Question

Which of the following is true of special cause variation? a. It cannot be detected using statistical methods. b. It occurs sporadically and can be prevented. c. It cannot be explained or understood. d. It accounts for about 80 to 95 percent of the observed variation in a process.

Which of the following is the upper control limit for a c-chart (UCL c) with the average number of nonconformances per unit equal to 7? a. More than 14 but less than or equal to 15 b. More than 11 but less than or equal to 12 c. More than 12 but less than or equal to 13 d. More than 13 but less than or equal to 14

The time taken for guests to check out at a hotel front desk was measured over the course of several weeks. The management believes that the target time for checking out guests should be between 2 and 3 minutes with a target of 2.5 minutes. The data gathered for the actual process had a mean time of 2.75 minutes with a standard deviation of 0.45 minutes. The process capability index will be: a. more than 3 but less than or equal to 5. b. less than or equal to 1. c. more than 4 but less than or equal to 5. d. more than 5.

The lower and upper specification limits for a mustard filling machine are 10.50 and 12.00 ounces, respectively. The standard deviation is 0.05. The process capability index of the machine will be: a. more than 4 but less than or equal to 5. b. less than or equal to 3. c. more than 5. d. more than 3 but less than or equal to 5.

Answer 1

1. Correct choice is option (b) It occurs sporadically and can be prevented.

2. UCL = u + 3(u/n) = 7 + 37 = 14.93

Hence, correct choice is Option (a) More than 14 but less than or equal to 15

3. Process capability index is the minimum of the below 2 values:

CP_k = Min ((UCL - Mean) / 3(standard deviation), (Mean - LCL) / 3(standard deviation))

= Min ((3-2.75/ 3* 0.45), (2.75 - 2/ 3 *0.45)) = Min (0.185, 0.556) = 0.185

Hence, correct choice is Option (b) less than or equal to 1

4. CP_k = Min ((UCL - Mean) / 3(standard deviation), (Mean - LCL) / 3(standard deviation))

= Min ((12-11.25/ 3* 0.05), (11.25 - 10.50/ 3 *0.05)) =5

Hence, Correct choice is (a) more than 4 but less than or equal to 5