6 SUPPLEMENT Statistical Process Control PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh Edition Principles of Operations Management, Ninth Edition PowerPoint slides by Jeff Heyl © 2014 © 2014 Pearson Pearson Education, Education, Inc.Inc S6 - Outline ► ► ► Statistical Process Control Process Capability Acceptance Sampling © 2014 Pearson Education, Inc S6 - Learning Objectives When you complete this supplement you should be able to : Explain the purpose of a control chart Explain the role of the central limit theorem in SPC Build x-charts and R-charts List the five steps involved in building control charts © 2014 Pearson Education, Inc S6 - Learning Objectives When you complete this supplement you should be able to : Build p-charts and c-charts Explain process capability and compute Cp and Cpk Explain acceptance sampling © 2014 Pearson Education, Inc S6 - Statistical Process Control The objective of a process control system is to provide a statistical signal when assignable causes of variation are present © 2014 Pearson Education, Inc S6 - Statistical Process Control (SPC) ► Variability is inherent in every process ► Natural or common causes ► Special or assignable causes ► Provides a statistical signal when assignable causes are present ► Detect and eliminate assignable causes of variation © 2014 Pearson Education, Inc S6 - Natural Variations ► Also called common causes ► Affect virtually all production processes ► Expected amount of variation ► Output measures follow a probability distribution ► For any distribution there is a measure of central tendency and dispersion ► If the distribution of outputs falls within acceptable limits, the process is said to be “in control” © 2014 Pearson Education, Inc S6 - Assignable Variations ► Also called special causes of variation ► Generally this is some change in the process ► Variations that can be traced to a specific reason ► The objective is to discover when assignable causes are present ► Eliminate the bad causes ► Incorporate the good causes © 2014 Pearson Education, Inc S6 - Samples To measure the process, we take samples and analyze the sample statistics following these steps Each of these represents one sample of five boxes of cereal (a) Samples of the product, say five boxes of cereal taken off the filling machine line, vary from each other in weight Frequency # # # # # # # # # # # # # # # # # Figure S6.1 © 2014 Pearson Education, Inc # # # # # # # # # Weight S6 - Samples To measure the process, we take samples and analyze the sample statistics following these steps Frequency (b) After enough samples are taken from a stable process, they form a pattern called a distribution The solid line represents the distribution Weight Figure S6.1 © 2014 Pearson Education, Inc S6 - 10 Process Capability Index New Cutting Machine New process mean x = 250 inches Process standard deviation  = 0005 inches Upper Specification Limit = 251 inches Lower Specification Limit = 249 inches Cpk = minimum of (.251) - 250 250 - (.249) , (3).0005 (3).0005 Both calculations result in 001 Cpk = = 0.67 0015 © 2014 Pearson Education, Inc New machine is NOT capable S6 - 63 Figure S6.8 Interpreting Cpk Cpk = negative number Cpk = zero Cpk = between and Cpk = Cpk > Lower specification limit © 2014 Pearson Education, Inc Upper specification limit S6 - 64 Acceptance Sampling ► ► Form of quality testing used for incoming materials or finished goods ► Take samples at random from a lot (shipment) of items ► Inspect each of the items in the sample ► Decide whether to reject the whole lot based on the inspection results Only screens lots; does not drive quality improvement efforts © 2014 Pearson Education, Inc S6 - 65 Acceptance Sampling ► Form of quality testing used for incoming materials or finished goods ► ► ► ► Rejected lots can be: Take samples at random from a lot 1.Returned to the supplier (shipment) of items 2.Culled for defectives Inspect each of the items in the sample (100% inspection) Decide whether to reject the whole lot 3.May be re-graded to a based on the inspection results lower specification Only screens lots; does not drive quality improvement efforts © 2014 Pearson Education, Inc S6 - 66 Operating Characteristic Curve ► Shows how well a sampling plan discriminates between good and bad lots (shipments) ► Shows the relationship between the probability of accepting a lot and its quality level © 2014 Pearson Education, Inc S6 - 67 The “Perfect” OC Curve P(Accept Whole Shipment) Keep whole shipment 100 – 75 – Return whole shipment 50 – 25 – Cut-Off – | | | 10 20 | | | | | | 30 40 50 60 70 80 | | 90 100 % Defective in Lot © 2014 Pearson Education, Inc S6 - 68 An OC Curve Figure S6.9  = 0.05 producer’s risk for AQL Probability of Acceptance  = 0.10 Consumer’s risk for LTPD | | | | | | AQL Good lots © 2014 Pearson Education, Inc | | LTPD Indifference zone | Percent defective Bad lots S6 - 69 AQL and LTPD ► Acceptable Quality Level (AQL) ► ► Poorest level of quality we are willing to accept Lot Tolerance Percent Defective (LTPD) ► Quality level we consider bad ► Consumer (buyer) does not want to accept lots with more defects than LTPD © 2014 Pearson Education, Inc S6 - 70 Producer’s and Consumer’s Risks ► ► Producer's risk () ► Probability of rejecting a good lot ► Probability of rejecting a lot when the fraction defective is at or above the AQL Consumer's risk () ► Probability of accepting a bad lot ► Probability of accepting a lot when fraction defective is below the LTPD © 2014 Pearson Education, Inc S6 - 71 OC Curves for Different Sampling Plans n = 50, c = n = 100, c = © 2014 Pearson Education, Inc S6 - 72 Average Outgoing Quality AOQ = (Pd)(Pa)(N – n) N where Pd = true percent defective of the lot Pa = probability of accepting the lot N = number of items in the lot n = number of items in the sample © 2014 Pearson Education, Inc S6 - 73 Average Outgoing Quality If a sampling plan replaces all defectives If we know the incoming percent defective for the lot We can compute the average outgoing quality (AOQ) in percent defective The maximum AOQ is the highest percent defective or the lowest average quality and is called the average outgoing quality limit (AOQL) © 2014 Pearson Education, Inc S6 - 74 Automated Inspection ► ► Modern technologies allow virtually 100% inspection at minimal costs Not suitable for all situations © 2014 Pearson Education, Inc S6 - 75 SPC and Process Variability Lower specification limit Upper specification limit (a) Acceptance sampling (Some bad units accepted; the “lot” is good or bad) (b) Statistical process control (Keep the process “in control”) Process mean,  © 2014 Pearson Education, Inc (c) Cpk > (Design a process that is in within specification) Figure S6.10 S6 - 76 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher Printed in the United States of America © 2014 Pearson Education, Inc S6 - 77 ... samples and analyze the sample statistics following these steps Each of these represents one sample of five boxes of cereal (a) Samples of the product, say five boxes of cereal taken off the... 17 16   16.1 ounces the first sample WEIGHT OF SAMPLE WEIGHT OF SAMPLE WEIGHT OF SAMPLE HOUR (AVG OF BOXES) HOUR (AVG OF BOXES) HOUR (AVG OF BOXES) 16.1 16.5 16.3 16.8 16.4 10 14.8 15.5 15.2... x x   n S6 - 17 Population and Sampling Distributions Population distributions Distribution of sample means = Mean of sample means = x Beta Standard deviation of the sample means Normal x