ABC Cookie Company takes samples of finished boxes of cookies weighing them to make sure the weight filled stays within the targeted amount. Some variation of course, is to be expected. But too much presents a production issue. Your job is to find out if this process is stable enough to continue. Samples are taken for 20 days. The number of boxes checked each day is 100. The 20 samples measured reveal the following proportions found to have defective weights: Sample Number Of Defectives Proportion Defective 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
ABC Cookie Company takes samples of finished boxes of cookies weighing them to make sure the weight filled stays within the targeted amount. Some variation of course, is to be expected. But too much presents a production issue. Your job is to find out if this process is stable enough to continue.
Samples are taken for 20 days. The number of boxes checked each day is 100. The 20 samples measured reveal the following proportions found to have defective weights:
Sample
Number Of Defectives
Proportion Defective
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
6 0.06 0 0.00 4 0.04
10 0.10 6 0.06 4 0.04
12 0.12 10 0.10 8 0.08 10 0.10 12 0.12 10 0.10 14 0.14 8 0.08 6 0.06 16 0.16 12 0.12 14 0.14 20 0.20 18 0.18
Complete the following:
Calculate the centerline (CL), upper control limit (UCL), and the lower control limit (LCL) for a P- Chart. You can use the Excel template to work through this problem.
Create a control chart, showing the CL, LCL, and UCL. Then plot the 20 data points on the chart. Again, the Excel template can graph the chart for you.
Assess whether the production process is in or out of control.
Tips:
Remember, the LCL can never go below zero.
N = 100, the sample size, not the number of times the inspection occurred.
20 is what you use to compute the center line, or the average of all the defects, which is the sum
of the defects divided the number of times samples were taken (20).
Have your answers and chart available during the practice quiz.
The Correct Answer and Explanation is :
Results:
- Centerline (CL): 0.10
- Upper Control Limit (UCL): 0.19
- Lower Control Limit (LCL): 0.01 (adjusted to 0 since LCL cannot be negative)
Analysis:
The P-chart demonstrates the proportion of defective samples across 20 observations. The green dashed line indicates the centerline, while the red and blue dashed lines represent the UCL and LCL, respectively.
From the chart:
- Points within the control limits suggest the process is stable for those samples.
- Points above the UCL or below the LCL indicate the process may be out of control.
In this case, two points (Samples 19 and 20) exceed the UCL, suggesting potential instability in the process. An investigation is required to determine the root cause (e.g., equipment malfunctions, changes in material quality) before continuing production.
By addressing these issues and maintaining consistency, the process can potentially be brought back under control.