Question

1. Twenty random samples, each containing 6 items, were taken in a control chart application and it was found that the grand average is = 5.240 cm and = 0.25.

a. What would be the upper and lower control limits for the and R charts.

b. The following measurements are taken last week: 5.2, 4.5, 5.5, 3.4, 5.3, and 5.5. Is the process still in control?

Answer 1

Xbarbar= 5.240,

Rbar = 0.25

Answer a: Control limits of Range are

D4 (n=6)=			2.004
D3 (n=6)=			0
control limits for Range,
CL or R-bar= Average of all sample Range			0.250
UCL=R-bar*D4			0.501
LCL=R-bar*D3			0.000

D4 and D3 are taken from the table of factors

Control limits of X bar chart are

A2 (n=6)			0.483
control limits for X bar,
CL or Xbarbar			5.240
UCL=Xbarbar+ (A2)*Rbar			5.361
LCL=Xbarbar- (A2)*Rbar			5.119

A2 is taken from the table of factors

Answer b: the average of new measurement = (5.2+ 4.5+ 5.5+ 3.4+ 5.3+ 5.5)/6= 29.4/6 = 4.9 (it is beyond control limits, therefore not capable)

Range= Max-Min= 5.5-3.4= 2.1 (within Range control limits)