response time Copyright 2009 John Wiley & Sons, Inc. 3-15 Process Control Chart Out of control Upper control limit Process average Lower control limit 1 2 3 4 5 6 7 8 9 10 Sample number Copyright 2009 John Wiley & Sons, Inc. 3-16 Control Charts for Variables Range chart ( R-Chart ) uses amount of dispersion in a sample Mean chart ( x -Chart ) uses process average of a sample Copyright 2009 John Wiley & Sons, Inc. 3-17 Control Charts for Variables Mean chart: sample means are plotted. Range chart: sample ranges are plotted. Two cases: The standard deviation is known The standard deviation is unknown. Copyright 2009 John Wiley & Sons, Inc. 3-18 SPC for Variables The Normal Distribution = the population mean = the standard deviation for the population 99.74% of the area under the normal curve is between - 3 and + 3 SPC for Variables The Central Limit Theorem Samples are taken from a distribution with mean and standard deviation . k = the number of samples n = the number of units in each sample The sample means are normally distributed with mean and standard deviation x n when k is large. x-bar Chart: Standard Deviation Known UCL = x= + zx LCL = =x - zx x1 + x2 + ... xn n x= = where = x = average of sample means Copyright 2009 John Wiley & Sons, Inc. 3-21 x-bar Chart Example: Standard Deviation Known (cont.) Given: The standard deviation is 0.08 Copyright 2009 John Wiley & Sons, Inc. 3-22 x-bar Chart Example: Standard Deviation Known (cont.) Copyright 2009 John Wiley & Sons, Inc. 3-23 x-bar Chart Example: Standard Deviation Unknown UCL = x= + A2R LCL = x= - A2R A2 is a factor that depends on n, the number of units in each sample Copyright 2009 John Wiley & Sons, Inc. 3-24 Control Limits In this problem, n=5 Copyright 2009 John Wiley & Sons, Inc. 3-25 x-bar Chart Example: Standard Deviation Unknown OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 1 2 3 4 5 x R 1 2 3 4 5 6 7 8 9 10 5.02 5.01 4.99 5.03 4.95 4.97 5.05 5.09 5.14 5.01 5.01 5.03 5.00 4.91 4.92 5.06 5.01 5.10 5.10 4.98 4.94 5.07 4.93 5.01 5.03 5.06 5.10 5.00 4.99 5.08 4.99 4.95 4.92 4.98 5.05 4.96 4.96 4.99 5.08 5.07 4.96 4.96 4.99 4.89 5.01 5.03 4.99 5.08 5.09 4.99 4.98 5.00 4.97 4.96 4.99 5.01 5.02 5.05 5.08 5.03 0.08 0.12 0.08 0.14 0.13 0.10 0.14 0.11 0.15 0.10 50.09 1.15 Example 15.4 Copyright 2009 John Wiley & Sons, Inc. 3-26 x-bar Chart Example: Standard Deviation Unknown (cont.) R= ∑R k = 1.15 10 = 0.115 50.09 = x x= = = 5.01 cm k 10 UCL = x= + A2R = 5.01 + (0.58)(0.115) = 5.08 LCL = x= - A2R = 5.01 - (0.58)(0.115) = 4.94 Retrieve Factor Value A2 Copyright 2009 John Wiley & Sons, Inc. 3-27 5.10 – 5.08 – UCL = 5.08 5.06 – Mean 5.04 – x- bar Chart Example (cont.) 5.02 – x= = 5.01 5.00 – 4.98 – 4.96 – LCL = 4.94 4.94 – 4.92 – | 1 | 2 Copyright 2009 John Wiley & Sons, Inc. | 3 | | | | 4 5 6 7 Sample number | 8 | 9 | 10 3-28 A Process Is in Control If … 1. There are no sample points outside limits & 2. Most points are near the process average & 3. The number of points above and below the center line is about equal & 4. The points appear to be randomly distributed This is only a rough guide. Quality analysts use more precise rules. Copyright 2009 John Wiley & Sons, Inc. 3-29 R- Chart UCL = D4R LCL = D3R R R= k where R = range of each sample k = number of samples Copyright 2009 John Wiley & Sons, Inc. 3-30 R-Chart Example OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 1 2 3 4 5 x R 1 2 3 4 5 6 7 8 9 10 5.02 5.01 4.99 5.03 4.95 4.97 5.05 5.09 5.14 5.01 5.01 5.03 5.00 4.91 4.92 5.06 5.01 5.10 5.10 4.98 4.94 5.07 4.93 5.01 5.03 5.06 5.10 5.00 4.99 5.08 4.99 4.95 4.92 4.98 5.05 4.96 4.96 4.99 5.08 5.07 4.96 4.96 4.99 4.89 5.01 5.03 4.99 5.08 5.09 4.99 4.98 5.00 4.97 4.96 4.99 5.01 5.02 5.05 5.08 5.03 0.08 0.12 0.08 0.14 0.13 0.10 0.14 0.11 0.15 0.10 50.09 1.15 Example 15.3 Copyright 2009 John Wiley & Sons, Inc. 3-31 R-Chart Example (cont.) UCL = D4R = 2.11(0.115) = 0.243 LCL = D3R = 0(0.115) = 0 Retrieve Factor Values D3 and D4 Example 15.3 Copyright 2009 John Wiley & Sons, Inc. 3-32 R-Chart Example (cont.) 0.28 – 0.24 – Range 0.20 – 0.16 – UCL = 0.243 R = 0.115 0.12 – 0.08 – 0.04 – 0– LCL = 0 | | | 1 2 3 Copyright 2009 John Wiley & Sons, Inc. | | | | 4 5 6 7 Sample number | 8 | 9 | 10 3-33 Using x- bar and R-Charts Together Process average and process variability must be in control It is possible for samples to have very narrow ranges, but their averages might be beyond control limits It is possible for sample averages to be in control, but ranges might be very large It is possible for an R-chart to exhibit a distinct downward trend, suggesting some nonrandom cause is reducing variation Copyright 2009 John Wiley & Sons, Inc. 3-34 Non-random Patterns in Control Charts Change in Mean UCL UCL LCL Sample observations consistently below the center line LCL Sample observations consistently above the center line Copyright 2009 John Wiley & Sons, Inc. 3-35 Non-random Patterns in Control Charts Trend UCL UCL LCL Sample observations consistently increasing LCL Sample observations consistently decreasing Copyright 2009 John Wiley & Sons, Inc. 3-36 Process Capability Tolerances design specifications reflecting product requirements Process capability range of natural variability in a process— what we measure with control charts A capable process consistently produces products that conform to specifications Copyright 2009 John Wiley & Sons, Inc. 3-37 Copyright 2009 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein. Copyright 2009 John Wiley & Sons, Inc. 3-38

© Copyright 2020