1. Dimensions of Quality

2. Recall: What is Quality?
Quality - fitness for use
Conformance to specifications
Ability to satisfy needs
Does it do what we want it to do?

3. Garvin’s Dimensions of Quality
Performance - Will the product do its job?
Does it complete the task
Will it do the job better than others?
Ex: Car - Better gas mileage
Reliability - How often will the product fail?
Ex: Car – Does it start? Does it break down on the highway?

4. Garvin’s Dimensions of Quality
Durability - How long does the product last?
Ex: Watch battery - does it fail after a few weeks?
Serviceability - How is easy is the product to repair?
How much does it cost to repair?

5. Garvin’s Dimensions of Quality
Aesthetics - What does the product look like?
Does it look cool?
Packaging (e.g. differentiate brands of soda)

6. Garvin’s Dimensions of Quality
Features - What does the product do?
Ex: Cell phone is also a camera
Perceived Quality - What is the reputation of the company or its product?
History

7. Garvin’s Dimensions of Quality
Conformance to Standards - Is the product made exactly as the designer intended?
Ex: Does jump drive fit in USB connection?

8. Product Characteristics
Each product has unique characteristics that are important to the consumer

9. Think about it… Choose a product
List characteristics that might be important when considering its quality

10. Product Characteristics
Each product has unique characteristics that are important to the consumer:
Physical (e.g. length, weight, voltage)
Sensory (e.g. appearance, color, taste)
Time orientation (e.g. reliability, durability, serviceability)

11. Product manufacturing
What goes into quality?
Product design
Products are typically designed with the dimensions of quality in mind.
Product manufacturing
Creation of the product
Does the product conform to specifications?
However, materials used to make a product can vary, as well as the degree to which employees carry out the specifications  

12. Alternate definition of quality
Quality can also be defined in terms of variability- a high quality product has low variability about the target value for a specific characteristic.
What the users of the product notice is the variability about the target.
Quality improvement is then reduction of variability in processes and products.

13. The role of statistics in quality improvement
Since variability can only be described in statistical terms, statistical methods play a role in quality improvement efforts.

14. Terminology Target value – desired value of a characteristic
Specification limits – range of values that characteristic can take on before it becomes unusable
USL – upper specification limit
largest allowable value
 LSL – lower specification limit
Smallest allowable value

15. Terminology Non-conforming – does not meet specifications
Product may still function
Defects – serious non-conformity
An area of non-conformance
A defective product has one or more defects that are serious enough to significantly affect the safe or effective use of the product.

16. Statistical Methods for quality control
Acceptance Sampling
Sample incoming or outbound components
Inspection of only a sample of items
This process can give hints that something is wrong, as too many defectives in a sample could be an indication that the process is not functioning properly

17. Statistical methods for quality control
Statistical process control (SPC)
Control charts, plus other problem-solving tools
Useful in monitoring processes, reducing variability through elimination of assignable causes
On-line technique
Plots averages of measurements of a quality characteristic through time
The chart has a center line (the target) and upper and lower control limits

18. Statistical methods for quality control
Designed experiments (DOE / DOX)
Controllable inputs (e.g. temperature, pressure) are varied to determine their effect on the process
Variables that have a large effect are the most important to monitor
Process optimization
This technique is carried on off-line

19. Management aspects of quality improvement
Quality planning – identify customers and their needs. Then products that meet or exceed their expectations must be developed.
Quality assurance – activities such as documentation of the procedures of the system to help ensure that quality is maintained.
Quality control and improvement – acceptance sampling, statistical process control, designed experiments

20. Deming
Leader in the revolution
Pushed statistical methods

21. Deming’s 14 points
Create constancy of purpose toward improvement (a long range plan)
2. Adopt a new philosophy that rejects poor workmanship, defective products, or bad service
3. Cease reliance on mass inspection to improve quality. Improve the process

22. Deming’s 14 points
4. End the practice of awarding business to suppliers the basis of price alone. Consider quality.
5. Improve the system of production and service constantly.
6. Institute modern training methods

23. Deming’s 14 points
7. Improve leadership, recognizing that the aim of supervision is helping people and equipment to do a better job 8. Drive out fear so that people feel free to ask questions and point out problems. 9. Break down barriers between departments

24. Deming’s 14 points
10. Eliminate slogans, targets and numerical goals for the workforce such as “zero defects.” The targets can be counterproductive without a plan to achieve them.
11. Eliminate numerical quotas and work standards. Quality should be considered, along with an effective plan to manage the work process.
12. Remove barriers (listen to suggestions, comments and complaints of workers; value their ideas)

25. Note that the 14 points are about change
Deming’s 14 points
13. Institute a vigorous program of education (for quality control procedures)
Put everyone to work to accomplish the transformation, beginning with top management.
Note that the 14 points are about change

26. Deming’s seven deadly diseases of management
Lack of constancy of purpose
Focus on short-term profits
Performance evaluation encourages rivalries, fear, and discouragement
Job hopping of managers
Managing by visible figures alone (defects, customer complaints, profits)
Excessive medical expenses
Liability and excessive damage awards

27. Recall: Distribution
Overall pattern of how often possible values occur (consider: shape, location, variability, if there are any deviations).
Famous probability distributions:
Binomial, Normal, t, F, Chi-square

28. Recall: Distribution Why bother with the probability distribution?
Idea: Use a mathematical model to answer questions about a distribution
If the model fits, we just need the model
Don’t need the entire histogram

29. Normal Distribution Good model for many situations
Many natural variables follow normal distribution
Good for modeling the sums of many small effects
Ex: Score of an exam with many problems, a sample mean
There are many mathematical models that we can use, in this course we will examine one that is useful in many situations. This model is called the normal distribution. The normal distribution is a good model for many situations. It is often a good model for a histogram that results form the sums of many small effects. For example if we have the score of an exam that has many problems then it might be well modeled by a normal distribution. We also see that many natural variables follow a normal distribution such as heights of adults, measurement errors in astronomy and many other things. More importantly for this course is that the normal distribution is a good model for the variability that we see in sample statistics.

30. Normal Distribution: Properties
Symmetric
mean = median
Bell shaped (mound shaped)
Center determined by mean 
Standard deviation determines spread 
Almost all of probability within 3 standard deviations
* Know  and  => know everything about distribution
The general characteristics of a normal distribution are that it is symmetric. So the mean would be equal to the median. It is bell shaped which means it is higher in the center and trails off on both sides. Its center is determined by the mean “mu” and the spread is determined by the standard deviation. In fact if we know the mean and standard deviation we know everything about the distribution. We can answer any questions we might have about the distribution.

31. Normal Distribution µ-3σ µ µ+3σ
When we look at the normal distribution we see the general outline of a histogram that is highest in the center and drops off on each end. We see that this distribution is symmetric and mound shaped.
µ-3σ
µ+3σ

32. Getting Probabilities:
Old way: tables (see Appendix II)
“New” way: computer/calculator
Not sure how on your calculator?
Google it. 

33. Example
The scores on a standardized math test have a normal distribution with a mean of 430 and a standard deviation 40. Janice scored a What percentage of students scored less than her?
In the previous sessions we saw how we could answer questions about variables that had a normal distribution if we knew the standard score of an individual. In this section we combine things together to see how to answer questions about raw values that come from a normal distribution
Lets consider an example that again deals with the standardized math test. The scores on a standardized math test have a normal distribution with a mean of 430 and a standard deviation Janice scored a What percentage of students scored less than her?

34. Example: Scores, µ = 430, σ = 40
Janice scored a What percentage of students scored less than her?
It is often helpful to look at a diagram of what is going on. We can draw our normal distribution on the original scale centered at 430 with standard deviation 40. We can also draw this on the standard normal scale with mean 0 and standard deviation 1. Notice how both graphs are essentially the same but with the scales changed.

