MBA Operations Management - Case Study Guides - 6S: BAYFIELD MUD COMPANY

 BAYFIELD MUD COMPANY

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1. The first thing that must be done is to develop quality control
limits for the sample means. This can be done as follows. Because
the process appears to be unstable, we can use the desired mean as
the nominal line. Desired x = 50.0,  = 1.2 (from past results of
Wet-Land Drilling),   x     / 1.2 6 1.2 / 2.45 0.489. n At
a 99.73% confidence interval Z = 3:
3 50 3 0.489 50 1.47 51.47
3 50 1.47 48.53
X x
X x
UCL X
LCL X
 
       
    
Now that we have appropriate control limits, these must be
applied to the samples taken on the individual shifts:
Day Shift*
Time Ave Low High Ave Low High Ave Low High
6:00 49.6 48.7 50.7 48.6 47.4 52.0 48.4 45.0 49.0
7:00 50.2 49.1 51.2 50.0 49.2 52.2 48.8 44.8 49.7
8:00 50.6 49.6 51.4 49.8 49.0 52.4 49.6 48.0 51.8
9:00 50.8 50.2 51.8 50.3 49.4 51.7 50.0 48.1 52.7
10:00 49.9 49.2 52.3 50.2 49.6 51.8 51.0 48.1 55.2
11:00 50.3 48.6 51.7 50.0 49.0 52.3 50.4 49.5 54.1
12:00 48.6 46.2 50.4 50.0 48.8 52.4 50.0 48.7 50.9
1:00 49.0 46.4 50.0 50.1 49.4 53.6 48.9 47.6 51.2
Evening Shift
Time Ave Low High Ave Low High Ave Low High
2:00 49.0 46.0 50.6 49.7 48.6 51.0 49.8 48.4 51.0
3:00 49.8 48.2 50.8 48.4 47.2 51.7 49.8 48.8 50.8
4:00 50.3 49.2 52.7 47.2 45.3 50.9 50.0 49.1 50.6
5:00 51.4 50.0 55.3 46.8 44.1 49.0 47.8 45.2 51.2
6:00 51.6 49.2 54.7 46.8 41.0 51.2 46.4 44.0 49.7
7:00 51.8 50.0 55.6 50.0 46.2 51.7 46.5 44.4 50.0
8:00 51.0 48.6 53.2 47.4 44.0 48.7 47.2 46.6 48.9
9:00 50.5 49.4 52.4 47.0 44.2 48.9 48.4 47.2 49.5
Night Shift
Time Ave Low High Ave Low High Ave Low High
10:00 49.2 46.1 50.7 47.2 46.6 50.2 49.2 48.1 50.7
11:00 49.0 46.3 50.8 48.6 47.0 50.0 48.4 47.0 50.8
12:00 48.4 45.4 50.2 49.8 48.2 50.4 47.2 46.4 49.2
1:00 47.6 44.3 49.7 49.6 48.4 51.7 47.4 46.8 49.0
2:00 47.4 44.1 49.6 50.0 49.0 52.2 48.8 47.2 51.4
3:00 48.2 45.2 49.0 50.0 49.2 50.0 49.6 49.0 50.6
4:00 48.0 45.5 49.1 47.2 46.3 50.5 51.0 50.5 51.5
5:00 48.4 47.1 49.6 47.0 44.1 49.7 50.5 50.0 51.9
* Boldfaced type indicates a sample outside the quality control limits.
(a) Day shift (6:00 A.M.–2:00 P.M.):
Number of means within control limits 23
96%
Total number of means 24
 
(b) Evening shift (2:00 P.M.–10:00 P.M.):
Number of means within control limits 12
50%
Total number of means 24
 
(c) Night shift (10:00 P.M.–6:00 A.M.):
Number of means within control limits 12
50%
Total number of means 24
 
As is now evident, none of the shifts meet the control specifications. Bag weight monitoring needs improvement on all shifts.
The problem is much more acute on the evening and night shifts
staffed by the more recent hires.
Note also, that the number of samples indicating a “short
weight” is much greater than the number indicating excess weight.
With regard to the range, 99.73% of the individual bag
weights should lie within 3 of the mean. This would represent a
range of 6, or 7.2. Only one of the ranges defined by the difference between the highest and lowest bag weights in each sample
exceeds this range. Alternatively: D4 × Sample range  UCLR and
D2 × Sample range  LCLR. This is dangerous if the process is out
of control, but the mean range for the first shift is 3.14 (the lowest
of any shift) and D4 × 3.14  6.28 and D3 × 3.14  0. A range of
0 to 6.28 compares favorably with 7.2, with only two values
exceeding the range limit. It would appear, then, that the problem
is not due to abnormal deviations between the highest and lowest
bag weights, but rather to poor adjustments of the bag weightfeeder causing assignable variations in average bag weights.
LO S6.3: Build x-bar charts and R-charts
AACSB: Analytical thinking
2. The proper procedure is to establish mean and range charts
to guide the bag packers. The foreman would then be alerted
when sample weights deviate from mean and range control limits.
The immediate problem, however, must be corrected by additional
 





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