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Statistical Process Control

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4-2 Lecture Outline Basics of Statistical Process Control Control Charts Control Charts for Attributes Control Charts for Variables Control Chart Patterns SPC with Excel Process Capability

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4-3 Basics of Statistical Process Control Statistical Process Control (SPC) monitoring production process to detect and prevent poor quality monitoring production process to detect and prevent poor quality Sample subset of items produced to use for inspection subset of items produced to use for inspection Control Charts process is within statistical control limits process is within statistical control limits UCL LCL

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4-4 Variability Random common causes common causes inherent in a process inherent in a process can be eliminated only through improvements in the system can be eliminated only through improvements in the system Non-Random special causes special causes due to identifiable factors due to identifiable factors can be modified through operator or management action can be modified through operator or management action

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4-5 SPC in TQM SPC tool for identifying problems and make improvements tool for identifying problems and make improvements contributes to the TQM goal of continuous improvements contributes to the TQM goal of continuous improvements

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4-6 Quality Measures Attribute a product characteristic that can be evaluated with a discrete response a product characteristic that can be evaluated with a discrete response good – bad; yes - no good – bad; yes - no Variable a product characteristic that is continuous and can be measured a product characteristic that is continuous and can be measured weight - length weight - length

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4-7 Nature of defect is different in services Service defect is a failure to meet customer requirements Monitor times, customer satisfaction Applying SPC to Service

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4-8 Applying SPC to Service (cont.) Hospitals timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts Grocery Stores waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors Airlines flight 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 flight 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

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4-9 Applying SPC to Service (cont.) Fast-Food Restaurants waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy Catalogue-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 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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4-10 Where to Use Control Charts Process has a tendency to go out of control Process is particularly harmful and costly if it goes out of control Examples at the beginning of a process because it is a waste of time and money to begin production process with bad supplies at the beginning of a process because it is a waste of time and money to begin production process with bad supplies before a costly or irreversible point, after which product is difficult to rework or correct before a costly or irreversible point, after which product is difficult to rework or correct before and after assembly or painting operations that might cover defects before and after assembly or painting operations that might cover defects before the outgoing final product or service is delivered before the outgoing final product or service is delivered

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4-11 Control Charts A graph that establishes control limits of a process Control limits upper and lower bands of a control chart upper and lower bands of a control chart Types of charts Attributes Attributes p-chart p-chart c-chart c-chart Variables Variables range (R-chart) range (R-chart) mean (x bar – chart) mean (x bar – chart)

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4-12 Process Control Chart 12345678910 Sample number Uppercontrollimit Processaverage Lowercontrollimit Out of control

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4-13 Normal Distribution =0 1111 2222 3333 -1 -2 -3 95% 99.74%

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4-14 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

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4-15 Control Charts for Attributes p-charts uses portion defective in a sample c-charts uses number of defects in an item

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4-16 p-Chart UCL = p + z p LCL = p - z p z=number of standard deviations from process average p=sample proportion defective; an estimate of process average p = standard deviation of sample proportion p =p =p =p = p(1 - p) n

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4-17 p-Chart Example 20 samples of 100 pairs of jeans NUMBER OFPROPORTION SAMPLEDEFECTIVESDEFECTIVE 16.06 20.00 34.04 ::: 2018.18 200

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4-18 p-Chart Example (cont.) UCL = p + z = p(1 - p) n UCL = LCL = LCL = p - z = p(1 - p) n = total defectives total sample observations p =

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4-19 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Proportion defective Sample number 2468101214161820 UCL = 0.190 LCL = 0.010 p = 0.10 p-Chart Example (cont.)

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4-20 c-Chart UCL = c + z c LCL = c - z c where c = number of defects per sample c = c

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4-21 c-Chart (cont.) Number of defects in 15 sample rooms 1 12 2 8 3 16 : : 15 15 190 190 SAMPLE c = = UCL= c + z c == LCL= c + z c == NUMBER OF DEFECTS

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4-22 3 6 9 12 15 18 21 24 Number of defects Sample number 246810121416 UCL = 23.35 LCL = 1.99 c = 12.67 c-Chart (cont.)

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4-23 Control Charts for Variables Mean chart ( x -Chart ) uses average of a sample Range chart ( R-Chart ) uses amount of dispersion in a sample

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4-24 x-bar Chart x =x =x =x = x 1 + x 2 +... x k k = UCL = x + A 2 RLCL = x - A 2 R == where x= average of sample means =

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4-25 x-bar 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

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4-26 UCL = x + A 2 R = = LCL = x - A 2 R = = = = x = = = cm = xkxk x- bar Chart Example (cont.) Retrieve Factor Value A 2

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4-27 x- bar Chart Example (cont.) 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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4-28 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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4-29 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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4-30 R-Chart Example (cont.) Example 15.3 RkRk R = = = UCL = D 4 R = = LCL = D 3 R = = Retrieve Factor Values D 3 and D 4 Retrieve Factor Values D 3 and D 4

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4-31 R-Chart Example (cont.) 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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4-32 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.

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4-33 Control Chart Patterns UCL LCL Sample observations consistently above the center line LCL UCL Sample observations consistently below the center line

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4-34 Control Chart Patterns (cont.) LCL UCL Sample observations consistently increasing UCL LCL Sample observations consistently decreasing

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4-35 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

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4-36 Process Capability Tolerances design specifications reflecting product requirements design specifications reflecting product requirements Process capability range of natural variability in a process what we measure with control charts range of natural variability in a process what we measure with control charts

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4-37 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

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4-38 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

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4-39 Process Capability Measures Process Capability Ratio Cp==Cp== tolerance range process range upper specification limit - lower specification limit 6

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4-40 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 = = upper specification limit - lower specification limit 6

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4-41 Process Capability Measures Process Capability Index C pk = minimum x - lower specification limit 3 = upper specification limit - x 3 =,

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4-42 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, = 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. Chapter 15 Statistical Quality Control.

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

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