Question

Is the process in control? Discuss by constructing the mean and range charts.

Observation Number Sample # mln 10.1 9.7 10.1 9.9 10.4 10.6 9.5 10.7 9.8 10.1 9.8 10.3 9.2 10.5 10.9 9.9 9.9 10.0 10.4 9.9 10

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Answer #1

n (Sample size) = 5

FACTORS FOR R CHARTS Number of Observations in Subgroup, Factor for X Chart, Lower Control Limit Upper Control Limit, A2 D3 D

A2 = 0.58, D3 = 0, D4 = 2.11

Mean = Average of observation for each sample

Range = Maximum value - Minimum value

Sample 1 2 3 4 5 Mean Range
1 10.1 10.6 9.8 9.9 10.9 10.26 1.1
2 9.7 9.5 10.3 9.9 10.5 9.98 1
3 10.1 10.7 9.2 10 10.1 10.02 1.5
4 9.9 9.8 10.5 10.4 10.1 10.14 0.7
5 10.4 10.1 10.9 9.9 10.3 10.32 1

X-bar = Average of Mean value = (10.26+9.98+10.02+10.14+10.32)/5 = 10.14

R-bar = Average of Range value = (1.1+1+1.5+0.7+1)/5 = 1.06

Mean chart:

UCL = X-bar + A2*R-bar = 10.14 + 0.58*1.06 = 10.75

LCL = X-bar - A2*R-bar = 10.14 - 0.58*1.06 = 9.53

Range cahrt:

UCL = D4*R-bar = 2.11*1.06 = 2.24

LCL = D3*R-bar = 0*1.06 = 0

Process is not in control as few values are out of range of Mean chart. Example: Sample 1 Observation 5, Sample 3 Observation 3 etc.

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