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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Chapter 15 Statistical Quality Control To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved.

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Statistical Process Control Take periodic samples from processTake periodic samples from process Plot sample points on control chartPlot sample points on control chart Determine if process is within limitsDetermine if process is within limits Prevent quality problemsPrevent quality problems UCL LCL

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Variation Common Causes Common Causes Variation inherent in a process Variation inherent in a process Can be eliminated only through improvements in the system Can be eliminated only through improvements in the system Special Causes Special Causes Variation due to identifiable factors Variation due to identifiable factors Can be modified through operator or management action Can be modified through operator or management action

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Types of Data Attribute data Attribute data Product characteristic evaluated with a discrete choice Product characteristic evaluated with a discrete choice Good/bad, yes/no Good/bad, yes/no Variable data Variable data Product characteristic that can be measured Product characteristic that can be measured Length, size, weight, height, time, velocity Length, size, weight, height, time, velocity

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. SPC Applied to Services Nature of defect is different in services Nature of defect is different in services Service defect is a failure to meet customer requirements Service defect is a failure to meet customer requirements Monitor times, customer satisfaction Monitor times, customer satisfaction

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Service Quality Examples Hospitals Hospitals Timeliness, responsiveness, accuracy of lab tests Timeliness, responsiveness, accuracy of lab tests Grocery Stores Grocery Stores Check-out time, stocking, cleanliness Check-out time, stocking, cleanliness Airlines Airlines Luggage handling, waiting times, courtesy Luggage handling, waiting times, courtesy Fast food restaurants Fast food restaurants Waiting times, food quality, cleanliness, employee courtesy Waiting times, food quality, cleanliness, employee courtesy

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Service Quality Examples Catalog-order companies Catalog-order companies Order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time Order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time Insurance companies Insurance companies Billing accuracy, timeliness of claims processing, agent availability and response time Billing accuracy, timeliness of claims processing, agent availability and response time

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Control Charts Graph establishing process control limits Graph establishing process control limits Charts for variables Charts for variables Mean (x-bar), Range (R) Mean (x-bar), Range (R) Charts for attributes Charts for attributes p and c p and c

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Process Control Chart Sample number Uppercontrollimit Processaverage Lowercontrollimit Out of control Figure 15.1

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. 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 & below centerline 4.Points appear randomly distributed

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Development of Control Chart Based on in-control data Based on in-control data If non-random causes present discard data If non-random causes present discard data Correct control chart limits Correct control chart limits

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Control Charts for Attributes p Charts p Charts Calculate percent defectives in sample Calculate percent defectives in sample c Charts c Charts Count number of defects in item Count number of defects in item

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. p-Chart UCL = p + z p LCL = p - z p where z=the number of standard deviations from the process average p=the sample proportion defective; an estimate of the process average p =the standard deviation of the sample proportion p =p =p =p = p(1 - p) n

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. The Normal Distribution =0 1111 2222 3333 -1 -2 -3 95% 99.74%

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Control Chart Z Values Smaller Z values make more sensitive charts Smaller Z values make more sensitive charts Z = 3.00 is standard Z = 3.00 is standard Compromise between sensitivity and errors Compromise between sensitivity and errors

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. p-Chart Example 20 samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE ::: Example 15.1

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. p-Chart Example 20 samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE ::: Example 15.1 p= = 200 / 20(100) = 0.10 total defectives total sample observations

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. p-Chart Example 20 samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE ::: Example 15.1 p = 0.10 UCL = p + z = p(1 - p) n 0.10( ) 100 UCL = LCL = LCL = p - z = p(1 - p) n 0.10( ) 100

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved Proportion defective Sample number UCL = LCL = p = 0.10 p-Chart

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. c-Chart UCL = c + z c LCL = c - z c c = c where c = number of defects per sample

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. c-Chart The number of defects in 15 sample rooms :: SAMPLENUMBER OF DEFECTS c = = UCL= c + z c = = LCL= c + z c = = 1.99 Example 15.2

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. c-Chart Number of defects Sample number UCL = LCL = 1.99 c = 12.67

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Control Charts for Variables Mean chart ( x -Chart ) Mean chart ( x -Chart ) Uses average of a sample Uses average of a sample Range chart ( R-Chart ) Range chart ( R-Chart ) Uses amount of dispersion in a sample Uses amount of dispersion in a sample

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Range ( R- ) Chart UCL = D 4 RLCL = D 3 R R =R =R =R = RRkkRRkkk where R= range of each sample k= number of samples

