Copyright 2006 John Wiley & Sons, Inc. 4-1 Basics of Statistical Process Control wStatistical Process Control (SPC) nmonitoring production process to detect and prevent poor quality wSample nsubset of items produced to use for inspection wControl Charts nprocess is within statistical control limits UCL LCL Copyright 2006 John Wiley & Sons, Inc. 4-2 Variability wRandom ncommon causes ninherent in a process ncan be eliminated only through improvements in the system wNon-Random nspecial causes ndue to identifiable factors ncan be modified through operator or management action > Copyright 2006 John Wiley & Sons, Inc. 4-3 Quality Measures wAttribute na product characteristic that can be evaluated with a discrete response ngood – bad; yes - no wVariable na product characteristic that is continuous and can be measured nweight - length > Copyright 2006 John Wiley & Sons, Inc. 4-4 wNature of defect is different in services wService defect is a failure to meet customer requirements wMonitor times, customer satisfaction Applying SPC to Service > Copyright 2006 John Wiley & Sons, Inc. 4-5 Applying SPC to Service wHospitals ntimeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts wGrocery stores nwaiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors wAirlines nflight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance wFast-food restaurants nwaiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy wCatalogue-order companies norder accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time wInsurance companies nbilling accuracy, timeliness of claims processing, agent availability and response time > Copyright 2006 John Wiley & Sons, Inc. 4-6 Where to Use Control Charts wProcess has a tendency to go out of control wProcess is particularly harmful and costly if it goes out of control wExamples nat the beginning of a process because it is a waste of time and money to begin production process with bad supplies nbefore a costly or irreversible point, after which product is difficult to rework or correct nbefore and after assembly or painting operations that might cover defects nbefore the outgoing final product or service is delivered > Copyright 2006 John Wiley & Sons, Inc. 4-7 Control Charts wA graph that establishes control limits of a process wControl limits nupper and lower bands of a control chart wTypes of charts nAttributes lp-chart lc-chart nVariables lrange (R-chart) lmean (x bar – chart) > Copyright 2006 John Wiley & Sons, Inc. 4-8 Process Control Chart 1 2 3 4 5 6 7 8 9 10 Sample number Upper control limit Process average Lower control limit Out of control Copyright 2006 John Wiley & Sons, Inc. 4-9 Normal Distribution =0 1 2 3 -1 -2 -3 95% 99.74% Copyright 2006 John Wiley & Sons, Inc. 4-10 A Process Is in Control If … 1.… no sample points outside limits 2.… most points near process average 3.… about equal number of points above and below centerline 4.… points appear randomly distributed Copyright 2006 John Wiley & Sons, Inc. 4-11 Control Charts for Attributes §p-charts §uses portion defective in a sample §c-charts §uses number of defects in an item Copyright 2006 John Wiley & Sons, Inc. 4-12 p-Chart UCL = p + zsp LCL = p - zsp z = number of standard deviations from process average p = sample proportion defective; an estimate of process average sp = standard deviation of sample proportion sp = p(1 - p) n Copyright 2006 John Wiley & Sons, Inc. 4-13 p-Chart Example 20 samples of 100 pairs of jeans NUMBER OF PROPORTION SAMPLE DEFECTIVES DEFECTIVE 1 6 .06 2 0 .00 3 4 .04 : : : : : : 20 18 .18 200 Copyright 2006 John Wiley & Sons, Inc. 4-14 p-Chart Example (cont.) UCL = p + z = 0.10 + 3 p(1 - p) n 0.10(1 - 0.10) 100 UCL = 0.190 LCL = 0.010 LCL = p - z = 0.10 - 3 p(1 - p) n 0.10(1 - 0.10) 100 = 200 / 20(100) = 0.10 total defectives total sample observations p = Copyright 2006 John Wiley & Sons, Inc. 4-15 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Sample number 2 4 6 8 10 12 14 16 18 20 UCL = 0.190 LCL = 0.010 p = 0.10 p-Chart Example (cont.) Copyright 