1. SJSU Bus 140 - David Bentley1 Week 03B – Statistical Process Control (Ch 6S) Control process, statistical process control (SPC): X-bar, R, p, c, process capability

2. SJSU Bus 140 - David Bentley2 SPC – The Control Process Define Measure Compare to a standard Evaluate Take corrective action (if necessary) Evaluate corrective action

3. SJSU Bus 140 - David Bentley3 Variation Random, chance, or common cause (natural) Assignable, non-random, or special cause (due to some specific change) Sampling used to detect non-random Sampling assumes a normal distribution Sample statistics calculated: Mean Range

4. SJSU Bus 140 - David Bentley4 Variables and Attributes Definition: Variable Degree of conformance Continuous (like an analog scale) E.g., fluorescent tube - certain amount of lumens Definition: Attribute (discuss later) Either present or not (is or is not) Limited number of discrete values (like a digital scale) Ex. – fluorescent tube lights or not

5. SJSU Bus 140 - David Bentley5 Control Charts for Variables x-bar (mean) – plot sample means R- (range) – plot sample ranges s- (standard deviation) of each sample Alternative to R chart Charts for individual items (not samples) x-charts Moving range charts THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM (mod. 10/14/02 DAB)

6. SJSU Bus 140 - David Bentley6 Control Charts Control limits When is a process out of control? Charts for variables Mean (X-bar) charts Range (R) charts Charts for attributes Proportion or percentage (p) charts Number [or defects per unit] (c) charts

7. SJSU Bus 140 - David Bentley7 Mean & Range Control Charts Take required number of samples (often 20-25) Create mean (X-bar) charts Calculate mean (X-bar) for each sample Calculate grand mean (X-double-bar) Calculate range (R) for each sample Calculate mean of all sample ranges (R-bar) Calculate UCL and LCL for means Plot grand mean and control limits on X-bar chart

8. SJSU Bus 140 - David Bentley8 Control Limit Factors for n Page 1 of 2 (from Gitlow, et al: Quality Management, McGraw-Hill/Irwin, 2005) Number ofUCL/LCLLCLUCL items infor X-barfor R sample: nA2A2 D3D3 D4D4 21.8800.0003.267 31.0230.0002.574 40.7290.0002.282 50.5770.0002.114 60.4830.0002.004 70.4190.0761.924 80.3730.1361.864 90.3370.1841.816 100.3080.2231.777

9. SJSU Bus 140 - David Bentley9 Control Limit Factors for n Page 2 of 2 (from Gitlow, et al: Quality Management, McGraw-Hill/Irwin, 2005) Number ofUCL/LCLLCLUCL items infor X-barfor R sample: nA2A2 D3D3 D4D4 110.2850.2561.744 120.2660.2831.717 130.2490.3071.693 140.2350.3281.672 150.2230.3471.653 160.2120.3631.637 170.2030.3781.622 180.1940.3911.608 190.1870.4031.597 200.1800.4151.585

10. SJSU Bus 140 - David Bentley10 Mean (X-bar) Chart Control Limits UCL X-bar = X-double-bar + A 2 (R-bar) LCL X-bar = X-double-bar - A 2 (R-bar) Where X-double-bar = the grand mean, And R-bar = the mean of the sample ranges And A 2 = the control limit factor in Table S6.1 (page 241) for the value of n Note: factors based on the size of each sample, not the number of samples!

11. SJSU Bus 140 - David Bentley11 Mean & Range Control Charts Range (R) charts Following already calculated for the mean chart Calculate range (R) for each sample Calculate mean of all sample ranges (R-bar) Calculate UCL and LCL for ranges Plot range mean and control limits on R- chart Plot additional samples and determine if within range limits

12. Range (R) Chart Control Limits UCLR = D4 (R-bar) LCLR = D3 (R-bar) Where R-bar = the mean of the sample ranges, and D4 and D3 = the control limit factors in Table S6.1 (page 241) for the value of n Note: Table factors are based on the size of the sample, not the number of samples! SJSU Bus 140 - David Bentley12

13. SJSU Bus 140 - David Bentley13 Run tests and charts Counting above/below the median Counting “ups” and “downs”

14. SJSU Bus 140 - David Bentley14 Process Capability Ratios Non-centered process (general case): choose c pk = the lower of: Upper spec – process mean c pu = ---------------------------------- or 3  Process mean – lower spec c pl = ---------------------------------- 3 

15. SJSU Bus 140 - David Bentley15 Process Capability Ratios Centered process (special case): specification width c p = ---------------------------- process width Upper spec limit – lower spec limit = ----------------------------------------- 6 

16. SJSU Bus 140 - David Bentley16 Process Capability Requirements Process must be normally distributed Process must be in control Process capability result: > 1.33 = capable and acceptable >1.00 but < 1.33 = capable but not acceptable = 1.00 = barely capable but not acceptable Companies may seek 2.0 (Six Sigma concept) > 5 or 10 is “overkill”, excessive resource use