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

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

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

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

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

6. Basics of Statistical Process Control Types of Variation (1)
Random variation
Also called common cause variation
This type of variation is inherent in a process.
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.
To reduce random variation, we must reduce variation in the inputs and the process
Copyright 2009 John Wiley & Sons, Inc.

7. Basics of Statistical Process Control Types of Variation (2)
Non-random 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.
The process is not behaving as it usually does.
The cause can and should be identified and corrected.
Copyright 2009 John Wiley & Sons, Inc.

8. 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.
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

9. 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
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.
Lower specification limit = ounces or LSPEC = ounces
Upper specification limit = ounces or USPEC = ounces

10. 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 2

11. Quality Measures Attributes and Variables
Discrete measures
Discrete means separate or distinct
Good/bad, yes/no (p charts) - Does the product meet standards?
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
Controlled with x-bar and R charts

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

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

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
Grocery stores
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
Copyright 2009 John Wiley & Sons, Inc.

15. SPC Applied to Services (4)
Fast-food restaurants
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
Insurance companies
billing accuracy, timeliness of claims processing, agent availability and response time
Copyright 2009 John Wiley & Sons, Inc.

16. Process Control Chart Out of control Upper control limit Process1 2 3 4 5 6 7 8 9 10
Sample number
Upper
control
limit
Process
average
Lower
Out of control
Copyright 2009 John Wiley & Sons, Inc.

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
Copyright 2009 John Wiley & Sons, Inc.

18. 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 unknown.
Copyright 2009 John Wiley & Sons, Inc.

19. 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

20. 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
when k is large.

21. x-bar Chart: Standard Deviation Known= =
UCL = x + zx LCL = x - zx
x1 + x xn n =
x =
where
x = average of sample means =
Copyright 2009 John Wiley & Sons, Inc.

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

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

24. x-bar Chart Example: Standard Deviation Unknown
A2 is a factor that depends on n,
the number of units in each sample = =
UCL = x + A2R LCL = x - A2R
Copyright 2009 John Wiley & Sons, Inc.

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

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

27. x-bar Chart Example: Standard Deviation Unknown (cont.)
1.15 10
R = = = 0.115
UCL = x + A2R = (0.58)(0.115) = 5.08
LCL = x - A2R = (0.58)(0.115) = 4.94 =
x = = = 5.01 cm x k
50.09 10
Retrieve Factor Value A2
Copyright 2009 John Wiley & Sons, Inc.

28. x- bar Chart Example (cont.)
UCL = 5.08
LCL = 4.94
Mean
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 =
x- bar Chart Example (cont.)
Copyright 2009 John Wiley & Sons, Inc.

29. A Process Is in Control If …
There are no sample points outside limits &
Most points are near the process average &
The number of points above and below the center line is about equal &
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.

30. R- Chart UCL = D4R LCL = D3R R k R = where R = range of each sample
k = number of samples
Copyright 2009 John Wiley & Sons, Inc.

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

32. R-Chart Example (cont.)
UCL = D4R = 2.11(0.115) = 0.243
LCL = D3R = 0(0.115) = 0
Retrieve Factor Values D3 and D4
Example 15.3
Copyright 2009 John Wiley & Sons, Inc.

33. R-Chart Example (cont.)
UCL = 0.243
LCL = 0
Range
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 2009 John Wiley & Sons, Inc.

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.

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

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.

37. Process Capability Tolerances Process capability
design specifications reflecting product requirements
Process capability
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.

38. Copyright 2009 John Wiley & Sons, Inc. All rights reserved
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.
Copyright 2009 John Wiley & Sons, Inc.