TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds)is too erratic and adversely affects expected profits.The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours.The sample mean and range for each hour are listed below. She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds,respectively.
-True or False: It is not possible for the chart to be out-of-control when the R chart is in control.

Question

TABLE 18-4
A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds)is too erratic and adversely affects expected profits.The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours.The sample mean and range for each hour are listed below.  She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds,respectively.
-True or False: It is not possible for the  chart to be out-of-control when the R chart is in control.

Quizplus · Accepted Answer

It is possible for the X chart to be out-of-control even if the R chart is in control. The R chart only measures the variability within each subgroup, while the X chart measures the average values across subgroups. Therefore, if there is a shift in the mean value of the process, it may cause the X chart to be out-of-control even if the R chart is in control.

TABLE 18-4 A Factory Supervisor Is Concerned That the Time It Takes