Question

Sample mean control charts can be created using:

I. the process standard deviation

II. the standard deviation of the sampling distribution

III. the sample range

IV. the average of sample ranges

Select one:

a. II or III

b. I or III

c. I or II

d. I or II or IV

e. II or IV

Answer 1

Answer:

The correct answer to the given question would be an Option d

Reason/Explanation:

Either of the following formulas can be used in order to find the control limits of Mean Chart:

(i) Using the Average Range:

CL = Average Mean (X=)

UCL = (X=) + (A2 * R-)

LCL = (X=) - (A2 * R-)

Where,

A2 = The value derived from the table of control chart constants for the subgroup size

R- = Average Range Value (Note: Sample Range = Max Observation Value - Min Observation Value for a Particular Sample)

(Ii) Using the Process Standard Deviation:

CL = Average Mean (X=)

UCL = (X=) + 3 (Sigma)

LCL = (X=) - 3 (Sigma)

Where. Sigma = Process Std Dev / SQRT (Sample Size)

(iii) Using the Standard Deviation of the Sampling Distribution:

CL = Average Mean (X=)

UCL = (X=) + 3 σ

LCL = (X=) - 3 σ

Where, σ = Standard Deviation of the Sampling Distribution

As per the above discussion, either of the average range, standard deviation of the sampling distribution or the process standard deviation can be used in order to find the control limits of the Mean Chart, hence, we conclude that the correct answer to the given question is option d.

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