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Range ( R- ) Chart nA2D3D4nA2D3D4 SAMPLE SIZEFACTOR FOR x-CHARTFACTORS FOR R-CHART Table 15.1

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. R-Chart Example OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR Example 15.3

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. R-Chart Example OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR Example 15.3 RkRk R = = = UCL = D 4 R = 2.11(0.115) = LCL = D 3 R = 0(0.115) = 0 UCL = LCL = 0 Range Sample number R = |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | – 0.24 – 0.20 – 0.16 – 0.12 – 0.08 – 0.04 – 0 –

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. x-Chart Calculations x =x =x =x = x 1 + x x k k= UCL = x + A 2 RLCL = x - A 2 R == where x= the average of the sample means =

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. x-Chart Example Example 15.4 OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR UCL = x + A 2 R = (0.58)(0.115) = 5.08 LCL = x - A 2 R = (0.58)(0.115) = 4.94 = = x = = = 5.01 cm = xkxk

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. x-Chart Example Example 15.4 OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR UCL = x + A 2 R = (0.58)(0.115) = 5.08 LCL = x - A 2 R = (0.58)(0.115) = 4.94 = = x = = = 5.01 cm = xkxk UCL = 5.08 LCL = 4.94 Mean Sample number |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | – 5.08 – 5.06 – 5.04 – 5.02 – 5.00 – 4.98 – 4.96 – 4.94 – 4.92 – x = 5.01 =

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Using x- and R-Charts Together Each measures the process differently Each measures the process differently Both process average and variability must be in control Both process average and variability must be in control

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Control Chart Patterns Figure 15.3 UCL LCL Sample observations consistently above the center line LCL UCL Sample observations consistently below the center line

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Control Chart Patterns Figure 15.3 LCL UCL Sample observations consistently increasing UCL LCL Sample observations consistently decreasing

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Zones for Pattern Tests UCL LCL Zone A Zone B Zone C Zone B Zone A Process average 3 sigma = x + A 2 R = 3 sigma = x - A 2 R = 2 sigma = x + (A 2 R) = sigma = x - (A 2 R) = sigma = x + (A 2 R) = sigma = x - (A 2 R) = 1313 x = Sample number |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | 10 | 11 | 12 | 13 Figure 15.4

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Control Chart Patterns 1.8 consecutive points on one side of the center line. 2.8 consecutive points up or down across Zones points alternating up or down. 4.2 out of 3 consecutive points in Zone A but still inside the control limits. 5.4 out of 5 consecutive points in Zone A or B.

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Performing a Pattern Test 14.98B—B 25.00BUC 34.95BDA 44.96BDA 54.99BUC 65.01—UC 75.02AUC 85.05AUB 95.08AUA ADB SAMPLExABOVE/BELOWUP/DOWNZONE Example 15.5

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Sample Size Determination Attribute control charts Attribute control charts 50 to 100 parts in a sample 50 to 100 parts in a sample Variable control charts Variable control charts 2 to 10 parts in a sample 2 to 10 parts in a sample

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Process Capability Range of natural variability in process Range of natural variability in process Measured with control charts. Measured with control charts. Process cannot meet specifications if natural variability exceeds tolerances Process cannot meet specifications if natural variability exceeds tolerances 3-sigma quality 3-sigma quality Specifications equal the process control limits. Specifications equal the process control limits. 6-sigma quality 6-sigma quality Specifications twice as large as control limits Specifications twice as large as control limits

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Process Capability (b) Design specifications and natural variation the same; process is capable of meeting specifications most the time. Design Specifications Process (a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time. Design Specifications Process Figure 15.5

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Process Capability Figure 15.5 (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

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Process Capability Measures Process Capability Ratio Cp=Cp===Cp=Cp==== tolerance range process range upper specification limit - lower specification limit 6

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Computing C p Net weight specification = 9.0 oz 0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz C p = = = 1.39 upper specification limit - lower specification limit 6 (0.12) Example 15.6

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Process Capability Measures Process Capability Index C pk = minimum x - lower specification limit 3 = upper specification limit - x 3 =,

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To Accompany Russell and Taylor, Operations Management, 4th Edition, 2003 Prentice-Hall, Inc. All rights reserved. Computing C pk Net weight specification = 9.0 oz 0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz C pk = minimum = minimum, = 0.83 x - lower specification limit 3 = upper specification limit - x 3 =, (0.12) (0.12) Example 15.7

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