1. Quality Control Chapter 10 Additional content from Jeff Heyl
MIS 373: Basic Operations Management
Additional content from Jeff Heyl

2. Learning Objectives After this lecture, students will be able to
Explain the need for quality control.
List and briefly explain the elements of the control process.
Explain Type I and Type II errors
Explain how control charts are used to monitor a process and the concepts that underlie their use.
MIS 373: Basic Operations Management

3. Background Knowledge
How many of you have had at least one statistics course?
Normal distribution?
Standard deviation?
Z score?

4. Motivations Making Beer Better With Quality and Statistics
Quality for Life: Psychic Pizza

5. What is Quality Control?
A process that evaluates output relative to a standard and takes corrective action when output doesn’t meet standards
If results are acceptable no further action is required
Unacceptable results call for correction action
Phases of Quality Assurance
MIS 373: Basic Operations Management

6. Inspection Inspection
An appraisal activity that compares goods or services to a standard
Inspection issues:
What to inspect
Count number of times defect occurs
Measure the value of a characteristic
How much to inspect and how often
At what points in the process to inspect
Raw materials and purchased parts
Finished products
Before a costly operation
Before an irreversible process
Costly, possibly destructive, and disruptive – non value-adding
Full inspection vs. Sampling
MIS 373: Basic Operations Management

7. How Much to Inspect
MIS 373: Basic Operations Management

8. How Much to Inspect Trying to catch: 1 defect in 1 thousand unites
1 defect in 1 million unites
1 defect in 1 billion unites
Trying to catch:
MIS 373: Basic Operations Management

9. Centralized vs. On-Site Inspection
Effects on cost and level of disruption are a major issue in selecting centralized vs. on-site inspection
Centralized
Specialized tests that may best be completed in a lab
More specialized testing equipment
More favorable testing environment
On-Site
Quicker decisions are rendered
Avoid introduction of extraneous factors
Quality at the source
MIS 373: Basic Operations Management

10. Statistical Process Control (SPC)
Quality control seeks
Quality of Conformance
A product or service conforms to specifications
A tool used to help in this process:
SPC
Statistical evaluation of the output of a process
Helps us to decide if a process is “in control” or if corrective action is needed
“In control” means that the variation in the provided products/services is tolerable
MIS 373: Basic Operations Management

11. Process Variability Two basic questions: concerning variability:
Issue of Process Control
Are the variations random? If nonrandom variation is present, the process is said to be unstable.
 Variations randomly distributed within control limits
Issue of Process Capability
Given a stable process, is the inherent variability of the process within a range that conforms to performance criteria?
 The control limits satisfy the design specification
MIS 373: Basic Operations Management

12. Variation Variation Illustration: M&M’s
Random (common cause) variation:
Natural variation in the output of a process, created by countless minor factors
Assignable (special cause) variation:
A variation whose cause can be identified.
A nonrandom variation
Illustration: M&M’s
Size
Color
MIS 373: Basic Operations Management

13. Variation Common cause Special cause Inappropriate procedures
Poor design
Poor maintenance of machines
Lack of clearly defined standard operating procedures
Poor working conditions, e.g. lighting, noise, dirt, temperature, ventilation
Substandard raw materials
Measurement error
Quality control error
Vibration in industrial processes
Ambient temperature and humidity
Normal wear and tear
Variability in settings
Special cause
Poor adjustment of equipment
Operator falls asleep
Faulty controllers
Machine malfunction
Fall of ground
Computer crash
Poor batch of raw material
Power surges
High healthcare demand from elderly people
Broken part
Abnormal traffic (click fraud) on web ads
Extremely long lab testing turnover time due to switching to a new computer system
Operator absent
MIS 373: Basic Operations Management

14. Sampling and Sample Distribution
SPC involves periodically taking samples of process output and computing sample statistics:
Sample means
The number of occurrences of some outcome
Sample statistics are used to judge the randomness of process variation
MIS 373: Basic Operations Management

15. Sampling and Sample Distribution
Sampling Distribution
A theoretical distribution that describes the random variability of sample statistics
The normal distribution is commonly used for this purpose
Central Limit Theorem
The distribution of sample averages tends to be normal regardless of the shape of the underlying process distribution
MIS 373: Basic Operations Management

16. Demo
Use simulation to test the Central Limit Theorem

17. The Normal Distribution
MIS 373: Basic Operations Management

18. Control Process
Sampling and corrective action are only a part of the control process
Steps required for effective control:
Define: What is to be controlled?
Measure: How will measurement be accomplished?
Compare: There must be a standard of comparison
Evaluate: Establish a definition of out of control
Correct: Uncover the cause of nonrandom variability and fix it
Monitor results: Verify that the problem has been eliminated
MIS 373: Basic Operations Management

19. Control Charts: The Voice of the Process
A time ordered plot of representative sample statistics obtained from an ongoing process (e.g. sample means), used to distinguish between random and nonrandom variability
Control limits
The dividing lines between random and nonrandom deviations from the mean of the distribution
Upper and lower control limits define the range of acceptable variation
Upper control limit = UCL = mean + zσ
Lower control limit = LCL = mean + zσ
MIS 373: Basic Operations Management

20. Variation due to natural causes
Control Chart Example
Variation due to assignable causes
Out of control
UCL
LCL
Mean
Variation due to natural causes
Out of control
| | | | | | | | | | | |
Sample number
Each point on the control chart represents a sample of n observations
MIS 373: Basic Operations Management

21. Errors Type I error Type II error Narrow control limits
Concluding a process is not in control when it actually is.
Manufacturer’s Risk
Type II error
Wide control limits
Concluding a process is in control when it is not.
Consumer’s Risk
Alarm
No Alarm
Process
In-Control
Type I
no-error
Process
Out-of-Control
no-error
Type II
MIS 373: Basic Operations Management

22. Errors Illustration
Q: I always get confused about Type I and II errors. Can you show me something to help me remember the difference?
Source: Effect Size FAQs by Paul Ellis

23. Control Charts UCL  LCL
Out of Control In Control Improved
LCL 
UCL
Every process displays variation in performance: normal or abnormal
Control charts monitor process to identify abnormal variation
Do not tamper with a process that is “in control” with normal variation
Correct an “out of control” process with abnormal variation
Control charts may cause false alarms – too narrow - (or missed signals – too wide) by mistaking normal (abnormal) variation for abnormal (normal) variation
MIS 373: Basic Operations Management

24. Control Charts Data that are measured “x-bar” charts (Mean)
Used to monitor the central tendency of a process.
R charts (Range)
Used to monitor the process dispersion
MIS 373: Basic Operations Management

25. x-bar (sample average) chart Control Limits
𝑥 = 𝑥 𝑥 = 𝜇 𝑥 (= 𝑥 𝑘 )
k = number of samples
𝜎 𝑥 = 𝜎 𝑥 𝑛
n = sample size
𝑈𝐶𝐿 𝑥 = 𝑥 +𝑧 𝜎 𝑥 = 𝜇 𝑥 +𝑧 𝜎 𝑥 𝑛
𝐿𝐶𝐿 𝑥 = 𝑥 −𝑧 𝜎 𝑥 = 𝜇 𝑥 +𝑧 𝜎 𝑥 𝑛
commonly: z = 3
𝑈𝐶𝐿 𝑥 = 𝑥 +3 𝜎 𝑥 = 𝜇 𝑥 +3 𝜎 𝑥 𝑛
𝐿𝐶𝐿 𝑥 = 𝑥 −3 𝜎 𝑥 = 𝜇 𝑥 +3 𝜎 𝑥 𝑛
MIS 373: Basic Operations Management

26. X-bar Chart Mean = 5.5. STD = 0.4 ft 99.74% within ± 3 STD
𝑥 ∓3𝜎=5.5∓3∗0.4=[4.3,6.7]
(random) 9 students {6.5, 6.4, 6.6, 6.3, 6.7, 6.5, 6.6, 6.4, 6.5} each within “normal”  average = 6.5 ft
Sample control limits  tighter than population
UCL= 𝑥 +3 𝜎 𝑛 = =5.9 ft.
GROUP above “normal” (outside control limits)
6.5
4.3
5.1
5.5
5.9
6.7
5.5
MIS 373: Basic Operations Management

27. R-Chart: Control Limits
Range charts or R-charts are used to monitor process dispersion
MIS 373: Basic Operations Management

28. Mean and range charts (a)
These sampling distributions result in the charts below
(Sampling mean is shifting upward but range is consistent)
x-chart
(x-chart detects shift in central tendency)
UCL
LCL
R-chart
(R-chart does not detect change in mean)
UCL
LCL
MIS 373: Basic Operations Management

29. Mean and range charts (b)
These sampling distributions result in the charts below
(Sampling mean is constant but dispersion is increasing)
x-chart
(x-chart does not detect the increase in dispersion)
UCL
LCL
R-chart
(R-chart detects increase in dispersion)
UCL
LCL
MIS 373: Basic Operations Management

30. Run Tests
Even if a process appears to be in control, the data may still not reflect a random process
Analysts often supplement control charts with a run test
Run test
A test for patterns in a sequence
Run
Sequence of observations with a certain characteristic
MIS 373: Basic Operations Management

31. Run Tests A: Above B: Below U: Upward D: Downward
MIS 373: Basic Operations Management

32. Patterns in Control Charts
Normal behavior. Process is “in control.”
UCL
Target
LCL
UCL
Target
LCL
One plot out above (or below). Process is “out of control.”
UCL
Target
LCL
Trends in either direction, 5 plots. Progressive change.
UCL
Target
LCL
Two plots very near lower (or upper) control.
UCL
Target
LCL
Run of 5 above (or below) central line.
UCL
Target
LCL
Erratic behavior.
MIS 373: Basic Operations Management

33. Demo ASQ Control chart template
tools/overview/asq-control-chart.xls

34. Key Points
All processes exhibit random variation. Quality control's purpose is to identify a process that also exhibits nonrandom (correctable) variation on the basis of sample statistics (e.g., sample means) obtained from the process.
Control charts and run tests can be used to detect nonrandom variation in sample statistics. It is also advisable to plot the data to visually check for patterns.
MIS 373: Basic Operations Management