1. Outline Statistical Process Control (SPC) Process Capability
Control Charts for Variables
The Central Limit Theorem
Setting Mean Chart Limits ( x-Charts)
Setting Range Chart Limits (R-Charts)
Using Mean and Range Charts
Control Charts for Attributes
Managerial Issues and Control Charts
Process Capability
Acceptance Sampling
Operating Characteristic (OC) Curves
Average Outgoing Quality

2. Learning Objectives
When you complete this chapter, you should be able to :
Identify or Define:
Natural and assignable causes of variation
Central limit theorem
Attribute and variable inspection
Process control
charts and R charts
LCL and UCL
p-charts and C-charts
Cpk
Acceptance sampling
OC curve
AQL and LTPD
AOQ
Producer’s and consumer’s risk

3. Learning Objectives - continued
When you complete this chapter, you should be able to :
Describe or explain:
The role of statistical quality control

4. Operations Management Quality and Statistical Process Control

5. In Class Exercise
You are the president of Hydro Message Inc. (HMI). HMI produces devises which deliver water pulsing message shower heads and hand held devices for the bath. For the following example assume 100,000 units will be produced over the life of the product.
Alternative 1: Is a simple-design hand-held. It has a 90% chance of yielding 95 good hand-helds out of every 100 manufactured. There is a 10% chance that the yield will be only 70 out of every Design cost is $400,000 and manufacturing cost is $25 per unit. Expected revenue is $45/unit.
Alternative 2: Is a more complicated design. It has only a 60% chance of yielding 95 good hand-helds out of every 100 manufactured. There is a 40% chance that the yield will be only 40 out of every Design cost is $700,000 and manufacturing cost is $40 per unit. Anticipated revenue is $85/unit.

6. Solution Do nothing = $0 Simple Design Complex Design 90% 10% 60% 40%
Sales =
Design =
Manu Cost =
Exp. Value =
90%
Simple Design
10%
Complex
Design
60%
40%
Do nothing = $0

7. Solution Simple Design Complex Design 90% 10% 60% 40%
Sales = .95*$45*100,000 = $4,275,000
Design = $400,000
Manu Cost = 100,000 *25 = $2,500,000
Exp. Value = $1,375,000
90%
Simple Design
10%
Complex
Design
60%
40%

8. Solution Simple Design Complex Design 90% 10% 60% 40%
Sales = .95*$45*100,000 = $4,275,000
Design = $400,000
Manu Cost = 100,000 *25 = $2,500,000
Exp. Value = $1,375,000
90%
Simple Design
10%
Sales = .70*$45*100,000 = $3,150,000
Design = $400,000
Manu Cost = 100,000 *25 = $2,500,000
Exp. Value = $250,000
Sales = .95*$85*100,000 = $8,075,000
Design = $700,000
Manu Cost = 100,000 *40 = $4,000,000
Exp. Value = $3,375,000
Complex
Design
60%
40%
Sales = .40*$85*100,000 = $3,400,000
Design = $700,000
Manu Cost = 100,000 *40 = $4,000,000
Exp. Value = $-1,300,000

9. Solution Simple Design EMV = (.9*1,375,000) + (.1*250,000)
= $1,262,500
Sales = .95*$45*100,000 = $4,275,000
Design = $400,000
Manu Cost = 100,000 *25 = $2,500,000
Exp. Value = $1,375,000
90%
10%
Sales = .70*$45*100,000 = $3,150,000
Design = $400,000
Manu Cost = 100,000 *25 = $2,500,000
Exp. Value = $250,000
Sales = .95*$85*100,000 = $8,075,000
Design = $700,000
Manu Cost = 100,000 *40 = $4,000,000
Exp. Value = $3,375,000
Complex
Design
EMV = $1,505,000
60%
40%
Sales = .40*$85*100,000 = $3,400,000
Design = $700,000
Manu Cost = 100,000 *40 = $4,000,000
Exp. Value = $-1,300,000
Complex - Simple Delta = $242,500

10. Part II
Alternative 1: The simple design has virtually no chance of shocking a customer in the bath (no change required to EMV of simple design).
Alternative 2: Has a /unit chance of shocking a customer in the bath. If a person is shocked in the bathtub, it is assumed they will die.
Legal has stated that each shock incident has a 20% chance of a $2,000,000 award and a 80% chance of being dismissed in a court of law due to adequate warning labels on the product.
What is the new EMV for the complex design?

11. New information for scenario II
Sales = .95*$85*100,000 = $8,075,000
Design = $700,000
Manu Cost = 100,000 *40 = $4,000,000
Shock Cost = .95*100,000* *.20*2,000,000 = $190,000
Exp. Value = $3,195,000
60%
40%
Sales = .40*$85*100,000 = $3,400,000
Design = $700,000
Manu Cost = 100,000 *40 = $4,000,000
Shock Cost = .40*100,000* *.20*2,000,000 = $80,000
Exp. Value = $-1,380,000
Complex Design EMV = .6 (3,195,000) + .4*(-1,380,000) = $1,365,000
Complex is still $102,500 better than the simple design. But is it worth taking the risk? What about the negative value of bad press? What about the ethical issues? Is one life worth more or less than $102,500?

12. Dimensions of Operations Strategy & Competitive Advantage
Time
Price
Quality
Variety
Competitive Advantage & Profit
Means to best satisfy
the customer
P. 133 of text

13. Ways in Which Quality Can Improve Productivity
Sales Gains
Improved response
Higher Revenues (Prices)
Improved reputation
Improved Quality
Increased Profits
Reduced Costs
Increased productivity
Lower rework and scrap costs
Lower warranty costs
This slide not only looks at the impact of quality on productivity - it also enables you to begin a discussion as to the meaning of quality (or perhaps the differing meanings among different people). To many people, the notion of “high quality” carries with it the assumption of “high price.” This slide provides an initial point to challenge that assumption.

14. Flow of Activities Necessary to Achieve Total Quality Management
Organizational Practices
Quality Principles
Employee Fulfillment
This slide simply introduces the four activities. Subsequent slides expand on each.
Customer Satisfaction

15. Traditional Quality Process (Manufacturing)
Customer
Marketing
Engineering
Operations
Specifies
Interprets
Designs
Produces
Need
Need
Product
Product
Defines
Plans
Students might be asked what problems they would foresee in implementing this process.
Quality
Quality
Quality is customer driven!
Monitors
Quality

16. Encompasses entire organization, from supplier to customer
TQM
Encompasses entire organization, from supplier to customer
Stresses a commitment by management to have a continuing company-wide drive toward excellence in all aspects of products and services that are important to the customer.
A point to be made here is that TQM is not a program but a philosophy.

17. Achieving Total Quality Management
Customer Satisfaction
Effective Business
Attitudes (e.g., Commitment)
Employee Fulfillment
How to Do
Quality Principles
Again, a point to be made here is the universality required to achieve TQM.
What to Do
Organizational Practices

18. Deming’s Fourteen Points
Create consistency of purpose
Lead to promote change
Build quality into the products
Build long term relationships
Continuously improve product, quality, and service
Start training
Emphasize leadership
One point to make here is that this list represents a recent expression of Demings 14 points - the list is still evolving.
Students may notice that many of these fourteen points seem to be simply common sense. If they raise this issue - ask them to consider jobs they have held. Were these points emphasized or implemented by their employers? If not, why not? This part of the discussion can be used to raise again the issue that proper approaches to quality are not “programs,” with limited involvement and finite duration, but rather philosophies which must become ingrained throughout the organization.

19. Deming’s Points - continued
Drive out fear
Break down barriers between departments
Stop haranguing workers
Support, help, improve
Remove barriers to pride in work
Institute a vigorous program of education and self-improvement
Put everybody in the company to work on the transformation

20. Benchmarking
Selecting best practices to use as a standard for performance
Determine what to benchmark
Form a benchmark team
Identify benchmarking partners
Collect and analyze benchmarking information
Take action to match or exceed the benchmark
Ask student to identify firms which they believe could serve as benchmarks. If students are unable to identify any firms - ask them to identify a college or university whose registration system or housing selection system could serve as a benchmark. Most students have enough knowledge of, or friends at,other colleges and universities so as to be able to respond to this question.

21. Resolving Customer Complaints Best Practices
Make it easy for clients to complain
Respond quickly to complaints
Resolve complaints on the first contact
Recruit the best for customer service jobs
One might ask students “Given that these suggestions seem to make intuitive sense, why would a company not wish to implement them?”

22. Just-in-Time (JIT) Relationship to quality: JIT cuts cost of quality
JIT improves quality
Better quality means less inventory and better, easier-to-employ JIT system
This slide introduces a discussion about JIT.
Subsequent slides elaborate.

23. Just-In-Time (JIT) Example
Scrap
Work in process inventory level (hides problems)
Unreliable Vendors
Capacity Imbalances

24. Just-In-Time (JIT) Example
Scrap
Reducing inventory reveals problems so they can be solved.
Unreliable Vendors
Capacity Imbalances
Note that reducing inventory enables problems to be seen - it does not necessarily fix them.

25. Quality Loss Function; Distribution of Products Produced
High loss
Quality Loss Function (a)
Unacceptable
Loss (to producing organization, customer, and society)
Target-oriented quality yields more product in the “best” category
Poor
Fair
Good
Best
Low loss
Target-oriented quality brings products toward the target value
Conformance-oriented quality keeps product within three standard deviations
Frequency
This slide may help clarify the differences between conformance and target-based quality control.
Distribution of specifications for product produced (b)
Lower
Target
Upper
Specification

26. Quality Loss Function
Shows social cost ($) of deviation from target value
Assumptions
Most measurable quality characteristics (e.g., length, weight) have a target value
Deviations from target value are undesirable
Equation: L = D2C
L = Loss ($); D = Deviation; C = Cost
One question to pose to your students: “Of what value is the notion of a “social cost?” How might a manager use this in decision making?

27. Quality Loss Function Graph
Loss = (Actual X - Target)2 • (Cost of Deviation)
Lower (upper) specification limit
Measurement
Greater deviation, more people are dissatisfied, higher cost
This slide may be used to provide a graphical representation of the Quality Loss Function.

28. Quality Loss Function Example
The specifications for the diameter of a gear are ± 0.25 mm. If the diameter is out of specification, the gear must be scrapped at a cost of $ What is the loss function?
How does one identify the “cost” given in this problem?
© T/Maker Co.

29. Quality Loss Function Solution
L = D2C = (X - Target)2C
L = Loss ($); D = Deviation; C = Cost
4.00 = ( )2C
Item scrapped if greater than (USL = ) with a cost of $4.00
C = 4.00 / ( )2 = 64
L = D2 • 64 = (X )264
Enter various X values to obtain L & plot

31. Pareto Analysis of Wine Glass Defects (Total Defects = 75)
This slide probably deserves more discussion than most of us would tend to allot it. Students need to understand the cost of “going the extra mile,” - the difference between something which may be very good, and something which is perfect.
The students also need to recognize that Pareto charts suggest where to place effort - on the item that looms largest on the chart. After progress is made on that item, then one performs a Pareto analysis on the remaining items, and repeats the procedure..
72%
16% 5% 4% 3%

32. Statistical Quality Control (SPC)
Measures performance of a process
Uses mathematics (i.e., statistics)
Involves collecting, organizing, & interpreting data
Objective: provide statistical when assignable causes of variation are present
Used to
Control the process as products are produced
Inspect samples of finished products
Points which might be emphasized include:
- Statistical process control measures the performance of a process, it does not help to identify a particular specimen produced as being “good” or “bad,” in or out of tolerance.
- Statistical process control requires the collection and analysis of data - therefore it is not helpful when total production consists of a small number of units
- While statistical process control can not help identify a “good” or “bad” unit, it can enable one to decide whether or not to accept an entire production lot. If a sample of a production lot contains more than a specified number of defective items, statistical process control can give us a basis for rejecting the entire lot. The issue of rejecting a lot which was actually good can be raised here, but is probably better left to later.

33. Figure S6.1

34. Types of Statistical Quality Control
Process
Control
Acceptance
Sampling
Variables
Charts
Attributes
This slide provides a framework for differentiating between “Process Control” and “Acceptance Sampling,” and “Variables” and “Attributes.”
One might also raise the distinction between producer (process control) and customer (acceptance sampling).
The next several slides deal with these distinctions.

35. Quality Characteristics
Variables
Attributes
Characteristics that you measure, e.g., weight, length
May be in whole or in fractional numbers
Continuous random variables
Characteristics for which you focus on defects
Classify products as either ‘good’ or ‘bad’, or count # defects
e.g., radio works or not
Categorical or discrete random variables
Once the categories are outlined, students may be asked to provide examples of items for which variable or attribute inspection might be appropriate. They might also be asked to provide examples of products for which both characteristics might be important at different stages of the production process.

