Question

A manager is in a tizzy and asks if you can construct an Individuals/Moving Range control chart for the data he provided, treating each data point as an independent measurement taken sequentially.

In addition, he wants an estimate of process capability for a specification of 74.000 ± 0.015 using this set of charts.

Table 5-3 Inside Diameter Measurements (mm) for Automobile Engine Piston Rings Sample Number Observations 2 3 4 5 6 7 8 9 10

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Answer #1

The control limits are:

Sample size 5
Number of samples 20
Mean Range
Upper Control Limit, UCL 74.01401 0.04725
Center 74.00111 0.02235
Lower Control Limit, LCL 73.98821 0.00000

The control charts are:

Control Chart for the Mean 74.020 74.015 74.01401 74.010 74.005 74.000 74/00111 Sample Mean 73.995 73.990 73.98821 73.985 73.

Control Chart for the Range 0.04725 0.050 0.045 0.040 0.035 0.030 Sample Range 0.025 Www 0.02235 0.020 0.015 0.010 0.005 0.00

The process is in statistical control.

Process capability index = minimum((74.00111- 73.98821)/(3*0.001006) , (74.01401 - 74.0011)/(3*0.001006)) = 4.274

74.03 74.002 74.019 73.992 74.008
73.995 73.992 74.001 74.011 74.004
73.988 74.024 74.021 74.005 74.002
74.002 73.996 73.993 74.015 74.009
73.992 74.007 74.015 73.989 74.014
74.009 73.994 73.997 73.985 73.993
73.995 74.006 73.994 74 74.005
73.985 74.003 73.993 74.015 73.988
74.008 73.995 74.009 74.005 74.004
73.998 74 73.99 74.007 73.995
73.994 73.998 73.994 73.995 73.99
74.004 74 74.007 74 73.996
73.983 74.002 73.998 73.997 74.012
74.006 73.967 73.994 74 73.984
74.012 74.014 73.998 73.999 74.007
74 73.984 74.005 73.998 73.996
73.994 74.012 73.986 74.005 74.007
74.006 74.01 74.018 74.003 74
73.984 74.002 74.003 74.005 73.997
74 74.01 74.013 74.02 74.003
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