1. 9/30/2012 TM 720: Statistical Process Control 1 TM 720 - Lecture 09 Control Charts for Individuals

2. 9/30/2012 TM 720: Statistical Process Control 2 Assignment: Reading: Finish Chapter 6 & 9+ 6.4 (pp. 231 � 238) 9.1 � 9.1.5 (pp. 400 � 410) 9.2 � 9.2.4 (pp. 419 � 425) 9.3 (pp. 425 � 430) End Chapter 8 Sections 8.4 � 8.8 Start Chapter 10 Sections 10 � 10.3.3 Assignments: Obtain the Chart Factors table from Materials Page Access Excel Template for P, NP, C, & U Control Charts: Download Assignment 6 for practice Use the data on the HW6 Excel sheet to do the charting, verify the control limits by hand calculations Access Excel Template for Individuals Control Charts

3. 9/30/2012 TM 720: Statistical Process Control 3 Review Shewhart Control charts Are for sample data from an approximate Normal distribution Three lines appear on all Shewhart Control Charts UCL, CL, LCL Two charts are used: X-bar for testing for change in location R or s-chart for testing for change in spread We check the charts using 4 Western Electric rules Attributes Control charts Are for Discrete distribution data Use p- and np-charts for tracking defective units Use c- and u-charts for tracking defects on units Use p- and u-charts for variable sample sizes Use np- and c-charts with constant sample sizes

4. 9/30/2012 TM 720: Statistical Process Control 4 Individual Measurements Sometimes repeated measures in a subsample don't make sense: inventory level accounts payable � price of an item Other reasons for using individual measurements Variation in sample only reflects measurement error, e.g., batch production of chemicals Automated inspection � every unit is analyzed Production rate very slow � inconvenient to wait for large enough sample

5. 9/30/2012 TM 720: Statistical Process Control 5 Control Charts for Individual Measurements Notes about Individuals Charts: Sample points must be relatively frequent There is more sampling error (false alarm & insensitivity) Sample points tend to be non-normal points are not averages and central limit theorem does not apply Control Chart Types for Individuals: Shewhart x-chart and Moving Range chart (2 charts!) MA � Moving Average chart EWMA � Exponentially Weighted Moving Average chart CUSUM � Cumulative Sum chart

6. 9/30/2012 TM 720: Statistical Process Control 6 Moving Range Control Chart MR2i = |xi � xi-1| - or - MR3i = |xi � xi-2|* Computation of the Moving Range: