1. Quality

2. Quality Overview Importance of quality
In this class, we are concerned about:
Attributes
Acceptance Sampling
Statistical Process Control

3. Acceptance sampling --- Single Sample
Acceptable Quality Level
Probability of False Rejection
Lot Tolerance Percent Defective
Probability of Accepting a bad batch
Sample Size
Rejection Cutoff
Operating Characteristics for a given n and c give the probability of acceptance for a batch as a function of actual quality.

4. Process Control Common Causes Special Causes Don't react to noise
Plot Values, if points are ``significantly'' away from the mean, adjust the process. (e.g. outside )
Similar chart for variability
for defectives, or other non-continuous attributes

5. How To Make X-Bar Charts for groups of size n
Collect 50 to 100 or more values (75 is a good number).
Estimate the standard deviation from the values using the square root of the sample variance. We will use the symbol σ (called sigma) for the standard deviation.
Make a chart for the group means with a line for the mean of the means and for one, two and three times away from the mean of the means.
(Typically, n will be on the order of 5 or 7.)
Continue to collect data and each time $n$ points have been collected, compute their mean and plot it on the chart.

6. How To Interpret X-Bar Charts
We want to know if the process is in control. The opposite question is ``Has anything unusual happened lately?''. Sometimes ``no'‘ is more important than a yes answer because it avoids over control.
We want to detect fundamental changes in the process.
We also want to detect ``special occasions.''

7. How To Interpret X-Bar Charts (cont.)
We say that something unusual has probably happened when one of the following is true (from Duncan's book):
one or more points are outside the three sigma ( ) limits,
one or more points are very close to the three sigma limit,
there is a run of seven or more points (a run can be either all increasing or decreasing, or all on one side of the mean),
two points in a row outside the two sigma limits,
four points in a row outside the one sigma limits,
cycles or other non-random patterns...

8. R, s Charts
Same thing, but track spread.

9. Uses of Control Charts To know when things have changed
To adjust or repair equipment.
To reward workers who improve.
To find out why things have gotten worse.
To avoid reacting to randomness
To avoid adjusting a machine when it is inherently variable
To avoid premature reactions to worker performance
To understand the nature of processes and to see process improvements
item The two and three sigma limits on a control chart can tell you what tolerance can be held by a process
As these are moved in, the process is becoming more predictable. As know, there are benefits associated with predictable processes.

10. Changes
If changes for the worse have occurred, corrective action should be taken.
After changes and/or corrective action, new control limits should be computed for the process.
Are there some motivational aspects?

11. Process Capability Indices
Centered: Specification Width 6 sigma
Noncentered: Narrower Half width 3 sigma
Note that ``6 sigma” is a PC index of 2 (not 1)
Images ,graph

12. Control Charts
Remember, these can be used for almost anything that can be quantified and measured such as volume of business, diameter of bolts, hours of work, transactions processed, customers served per hour, etc.
We must be careful to get homogeneous groupings if possible.
Try to avoid inter-group correlations.
If there are a large number of values, all of them do not need to be included in the chart; they can be sampled.
Use p-charts to track number of defects (these are interpreted much the same way as R-Charts).

13. Discussion Topics Bottleneck issues? iso 9000, 9001
``line certification'‘
6 sigma