Copyright 2009 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Statistical Process Control Operations Management - 6 th Edition Chapter 3 Roberta Russell & Bernard W. Taylor, III

Copyright 2009 John Wiley & Sons, Inc.3-2 Lecture Outline  Basics of Statistical Process Control  Control Charts  Control Charts for Attributes  Control Charts for Variables  Control Chart Patterns  Process Capability

Customer Requirements Product Specifications Statistical Process Control: Measure & monitor quality Meets Specifications? Process Specifications Yes Conformance Quality Fix process or inputs No Product launch activities: Revise periodically Ongoing Activities

Copyright 2009 John Wiley & Sons, Inc.3-4 Basics of Statistical Process Control  Statistical Process Control (SPC) monitoring production process to detect, correct, and prevent poor quality monitoring production process to detect, correct, and prevent poor quality  Sample subset of items produced to use for inspection subset of items produced to use for inspection  Control Chart Is the process within statistical control limits? Is the process within statistical control limits? UCL LCL

Variation in a Transformation Process Transformation Process Inputs Facilities Equipment Materials Energy Employees Outputs Goods & Services Variation in inputs create variation in outputs Variations in the transformation process create variation in outputs

Basics of Statistical Process Control Types of Variation (1) 1.Random variation Also called common cause variation Also called common cause variation This type of variation is inherent in a process. This type of variation is inherent in a process. Caused by usual variations in equipment, tooling, employee actions, facility environment, materials, measurement system, etc. Caused by usual variations in equipment, tooling, employee actions, facility environment, materials, measurement system, etc. If random variation is excessive, the goods or services will not meet quality standards. If random variation is excessive, the goods or services will not meet quality standards. To reduce random variation, we must reduce variation in the inputs and the process To reduce random variation, we must reduce variation in the inputs and the process Copyright 2009 John Wiley & Sons, Inc.3-6

Basics of Statistical Process Control Types of Variation (2) 2.Non-random variation Also called special cause variation or assignable cause variation Also called special cause variation or assignable cause variation Caused by equipment out of adjustment, worn tooling, operator errors, poor training, defective materials, measurement errors, etc. Caused by equipment out of adjustment, worn tooling, operator errors, poor training, defective materials, measurement errors, etc. The process is not behaving as it usually does. The process is not behaving as it usually does. The cause can and should be identified and corrected. The cause can and should be identified and corrected. Copyright 2009 John Wiley & Sons, Inc.3-7

Statistical Process Control (SPC) When is a process in control?  A process is in control if it has no special cause variation. The process is consistent or predictable. The process is consistent or predictable.  SPC distinguishes between common cause and special cause variation  Measure characteristics of goods or services that are important to customers  Make a control chart for each characteristic The chart is used to determine whether the process is in control The chart is used to determine whether the process is in control

Specification Limits  The target is the ideal value Example: if the amount of beverage in a bottle should be 16 ounces, the target is 16 ounces Example: if the amount of beverage in a bottle should be 16 ounces, the target is 16 ounces  Specification limits are the acceptable range of values for a variable  Example: the amount of beverage in a bottle must be at least ounces and no more than ounces. Range is – ounces. Range is – ounces. Lower specification limit = ounces or LSPEC = ounces Lower specification limit = ounces or LSPEC = ounces Upper specification limit = ounces or USPEC = ounces Upper specification limit = ounces or USPEC = ounces

Specifications and Conformance Quality  A product which meets its specification has conformance quality.  Capable process: a process which consistently produces products that have conformance quality. Must be in control and meet specifications Must be in control and meet specifications

Quality Measures Attributes and Variables  Discrete measures Discrete means separate or distinct Discrete means separate or distinct Good/bad, yes/no (p charts) - Does the product meet standards? Good/bad, yes/no (p charts) - Does the product meet standards? Count of defects (c charts) – the count is a whole number Count of defects (c charts) – the count is a whole number  Variables – continuous numerical measures Length, diameter, weight, height, time, speed, temperature, pressure - does not have to be a whole number Length, diameter, weight, height, time, speed, temperature, pressure - does not have to be a whole number Controlled with x-bar and R charts Controlled with x-bar and R charts

SPC Applied to Services (1)  A service defect is a failure to meet customer requirements. Different customers have different requirements. Different customers have different requirements.  Examples of attribute measures used in services Customer satisfaction surveys – provides customer perceptions Customer satisfaction surveys – provides customer perceptions Reports from mystery shoppers, based on standards Reports from mystery shoppers, based on standards Employee or supervisor inspects cleanliness, etc., according to standards Employee or supervisor inspects cleanliness, etc., according to standards Copyright 2009 John Wiley & Sons, Inc.3-12

SPC Applied to Services (2)  Examples of variable measures used in services Waiting time and service time Waiting time and service time On-time service delivery On-time service delivery Accuracy Accuracy Number of stockouts (retail and distribution) Number of stockouts (retail and distribution) Percentage of lost luggage (airlines) Percentage of lost luggage (airlines) Web site availability (online retailing or technical support) Web site availability (online retailing or technical support) Copyright 2009 John Wiley & Sons, Inc.3-13

