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2000 by Prentice-Hall, Inc1 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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2000 by Prentice-Hall, Inc2 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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2000 by Prentice-Hall, Inc3 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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2000 by Prentice-Hall, Inc4 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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2000 by Prentice-Hall, Inc5 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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2000 by Prentice-Hall, Inc6 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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2000 by Prentice-Hall, Inc7 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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2000 by Prentice-Hall, Inc8 Process Control Chart 12345678910 Sample number Uppercontrollimit Processaverage Lowercontrollimit Out of control Figure 15.1

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2000 by Prentice-Hall, Inc9 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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2000 by Prentice-Hall, Inc10 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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2000 by Prentice-Hall, Inc11 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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2000 by Prentice-Hall, Inc12 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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2000 by Prentice-Hall, Inc13 The Normal Distribution =0 1111 2222 3333 -1 -2 -3 95% 99.74%

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2000 by Prentice-Hall, Inc14 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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2000 by Prentice-Hall, Inc15 p-Chart Example 20 samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE 16.06 20.00 34.04 ::: 2018.18 200 Example 15.1

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2000 by Prentice-Hall, Inc16 p-Chart Example 20 samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE 16.06 20.00 34.04 ::: 2018.18 200 Example 15.1 p= = 200 / 20(100) = 0.10 total defectives total sample observations

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2000 by Prentice-Hall, Inc17 p-Chart Example 20 samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE 16.06 20.00 34.04 ::: 2018.18 200 Example 15.1 p = 0.10 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

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2000 by Prentice-Hall, Inc18 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.180.20 Proportion defective Sample number 2468101214161820 UCL = 0.190 LCL = 0.010 p = 0.10 p-Chart

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2000 by Prentice-Hall, Inc19 c-Chart UCL = c + z c LCL = c - z c c = c where c = number of defects per sample

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2000 by Prentice-Hall, Inc20 c-Chart The number of defects in 15 sample rooms 112 28 316 :: 1515 190 SAMPLENUMBER OF DEFECTS c = = 12.67 19015 UCL= c + z c = 12.67 + 3 12.67 = 23.35 LCL= c + z c = 12.67 - 3 12.67 = 1.99 Example 15.2

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2000 by Prentice-Hall, Inc21 c-Chart 3 6 9 12 15 18 2124 Number of defects Sample number 246810121416 UCL = 23.35 LCL = 1.99 c = 12.67

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2000 by Prentice-Hall, Inc22 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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2000 by Prentice-Hall, Inc23 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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2000 by Prentice-Hall, Inc24 Range ( R- ) Chart nA2D3D4nA2D3D4 SAMPLE SIZEFACTOR FOR x-CHARTFACTORS FOR R-CHART 21.880.003.27 31.020.002.57 40.730.002.28 50.580.002.11 60.480.002.00 70.420.081.92 80.370.141.86 90.440.181.82 100.110.221.78 110.990.261.74 120.770.281.72 130.550.311.69 140.440.331.67 150.220.351.65 160.110.361.64 170.000.381.62 180.990.391.61 190.990.401.61 200.880.411.59 Table 15.1

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2000 by Prentice-Hall, Inc25 R-Chart Example OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR 15.025.014.944.994.964.980.08 25.015.035.074.954.965.000.12 34.995.004.934.924.994.970.08 45.034.915.014.984.894.960.14 54.954.925.035.055.014.990.13 64.975.065.064.965.035.010.10 75.055.015.104.964.995.020.14 85.095.105.004.995.085.050.11 95.145.104.995.085.095.080.15 105.014.985.085.074.995.030.10 50.091.15 Example 15.3

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2000 by Prentice-Hall, Inc26 R-Chart Example OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR 15.025.014.944.994.964.980.08 25.015.035.074.954.965.000.12 34.995.004.934.924.994.970.08 45.034.915.014.984.894.960.14 54.954.925.035.055.014.990.13 64.975.065.064.965.035.010.10 75.055.015.104.964.995.020.14 85.095.105.004.995.085.050.11 95.145.104.995.085.095.080.15 105.014.985.085.074.995.030.10 50.091.15 Example 15.3 RkRk R = = = 0.115 1.15 10 UCL = D 4 R = 2.11(0.115) = 0.243 LCL = D 3 R = 0(0.115) = 0 UCL = 0.243 LCL = 0 Range Sample number R = 0.115 |1|1 |2|2 |3|3 |4|4 |5|5 |6|6 |7|7 |8|8 |9|9 | 10 0.28 – 0.24 – 0.20 – 0.16 – 0.12 – 0.08 – 0.04 – 0 –

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2000 by Prentice-Hall, Inc27 x-Chart Calculations x =x =x =x = x 1 + x 2 +... x k k= UCL = x + A 2 RLCL = x - A 2 R == where x= the average of the sample means =

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2000 by Prentice-Hall, Inc28 x-Chart Example Example 15.4 OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR 15.025.014.944.994.964.980.08 25.015.035.074.954.965.000.12 34.995.004.934.924.994.970.08 45.034.915.014.984.894.960.14 54.954.925.035.055.014.990.13 64.975.065.064.965.035.010.10 75.055.015.104.964.995.020.14 85.095.105.004.995.085.050.11 95.145.104.995.085.095.080.15 105.014.985.085.074.995.030.10 50.091.15 UCL = x + A 2 R = 5.01 + (0.58)(0.115) = 5.08 LCL = x - A 2 R = 5.01 - (0.58)(0.115) = 4.94 = = x = = = 5.01 cm = xkxk 50.09 10

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2000 by Prentice-Hall, Inc29 x-Chart Example Example 15.4 OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR 15.025.014.944.994.964.980.08 25.015.035.074.954.965.000.12 34.995.004.934.924.994.970.08 45.034.915.014.984.894.960.14 54.954.925.035.055.014.990.13 64.975.065.064.965.035.010.10 75.055.015.104.964.995.020.14 85.095.105.004.995.085.050.11 95.145.104.995.085.095.080.15 105.014.985.085.074.995.030.10 50.091.15 UCL = x + A 2 R = 5.01 + (0.58)(0.115) = 5.08 LCL = x - A 2 R = 5.01 - (0.58)(0.115) = 4.94 = = x = = = 5.01 cm = xkxk 50.09 10 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 | 10 5.10 – 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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2000 by Prentice-Hall, Inc30 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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2000 by Prentice-Hall, Inc31 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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2000 by Prentice-Hall, Inc32 Control Chart Patterns Figure 15.3 LCL UCL Sample observations consistently increasing UCL LCL Sample observations consistently decreasing

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2000 by Prentice-Hall, Inc33 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) = 2323 2 sigma = x - (A 2 R) = 2323 1 sigma = x + (A 2 R) = 1313 1 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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2000 by Prentice-Hall, Inc34 Control Chart Patterns 1.8 consecutive points on one side of the center line. 2.8 consecutive points up or down across Zones. 3.14 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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2000 by Prentice-Hall, Inc35 Performing a Pattern Test 14.98B—B 25.00BUC 34.95BDA 44.96BDA 54.99BUC 65.01—UC 75.02AUC 85.05AUB 95.08AUA 105.03ADB SAMPLExABOVE/BELOWUP/DOWNZONE Example 15.5

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2000 by Prentice-Hall, Inc36 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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