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MIE364H1S
Methods of Quality Control and Improvement
Course Instructor: Prof. V. Makis
Tutorial #3
1.
A quality characteristic is monitored by a control chart designed so that the
probability that a certain outofcontrol condition will be detected on the first
sample following the shift to that state is 1
β
. Find the following:
a.
The probability that the outofcontrol condition will be detected on the
second sample following the shift.
b.
The probability that the outofcontrol condition will be detected on the k
th
sample following the shift.
c.
The expected number of subgroups analyzed before the shift is detected.
d.
The probability that the first sample following the shift produces a statistic
that plots inside the control limits.
e.
The probability that the shift is not detected on a sample.
f.
The probability that two consecutive samples produce statistics that plot
outside of the control limits.
g.
The probability that at least one of the next k samples yields values of the
test statistic that plot outside the control limits.
2.
An
X
chart with 3sigma control limits has parameters as follows:
UCL = 20.5
LCL = 19.5
Construct an OC curve for the chart.
3.
An
X
chart with 3sigma control limits is used to monitor a manufacturing
process. The process mean (
µ
) and standard deviation (
σ
) are given as 23.51 and
1.8344, respectively. Samples of size n = 5 are taken from the process every hour.
a.
Suppose the process mean shifts to 22 while the standard deviation
remains constant. Find the average run length for the chart.
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 Spring '10
 Makis

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