36. Statistical Process Control (SPC)
Statistical technique used to ensure process is making product to standard
All process are subject to variability
Natural causes: Random variations
Assignable causes: Correctable problems
Machine wear, unskilled workers, poor material
Objective: Identify assignable causes
Uses process control charts
This slide introduces the difference between “natural” and “assignable” causes.
The next several slides expand the discussion and introduce some of the statistical issues.

37. Process Control: Three Types of Process Outputs
Frequency
Lower control limit
Size
Weight, length, speed, etc.
Upper control limit
(b) In statistical control, but not capable of producing within control limits. A process in control (only natural causes of variation are present) but not capable of producing within the specified control limits; and
(c) Out of control. A process out of control having assignable causes of variation.
(a) In statistical control and capable of producing within control limits. A process with only natural causes of variation and capable of producing within the specified control limits.
This slide helps introduce different process outputs.
It can also be used to illustrate natural and assignable variation.

38. The Relationship Between Population and Sampling Distributions
Uniform
Normal
Beta
Distribution of sample means
Standard deviation of the sample means
(mean)
Three population distributions

39. Sampling Distribution of Means, and Process Distribution
Sampling distribution of the means
Process distribution of the sample
It may be useful to spend some time explicitly discussing the difference between the sampling distribution of the means and the mean of the process population.

40. Process Control Charts
An example of a control chart. .

41. Control Chart Purposes
Show changes in data pattern
e.g., trends
Make corrections before process is out of control
Show causes of changes in data
Assignable causes
Data outside control limits or trend in data
Natural causes
Random variations around average

42. Theoretical Basis of Control Charts
As sample size gets large enough,
sampling distribution becomes almost normal regardless of population distribution.
Central Limit Theorem
The next three slides can be used in a discussion of the theoretical basis for statistical process control.

43. Theoretical Basis of Control Charts
Central Limit Theorem
Mean
Standard deviation

44. Theoretical Basis of Control Charts
Properties of normal distribution

45. Control Chart Types Continuous Numerical Data
Categorical or Discrete Numerical Data
Control
Charts
Variables
Attributes
Charts
Charts
This slide simply introduces the various types of control charts. R X P C
Chart
Chart
Chart
Chart

46. Statistical Process Control StepsNo
Produce Good
Start
Provide Service
Assign.
Take Sample
Causes?
Yes
Inspect Sample
Stop Process
This slide introduces the statistical control process.
It may be helpful here to walk students through an example or two of the process. The first walk through should probably be for a manufacturing process.
The next several slides present information about the various types of process control slides:
Create
Find Out Why
Control Chart

47. X Chart Type of variables control chart Shows sample means over time
Interval or ratio scaled numerical data
Shows sample means over time
Monitors process average
Example: Weigh samples of coffee & compute means of samples; Plot

48. X Chart Control Limits
From Table S6.1
Sample Range at Time i
Sample Mean at Time i
The following slide provides much of the data from Table S4.1.
# Samples

49. Factors for Computing Control Chart Limits

50. R Chart Type of variables control chart Shows sample ranges over time
Interval or ratio scaled numerical data
Shows sample ranges over time
Difference between smallest & largest values in inspection sample
Monitors variability in process
Example: Weigh samples of coffee & compute ranges of samples; Plot

51. R Chart Control Limits From Table S6.1 Sample Range at Time i
# Samples

52. Steps to Follow When Using Control Charts
Collect 20 to 25 samples of n=4 or n=5 from a stable process and compute the mean.
Compute the overall means, set approximate control limits,and calculate the preliminary upper and lower control limits.If the process is not currently stable, use the desired mean instead of the overall mean to calculate limits.
Graph the sample means and ranges on their respective control charts and determine whether they fall outside the acceptable limits.

53. Steps to Follow When Using Control Charts - continued
Investigate points or patterns that indicate the process is out of control. Assign causes for the variations.
Collect additional samples and revalidate the control limits.