Copyright 2009 John Wiley & Sons, Inc.3-14 SPC Applied to Services (3)  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

Copyright 2009 John Wiley & Sons, Inc.3-15 SPC Applied to Services (4)  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

Copyright 2009 John Wiley & Sons, Inc.3-16 Process Control Chart Sample number Uppercontrollimit Processaverage Lowercontrollimit Out of control

Copyright 2009 John Wiley & Sons, Inc.3-17 Control Charts for Variables  Range chart ( R-Chart )  uses amount of dispersion in a sample  Mean chart ( x -Chart )  uses process average of a sample

Control Charts for Variables  Mean chart: sample means are plotted.  Range chart: sample ranges are plotted.  Two cases: The standard deviation is known The standard deviation is known The standard deviation is unknown. The standard deviation is unknown. Copyright 2009 John Wiley & Sons, Inc.3-18

SPC for Variables The Normal Distribution  = the population mean  = the standard deviation for the population 99.74% of the area under the normal curve is between  - 3  and  + 3 

SPC for Variables The Central Limit Theorem  Samples are taken from a distribution with mean  and standard deviation . k = the number of samples n = the number of units in each sample  The sample means are normally distributed with mean  and standard deviation with mean  and standard deviation when k is large. when k is large.

Copyright 2009 John Wiley & Sons, Inc.3-21 x-bar Chart: Standard Deviation Known UCL = x + z  x LCL = x - z  x x 1 + x x n n n x = == where x = average of sample means where ==== ==

Copyright 2009 John Wiley & Sons, Inc.3-22 x-bar Chart Example: Standard Deviation Known (cont.) Given: The standard deviation is 0.08

Copyright 2009 John Wiley & Sons, Inc.3-23 x-bar Chart Example: Standard Deviation Known (cont.)

A 2 is a factor that depends on n, the number of units in each sample A 2 is a factor that depends on n, the number of units in each sample Copyright 2009 John Wiley & Sons, Inc.3-24 x-bar Chart Example: Standard Deviation Unknown UCL = x + A 2 RLCL = x - A 2 R = = = =

Copyright 2009 John Wiley & Sons, Inc.3-25 Control Limits In this problem, n = 5

Copyright 2009 John Wiley & Sons, Inc.3-26 x-bar Chart Example: Standard Deviation Unknown Example 15.4 OBSERVATIONS (SLIP- RING DIAMETER, CM) SAMPLE k 12345xR

Copyright 2009 John Wiley & Sons, Inc.3-27 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 = xkxk x-bar Chart Example: Standard Deviation Unknown (cont.) Retrieve Factor Value A 2 R === ∑ R k ∑ R k

Copyright 2009 John Wiley & Sons, Inc.3-28 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 | – 5.08 – 5.06 – 5.04 – 5.02 – 5.00 – 4.98 – 4.96 – 4.94 – 4.92 – x = 5.01 =

Copyright 2009 John Wiley & Sons, Inc.3-29 A Process Is in Control If … 1.There are no sample points outside limits & 2.Most points are near the process average & 3.The number of points above and below the center line is about equal & 4.The points appear to be randomly distributed This is only a rough guide. Quality analysts use more precise rules.

Copyright 2009 John Wiley & Sons, Inc.3-30 R- Chart UCL = D 4 RLCL = D 3 R R =R =R =R = RRkkRRkkk where R= range of each sample k= number of samples

Copyright 2009 John Wiley & Sons, Inc.3-31 R-Chart Example OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 12345xR Example 15.3

Copyright 2009 John Wiley & Sons, Inc.3-32 R-Chart Example (cont.) Example 15.3 Retrieve Factor Values D 3 and D 4 Retrieve Factor Values D 3 and D 4 UCL = D 4 R = 2.11(0.115) = LCL = D 3 R = 0(0.115) = 0 UCL = D 4 R = 2.11(0.115) = LCL = D 3 R = 0(0.115) = 0

Copyright 2009 John Wiley & Sons, Inc.3-33 R-Chart Example (cont.) 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 –

Copyright 2009 John Wiley & Sons, Inc.3-34 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 might be beyond control limits  It is possible for sample averages to be in control, but ranges might be very large  It is possible for an R-chart to exhibit a distinct downward trend, suggesting some nonrandom cause is reducing variation

Copyright 2009 John Wiley & Sons, Inc.3-35 Non-random Patterns in Control Charts Change in Mean UCL LCL Sample observations consistently above the center line LCL UCL Sample observations consistently below the center line

Copyright 2009 John Wiley & Sons, Inc.3-36 Non-random Patterns in Control Charts Trend LCL UCL Sample observations consistently increasing UCL LCL Sample observations consistently decreasing

Copyright 2009 John Wiley & Sons, Inc.3-37 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  A capable process consistently produces products that conform to specifications

Copyright 2009 John Wiley & Sons, Inc.3-38 Copyright 2009 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.