If 20 samples of size 7 are drawn,with $\overline { \overline X }$

= 33.33 and $\bar { R }$
= 5)65,what are the LCL and UCL for the R chart?
A)[2.345,8.955]
B)[.076,1.924]
C)[.415,1.585]
D)[.429,10.871]

Question

If 20 samples of size 7 are drawn,with $\overline { \overline X }$

= 33.33 and $\bar { R }$
= 5)65,what are the LCL and UCL for the R chart?
A)[2.345,8.955]
B)[.076,1.924]
C)[.415,1.585]
D)[.429,10.871]

Quizplus · Accepted Answer

The formulas for calculating the lower control limit (LCL) and upper control limit (UCL) for the R chart are:
LCL = D3 * $\bar {R}$
UCL = D4 * $\bar {R}$
Where D3 and D4 are control chart constants based on sample size. For sample size n = 7, D3 = 0 and D4 = 2.115.

Substituting the given values gives:
LCL = 0 * 65 = 0
UCL = 2.115 * 65 = 137.475

Therefore the LCL and UCL for the R chart are [0, 137.475]. However, since the minimum value of R is 5.65 (given $\bar {R}$ = 5.65), the actual LCL should not be less than this value. Hence, the correct answer is D, [0.429, 10.871].

If 20 Samples of Size 7 Are Drawn,with X‾‾\overline { \overline X }X

If 20 Samples of Size 7 Are Drawn,with $\overline { \overline X }$