vdoc

Chapter 19: B. Statistical Process Control 265
LCL = R 3sˆ
R
= R
3d R 3
d
d
3
=
1 3
d
R
= DR
3
2
2
(19.13)
where the values of D 3 and D 4 for various sample sizes are given in
Appendix E. The first implementation of control charts is referred
to as phase I. In phase I, it is important that we calculate the
preliminary control limits. The preliminary control limits are
calculated to find the extent of variation in sample means and sample
ranges if the process is stable. In other words, at this point, only
common causes would be affecting the process. If all of the plotted
points fall within the control limits and there is no evidence of any
pattern, then it means the control limits are suitable for the current
or future process. However, if some points exceed the control limits,
then such points are ignored and every effort is made to eliminate
any evident special causes that may be present in the process. Then
fresh control limits are calculated by using the remaining data and
the whole process is repeated again. Remember that ignoring the
points that exceed the control limits without eliminating the special
causes may result in unnecessarily narrow control limits, which may
cause different kinds of headaches such as putting points beyond
the control limits when, in fact, they should not be. Furthermore, it is
highly recommended that for preliminary control limits, we use at
least 25 samples of size four or five. Otherwise, the control limits may
not be suitable for the current and future process.
Part IV.B.3
EXAMPLE 19.4
Table 19.3 provides the data on the diameter measurements of ball bearings used in
the wheels of heavy construction equipment. Twenty five samples each of size four
are taken directly from the production line. Samples come from all three shifts and no
sample contains data from two or more shifts. Use this data to construct an X – and R
chart and to verify that the process is stable.
Solution:
From Appendix E for sample of size n = 4, we have D 3 = 0, and D 4 = 2.282. Thus, the
control limits for the R chart are
LCL = DR
3
= 0× 0.
03479 = 0
UCL = DR= 2. 282× 0. 03479 = 0.07936.
4
Continued