Download Quality - david l. woodruff

Quality
Quality Overview
• Importance of quality
• In this class, we are concerned about:
– Attributes
– Acceptance Sampling
– Statistical Process Control
Acceptance sampling --- Single Sample
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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.
Process Control
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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
3 )
• Similar chart for variability
• for defectives, or other non-continuous attributes
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
 n 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.
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.''
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 ( 3 )
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...
R, s Charts
Same thing, but track spread.
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.
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?
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)
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).
Discussion Topics
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Bottleneck issues?
iso 9000, 9001
``line certification'‘
6 sigma