# CQE 3rd edition Chapter 37 - Mercer University

The Certified Quality Engineer Handbook Ch. 37: Statistical Process Control (SPC) Dr. Joan Burtner Certified Quality Engineer Associate Professor of Industrial Engineering and Industrial Management Chapter 37 Topics Introduction to SPC Construction of Control Charts

Control Charts for Attributes Control Charts for Variables Interpretation of Control Charts Objectives Theory of Process Variation Rational Subgroups Types of Control Charts Manual Application of Tests Statistical Software Application of Tests Other Process Charts ISE 428 ETM 528 JMB CH 37 2 Spring 2016 2 Characterizing Causes of Variation

The intent of process monitoring is to distinguish between random and non-random variation. Random Cause Non-random Cause Common Special Chance Assignable Chronic Sporadic System fault Local fault ISE 428 ETM 528 JMB CH 37 3

Spring 2016 3 Theory of Process Variation: Statistical Control The common variations in process variability that are caused by natural incidences are in general not repetitive, but various factors due to chance and are called random variation. All processes are subject to random variation. If the cause of variation is systematic (not natural) the process variation is called non-random variation. When non-random variation is present, the quality engineer should identify and eliminate the source of the variation. When a process is subject to non-random variation the process is described as out-of-control. If only random variation is present, the process is described as in-control. ISE 428 ETM 528 JMB CH 37 Spring 2016 4 4

Control Limits, Random and Nonrandom Sample Observations Upper Control Limit (UCL) Non-random Non-random 99.7% +3 Process Mean Lower Control Limit (LCL) -3 1 2 3

4 5 6 7 8 9 10 11 12 Sample number 5 Source: Ozcan Figure 12.4 (Modified for Three Sigma Limits) ISE 428 ETM 528 JMB CH 37

Spring 2016 5 Statistical Control Chart Types Attribute s c-chart p-chart Variables(Subgroups) u-chart Mean Charts (X-bar Charts) Method ISE 428 ETM 528 JMB CH 37 Variation Charts

6 Range Method Spring 2016 6 Variables Control Charts (Continuous Data) When process characteristics can be measured, variables control charts are the appropriate way to display the process monitoring. The Xbar-chart and the Range chart are displayed and interpreted together. When the Range chart exhibits out-of-control status, the rules for evaluating the Xbar-chart should not be used. The Xbar chart is appropriately evaluated after the Range chart indicates that the process is in-control. Use caution when statistical software evaluates both charts simultaneously. See examples on pages 496-499. ISE 428 ETM 528 JMB CH 37 Spring 2016 7

7 Variables Control Chart for n = 1 Variables (Individuals) Individual observation Moving Range Note that the tests that apply to the subgroup charts do not apply to the Individuals Charts. ISE 428 ETM 528 JMB CH 37 Variables(Subgroups) Mean Charts (X-bar Charts) Method Variation

Charts 8 Range Method Spring 2016 8 Attribute Control Charts (Discrete Data) When process characteristics can be counted, attribute-based control charts are the appropriate way to display the process monitoring. The p-chart is the appropriate control chart for a process with only two outcomes (defective or not defective) when the proportion defective is calculated. The c-chart is the appropriate tool to display monitoring if the number of occurrences per sampling period is recorded. The u-chart is the appropriate control chart if the number of occurrences and the number of items per sampling period is recorded. The average number of occurrences per sample is calculated. ISE 428 ETM 528 JMB CH 37 Spring 2016

9 9 Attribute Control Charts (Discrete Data) See text for examples of p-chart. See text for examples of c-chart. We will discuss the u-chart example in class. 10 ISE 428 ETM 528 JMB CH 37 Spring 2016 10 Other Charts Cumulative Sum Charts EWMA Charts Moving Average Charts *******Pre-control Charts ******* 11 ISE 428 ETM 528 JMB CH 37

Spring 2016 11 Contact Information Dr. Joan Burtner Quality Engineering [email protected] 12 ISE 428 ETM 528 JMB CH 37 Spring 2016 12

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