54. Figure S6.5

55. p Chart Type of attributes control chart
Nominally scaled categorical data
e.g., good-bad
Shows % of nonconforming items
Example: Count # defective chairs & divide by total chairs inspected; Plot
Chair is either defective or not defective

56. p Chart Control Limits z = 2 for 95.5% limits; z = 3 for 99.7% limits
# Defective Items in Sample i
Size of sample i

57. c Chart Type of attributes control chart
Discrete quantitative data
Shows number of nonconformities (defects) in a unit
Unit may be chair, steel sheet, car etc.
Size of unit must be constant
Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot

58. c Chart Control Limits Use 3 for 99.7% limits # Defects in Unit i
# Units Sampled

59. Figure S6.7

60. Process Capability Cpk
Assumes that the process is:
under control
normally distributed

61. Meanings of Cpk Measures
Cpk = negative number
Cpk = zero
Cpk = between 0 and 1
Cpk = 1
Cpk > 1

62. What Is Acceptance Sampling?
Form of quality testing used for incoming materials or finished goods
e.g., purchased material & components
Procedure
Take one or more samples at random from a lot (shipment) of items
Inspect each of the items in the sample
Decide whether to reject the whole lot based on the inspection results
Here again it is useful to stress that acceptance sampling relates to the aggregate, not the individual unit. You might also discuss the decision as to whether one should take only a single sample, or whether multiple samples are required.

63. What Is an Acceptance Plan?
Set of procedures for inspecting incoming materials or finished goods
Identifies
Type of sample
Sample size (n)
Criteria (c) used to reject or accept a lot
Producer (supplier) & consumer (buyer) must negotiate

64. Operating Characteristics Curve
Shows how well a sampling plan discriminates between good & bad lots (shipments)
Shows the relationship between the probability of accepting a lot & its quality
You can use this and the next several slides to begin a discussion of the “quality” of the acceptance sampling plans. You will find additional slides on “consumer’s” and “producer’s” risk to pursue the issue in a more formal manner in subsequent slides.

65. OC Curve 100% Inspection P(Accept Whole Shipment) 100% 0% 1 2 3 4 5 6
Keep whole shipment
Return whole shipment 0% 1 2 3 4 5 6 7 8 9 10
Cut-Off
% Defective in Lot

66. OC Curve with Less than 100% Sampling
P(Accept Whole Shipment)
100% 0%
% Defective in Lot
Cut-Off 1 2 3 4 5 6 7 8 9 10
Return whole shipment
Keep whole shipment
Probability is not 100%: Risk of keeping bad shipment or returning good one.

67. AQL & LTPD Acceptable quality level (AQL)
Quality level of a good lot
Producer (supplier) does not want lots with fewer defects than AQL rejected
Lot tolerance percent defective (LTPD)
Quality level of a bad lot
Consumer (buyer) does not want lots with more defects than LTPD accepted
Once the students understand the definition of these terms, have them consider how one would go about choosing values for AQL and LTPD.

68. Producer’s & Consumer’s Risk
Producer's risk ()
Probability of rejecting a good lot
Probability of rejecting a lot when fraction defective is AQL
Consumer's risk (ß)
Probability of accepting a bad lot
Probability of accepting a lot when fraction defective is LTPD
This slide introduces the concept of “producer’s” risk and “consumer’s” risk. The following slide explores these concepts graphically.

69. An Operating Characteristic (OC) Curve Showing Risks
 = 0.05 producer’s risk for AQL
= 0.10
Consumer’s risk for LTPD
Probability of Acceptance
Percent Defective
Bad lots
Indifference zone
Good lots
LTPD
AQL
100 95 75 50 25 10

70. OC Curves for Different Sampling Plans1 2 3 4 5 6 7 8 9 10
% Defective in Lot
P(Accept Whole Shipment)
100% 0%
LTPD
AQL
n = 50, c = 1
n = 100, c = 2
This slide presents the OC curve for two possible acceptance sampling plans.

71. Developing a Sample Plan
Negotiate between producer (supplier) and consumer (buyer)
Both parties attempt to minimize risk
Affects sample size & cut-off criterion
Methods
MIL-STD-105D Tables
Dodge-Romig Tables
Statistical Formulas

72. Statistical Process Control - Identify and Reduce Process Variability
Lower specification limit
Upper specification limit
(a) Acceptance sampling
(b) Statistical process control
(c) cpk >1
This may be a good time to stress that an overall goal of statistical process control is to “do it better,” i.e., improve over time.