SCENARIO 19-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic.Accordingly,the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.

-Referring to Scenario 19-3,suppose the analyst constructs an x̄ chart to see if the production process is in-control.What is the lower control limit (LCL)for this chart?
A)47.60
B)56.15
C)57.15
D)58.05

Question

SCENARIO 19-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic.Accordingly,the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.

-Referring to Scenario 19-3,suppose the analyst constructs an x̄ chart to see if the production process is in-control.What is the lower control limit (LCL)for this chart?
A)47.60 
B)56.15 
C)57.15 
D)58.05

Quizplus · Accepted Answer

To calculate the lower control limit (LCL) for an x̄ chart, we use the formula:
LCL = X̄ - A2(R̅)
where X̄ is the average of all sample means, A2 is a constant based on the sample size (in this case, 10), and R̅ is the average of all sample ranges.

From the data provided in the scenario, we can calculate:
X̄ = 58.1 (average of all 140 sample means)
R̅ = 4.26 (average of all 140 sample ranges)
A2 = 0.577 (from the control charts constants table)

Plugging in these values to the formula, we get:
LCL = 58.1 - 0.577(4.26) = 56.15

Therefore, the lower control limit (LCL) for the x̄ chart is 56.15, which corresponds to choice (B).

SCENARIO 19-3 A Quality Control Analyst for a Light Bulb Manufacturer Is