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

Spring 2014ISE 428 ETM 591 JMB CH 37 2 Chapter 37 Topics  Introduction to SPC  Objectives  Theory of Process Variation  Rational Subgroups  Types of Control Charts  Construction of Control Charts  Control Charts for Attributes  Control Charts for Variables  Interpretation of Control Charts  Manual Application of Tests  Statistical Software Application of Tests  Other Process Charts 2

Spring 2014ISE 428 ETM 591 JMB CH 37 3 Characterizing Causes of Variation 3 randomnon-random The intent of process monitoring is to distinguish between random and non-random variation. Random CauseNon-random Cause CommonSpecial ChanceAssignable ChronicSporadic System faultLocal fault

Spring 2014ISE 428 ETM 591 JMB CH 37 4 Theory of Process Variation: Statistical Control 4 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 random variation. All processes are subject to random variation. non-random 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.

Spring 2014ISE 428 ETM 591 JMB CH Control Limits, Random and Nonrandom Sample Observations Upper Control Limit (UCL) Lower Control Limit (LCL) Process Mean Sample number Non-random 99.7% +3 σ -3 σ Source: Ozcan Figure 12.4 (Modified for Three Sigma Limits) Non-random

Spring 2014ISE 428 ETM 591 JMB CH 37 6 Statistical Control Chart Types Attributes Mean Charts (X-bar Charts) c-chartp-chart Variables(Subgroups) Variation Charts σ Method Range Method u-chart

Spring 2014ISE 428 ETM 591 JMB CH 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

Spring 2014ISE 428 ETM 591 JMB CH 37 8 Variables Control Chart for n = 1 Variables (Individuals) Mean Charts (X-bar Charts) Individual observation Variables(Subgroups) Variation Charts σ Method Range Method Moving Range Note that the tests that apply to the subgroup charts do not apply to the Individuals Charts.

Spring 2014ISE 428 ETM 591 JMB CH 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.

Spring 2014ISE 428 ETM 591 JMB CH 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.

Spring 2014ISE 428 ETM 591 JMB CH Other Charts Cumulative Sum Charts EWMA Charts Moving Average Charts *******Pre-control Charts *******

Spring 2014ISE 428 ETM 591 JMB CH Dr. Joan Burtner Quality Engineering Contact Information