Asked by Vonda Simpson on May 20, 2024
Verified
An operator trainee is attempting to monitor a filling process that has an overall average of 705 cc. The average range is 17 cc. If you use a sample size of 6, what are the upper and lower control limits for the x-bar and R chart?
Control Limits
Statistical boundaries within a control chart that distinguish between random variation from the process and variation due to changes in the process.
Average Range
A statistical measure used to establish the central tendency or typical value of a set of numbers, calculated as the difference between the highest and the lowest values in a dataset.
X-bar
Another term for X-bar charts, it represents the mean value in a set of data as part of statistical quality control processes.
- Advance in calculating and interpreting the thresholds and capabilities of processes within various control chart models including X-bar, R-chart, p-chart, and c-chart.
- Implement three-sigma benchmarks to evaluate process control.
- Ascertain the average and standard deviation for subsets and the entirety of processes.
Verified Answer
GG
GNIOT Group of InstitutionsMay 24, 2024
Final Answer :
From table, A2 = 0.483, D4 = 2.004, D3 = 0
UCL xˉ\bar xxˉ = xˉ\bar xxˉ + A2 ∗ Rˉ\bar RRˉ LCL xˉ\bar xxˉ = xˉ\bar xxˉ - A2 ∗ Rˉ\bar RRˉ UCLR = D4 ∗ Rˉ\bar RRˉ = 705 + 0.483 × 17 = 705 - 0.483 ∗ 17 = 2.004 ∗ 17
= 713.211 = 696.789 = 34.068
LCLR = D3 ∗ Rˉ\bar RRˉ = 0 ∗ 17
= 0
UCL xˉ\bar xxˉ = xˉ\bar xxˉ + A2 ∗ Rˉ\bar RRˉ LCL xˉ\bar xxˉ = xˉ\bar xxˉ - A2 ∗ Rˉ\bar RRˉ UCLR = D4 ∗ Rˉ\bar RRˉ = 705 + 0.483 × 17 = 705 - 0.483 ∗ 17 = 2.004 ∗ 17
= 713.211 = 696.789 = 34.068
LCLR = D3 ∗ Rˉ\bar RRˉ = 0 ∗ 17
= 0
Learning Objectives
- Advance in calculating and interpreting the thresholds and capabilities of processes within various control chart models including X-bar, R-chart, p-chart, and c-chart.
- Implement three-sigma benchmarks to evaluate process control.
- Ascertain the average and standard deviation for subsets and the entirety of processes.