2006 John Wiley & Sons, Inc. 4-16 c-Chart UCL = c + zsc LCL = c - zsc where c = number of defects per sample sc = c Copyright 2006 John Wiley & Sons, Inc. 4-17 c-Chart (cont.) Number of defects in 15 sample rooms 1 12 2 8 3 16 : : : : 15 15 190 SAMPLE c = = 12.67 190 15 UCL = c + zsc = 12.67 + 3 12.67 = 23.35 LCL = c + zsc = 12.67 - 3 12.67 = 1.99 NUMBER OF DEFECTS Copyright 2006 John Wiley & Sons, Inc. 4-18 3 6 9 12 15 18 21 24 Sample number 2 4 6 8 10 12 14 16 UCL = 23.35 LCL = 1.99 c = 12.67 c-Chart (cont.) Copyright 2006 John Wiley & Sons, Inc. 4-19 Control Charts for Variables §Mean chart ( x -Chart ) §uses average of a sample §Range chart ( R-Chart ) §uses amount of dispersion in a sample Copyright 2006 John Wiley & Sons, Inc. 4-20 x-bar Chart x = x1 + x2 + ... xk k = UCL = x + A2R LCL = x - A2R = = where x = average of sample means = Copyright 2006 John Wiley & Sons, Inc. 4-21 x-bar Chart Example Example 15.4 OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 Copyright 2006 John Wiley & Sons, Inc. 4-22 UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08 LCL = x - A2R = 5.01 - (0.58)(0.115) = 4.94 = = x = = = 5.01 cm = åx k 50.09 10 x- bar Chart Example (cont.) Retrieve Factor Value A2 Copyright 2006 John Wiley & Sons, Inc. 4-23 x- bar Chart Example (cont.) UCL = 5.08 LCL = 4.94 Sample number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 5.10 – 5.08 – 5.06 – 5.04 – 5.02 – 5.00 – 4.98 – 4.96 – 4.94 – 4.92 – x = 5.01 = Copyright 2006 John Wiley & Sons, Inc. 4-24 R- Chart UCL = D4R LCL = D3R R = åR k where R = range of each sample k = number of samples Copyright 2006 John Wiley & Sons, Inc. 4-25 R-Chart Example OBSERVATIONS () SAMPLE k 1 2 3 4 5 x R 1 5.02 5.01 4.94 4.99 4.96 4.98 0.08 2 5.01 5.03 5.07 4.95 4.96 5.00 0.12 3 4.99 5.00 4.93 4.92 4.99 4.97 0.08 4 5.03 4.91 5.01 4.98 4.89 4.96 0.14 5 4.95 4.92 5.03 5.05 5.01 4.99 0.13 6 4.97 5.06 5.06 4.96 5.03 5.01 0.10 7 5.05 5.01 5.10 4.96 4.99 5.02 0.14 8 5.09 5.10 5.00 4.99 5.08 5.05 0.11 9 5.14 5.10 4.99 5.08 5.09 5.08 0.15 10 5.01 4.98 5.08 5.07 4.99 5.03 0.10 50.09 1.15 Example 15.3 Copyright 2006 John Wiley & Sons, Inc. 4-26 R-Chart Example (cont.) Example 15.3 åR k R = = = 0.115 1.15 10 UCL = D4R = 2.11(0.115) = 0.243 LCL = D3R = 0(0.115) = 0 Retrieve Factor Values D3 and D4 Copyright 2006 John Wiley & Sons, Inc. 4-27 R-Chart Example (cont.) UCL = 0.243 LCL = 0 Sample number R = 0.115 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 0.28 – 0.24 – 0.20 – 0.16 – 0.12 – 0.08 – 0.04 – 0 – Copyright 2006 John Wiley & Sons, Inc. 4-28 Using x- bar and R-Charts Together §Process average and process variability must be in control §It is possible for samples to have very narrow ranges, but their averages is beyond control limits §It is possible for sample averages to be in control, but ranges might be very large § 4-29 Slack a kol., 2009 Copyright 2006 John Wiley & Sons, Inc. 4-30 Control Chart Patterns UCL LCL Sample observations consistently above the center line LCL UCL Sample observations consistently below the center line Copyright 2006 John Wiley & Sons, Inc. 4-31 Control Chart Patterns (cont.) LCL UCL Sample observations consistently increasing UCL LCL Sample observations consistently decreasing Copyright 2006 John Wiley & Sons, Inc. 4-32 Process Capability wTolerances ndesign specifications reflecting product requirements wProcess capability nrange of natural variability in a process what we measure with control charts w w > Copyright 2006 John Wiley & Sons, Inc. 4-33 Process Capability (b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time. Design Specifications Process (a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time. Design Specifications Process Copyright 2006 John Wiley & Sons, Inc. 4-34 Process Capability (cont.) (c) Design specifications greater than natural variation; process is capable of always conforming to specifications. Design Specifications Process (d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification. Design Specifications Process