Asked by Abdullah Elalami on Apr 26, 2024
Verified
The defect rate for a product has historically been about 1.6%. What are the upper and lower control chart limits for a p-chart, if you wish to use a sample size of 100 and 3-sigma limits?
Defect Rate
The proportion of manufactured items that do not meet the prescribed quality standards.
Control Chart Limits
the pre-determined upper and lower boundaries on a control chart within which a process is considered to be in control and performing as expected.
P-chart
A type of control chart used in statistical quality control to monitor the proportion of defective units in a process.
- Carry out computations and offer interpretations of control limits and process capabilities in different types of control charts, specifically X-bar, R-chart, p-chart, and c-chart.
- Enforce three-sigma guidelines to assess control within process operations.
Verified Answer
BN
Braden NobleApr 28, 2024
Final Answer :
UCLp =
pˉ\bar ppˉ + 3 pˉ(1−pˉ)n\sqrt { \frac{\bar p(1-\bar p)}{n}}npˉ(1−pˉ) = 0.016 + 3 ∙ (0.016∗0.984)/100\sqrt { ( 0.016 * 0.984 ) / 100 }(0.016∗0.984)/100 = .0536
UCLp =
pˉ\bar ppˉ - 3 pˉ(1−pˉ)n\sqrt { \frac{\bar p(1-\bar p)}{n}}npˉ(1−pˉ) = 0.016 - 3 ∙ (0.016∗0.984)/100\sqrt { ( 0.016 * 0.984 ) / 100 }(0.016∗0.984)/100 = 0.0216, or zero
pˉ\bar ppˉ + 3 pˉ(1−pˉ)n\sqrt { \frac{\bar p(1-\bar p)}{n}}npˉ(1−pˉ) = 0.016 + 3 ∙ (0.016∗0.984)/100\sqrt { ( 0.016 * 0.984 ) / 100 }(0.016∗0.984)/100 = .0536
UCLp =
pˉ\bar ppˉ - 3 pˉ(1−pˉ)n\sqrt { \frac{\bar p(1-\bar p)}{n}}npˉ(1−pˉ) = 0.016 - 3 ∙ (0.016∗0.984)/100\sqrt { ( 0.016 * 0.984 ) / 100 }(0.016∗0.984)/100 = 0.0216, or zero
Learning Objectives
- Carry out computations and offer interpretations of control limits and process capabilities in different types of control charts, specifically X-bar, R-chart, p-chart, and c-chart.
- Enforce three-sigma guidelines to assess control within process operations.