Question

Which of the following statements about the upper and lower control limits of a control chart is true?

Group of answer choices

The upper and lower control limits for a p chart depend on the sample size.

The lower control limit of a p chart will ALWAYS be a negative value.

The upper control limit of an X-bar chart does NOT depend on the average range R-bar.

The upper and lower control limits of an R chart are always the SAME distance from R-bar.

Answer 1

Answer:

The option which is true is “The upper and lower control limits for a p chart depend on the sample size”

Because,

UCL= p bar+3σ

LCL = p bar-3σ

p bar is mean or average of the proportions

n is Sample size

Standard Deviation (σ) = √[p bar * (1- p bar)]/n

UCL and LCL are dependent on Standard deviation.

And Standard deviation is dependent on n which is observations of all sample size.

Also Standard deviation is also dependent on p bar (which is dependent on the average proportions % of all samples).

Hence the upper and lower control limits for a p chart depend on the sample size.

The other statements are false:

• The lower control limit of a p chart will ALWAYS be a negative value.

FALSE

Because,

LCL = p bar-3σ

It is not always negative because if p bar is bigger than 3σ, then the LCL value can be positive.

• The upper control limit of an X-bar chart does NOT depend on the average range R-bar.

FALSE

Because,

In X bar chart,

UCL = X double bar + A2*R bar

Thus, upper control limit of an X-bar chart depends on the average range R-bar.

• The upper and lower control limits of an R chart are always the SAME distance from R-bar.

FALSE

Because,

UCL = D4*R bar

LCL = D3*R bar

Since UCL and LCL depends on D4 and D3 respectively and are not always same, so upper and lower control limits of an R chart are NOT always the SAME distance from R-bar.