35. Example: Scores, µ = 430, σ = 40
Janice scored a What percentage of students scored less than her?
We want to know the percentage below Janice. So these are to the left of the line. However, if we look at the table the table does not give us this probability.
89.4%

36. Example: Scores, µ = 430, σ = 40 Pr(X < 480) = 0.89435
89.4% of students scored below Janice
Calculator notes:
Found using normalcdf() function
TI-83/84 path: 2nd -> VARS -> normalcdf( -> ENTER
Syntax:
normalcdf(LowerBound, UpperBound, Mean, StdDev)
Our example: normalcdf(-E99, 480, 430, 40)
So we find that 89.44% of students scored less than Janice. Again without having a complete histogram but by just knowing the mean, standard deviation and the fact that the shape followed the normal distribution we could answer questions about the distribution and know what percent were below Janice.

37. Example
A company produces bottles of cleaning fluids that have a maximum capacity of 700ml.
Two machines that fill the bottles with cleaning fluid.
Machine 1: normally distributed with a mean of 600ml with a standard deviation of 10 ml
Machine 2: normally distributed with a mean of 640ml and a standard deviation of 10 ml

38. Example: Bottles, Machine 1: N(600, 10), Machine 2: N(640, 10)
We find a bottle that has 629 ml in it. Which machine do you think it came from? Pick either machine 1 or machine 2 and explain.

39. Example: Bottles, Machine 1: N(600, 10), Machine 2: N(640, 10)

40. Example: Bottles, Machine 1: N(600, 10), Machine 2: N(640, 10)
629

41. Example: Bottles, Machine 1: N(600, 10), Machine 2: N(640, 10)
629

42. Binomial Distribution
Good model when we are counting the number of successes in n trials 

43. Binomial Distribution
Assumptions
1. n independent trials
2. Each trial has two possible outcomes (success or failure)
3. Probability of success (p) same for all trials
The random variable X is the number of successes observed in the n trials

44. Binomial Distribution
Getting Probabilities from the Binomial Dist.:

45. Binomial Distribution
Getting Probabilities from the Binomial Dist.:

46. Binomial Distribution
Getting Probabilities from the Binomial Dist.: (Given values for n & p, calculate probabilities for various values of x)

47. Example
Suppose that 90% of all batteries from a certain supplier have acceptable voltages. A certain type of flashlight requires two type-D batteries, and the flashlight will work only if both of its batteries have acceptable voltages. In ten randomly selected flashlights, what is the probability that at least nine will work?
(What assumptions will you make?)

48. Let X = the number of flashlights that work
Ex: Flashlight needs 2 batteries to work. Select 10 flashlights; find probability at least 9 work.
Let X = the number of flashlights that work
Want to calculate P(X≥9) using Binomial dist.
n =
p =

49. Let X = the number of flashlights that work
Ex: Flashlight needs 2 batteries to work. Select 10 flashlights; find prob. at least 9 work.
Let X = the number of flashlights that work
Want to calculate P(X≥9) using Binomial dist.
n = 10
p =

50. Let X = the number of flashlights that work
Ex: Flashlight needs 2 batteries to work. Select 10 flashlights; find prob. at least 9 work.
Let X = the number of flashlights that work
Want to calculate P(X≥9) using Binomial dist.
n = 10
p = P(success)

51. Let X = the number of flashlights that work
Ex: Flashlight needs 2 batteries to work. Select 10 flashlights; find prob. at least 9 work.
Let X = the number of flashlights that work
Want to calculate P(X≥9) using Binomial dist.
n = 10
p = P(success) = P(flashlight works)

52. Let X = the number of flashlights that work
Ex: Flashlight needs 2 batteries to work. Select 10 flashlights; find prob. at least 9 work.
Let X = the number of flashlights that work
Want to calculate P(X≥9) using Binomial dist.
n = 10
p = P(success) = P(flashlight works)
= P(both batteries work) = (0.9)(0.9) = 0.81
Implicit assumption here: whether or not the batteries have acceptable voltages is independent from one battery to the next

53. There is a 40.7% chance that at least 9 flashlights will work.
Ex: Flashlight needs 2 batteries to work. Select 10 flashlights; find prob. at least 9 work.
So:
𝑃 𝑋≥9 =𝑃 𝑋=9 +𝑃 𝑋=10
= 10! 9!1! ! 10!0!
= =0.407
There is a 40.7% chance that at least 9 flashlights will work.