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 sample mean and range data were based on 11 observations per day instead of 10.How would this change affect the lower and upper control limits of the R chart?
A)LCL would increase;UCL would decrease.
B)LCL would remain the same;UCL would decrease.
C)Both LCL and UCL would remain the same.
D)LCL would decrease;UCL would increase.

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 sample mean and range data were based on 11 observations per day instead of 10.How would this change affect the lower and upper control limits of the R chart?
A)LCL would increase;UCL would decrease. 
B)LCL would remain the same;UCL would decrease. 
C)Both LCL and UCL would remain the same. 
D)LCL would decrease;UCL would increase.

Quizplus · Accepted Answer

The control limits for the R chart are calculated using the formula:
LCL = D3 R̄
UCL = D4 R̄
where D3 and D4 are constants based on the sample size, and R̄ is the average range across all samples. As the sample size increases from 10 to 11, the value of D3 increases while the value of D4 decreases. Since the lower control limit (LCL) is directly proportional to D3 and the upper control limit (UCL) is directly proportional to D4, the LCL would increase and the UCL would decrease. Therefore, choice A is the correct answer.

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