Jim, a quality control manager at an apparel manufacturing company, studies and monitors quality using R-charts. He discovers a quality problem with the construction of zippers. Jim proposes that 25 samples of eight observations each be collected on a daily basis. He plans to prepare an R-chart to monitor the variation in the size of the zippers. The data collected shows that the mean length of the zippers is 15 inches and the average range is 0.5 inches. If D 3 for the R-chart is 0.136, the lower control limit (LCL R) for the R-chart will be:
A) less than or equal to 1.
B) more than 1 but less than or equal to 2.
C) more than 2 but less than or equal to 3.
D) more than 4.

Question

Quizplus · Accepted Answer

To calculate the LCL R for the R-chart, we use the formula LCL R = D 3 x R¯, where D 3 is a constant factor based on the number of observations per sample (in this case, 8), and R¯ is the average range.

Given that D 3 = 0.136 and R¯ = 0.5 inches, we have LCL R = 0.136 x 0.5 = 0.068

Therefore, the lower control limit (LCL R) for the R-chart will be less than or equal to 1, as 0.068 is much less than 1. This suggests that the variation in the size of the zippers is within acceptable bounds.

Jim, a Quality Control Manager at an Apparel Manufacturing Company