Question

Hello , Can someone answer these questions

Q1: 60 units were found defective in 50 samples of 120 units each, construct the control chart for this situation, i.e. the control limits using Z=3 for the percentage of defects and for the number of defects? Would the results be different? Why? How would you as an operations manager use the upper control limit with your customers?

Q2: In a manufacturing process for product X, there are several causes for poor quality. A frequency distribution of the defects is as follows:

Defect cause

1

2

3

4

5

6

7

8

9

10

No. of defects

2

23

97

6

102

12

4

9

5

7

Use Pareto analysis to show the major causes of defects.

Answer 1

1)

Control chart for the percentage of defects (p-Chart)

From the data values,

The control limits are obtained using the following formula,

and

Control chart for the number of defects (c-Chart)

The c chart is used to calculate the control limit for the number of defects.

The control limits are defined as,

where = mean number of defects in the sample,

Conclusion:

The p-chart is used to estimate the percentage of defects while the c chart is used to estimate the number of defects hence the result will be different.

The p-chart is used when the sample size is variables while the c-chart is used when the sample size is fixed. In this situation, the sample size is fixed hence the c-chart will be appropriate.

2)

The Pareto chart is obtained in excel by following these steps,

Step 1: Write the data values in excel in decreasing order.

Defect cause	No. of defects
5	102
3	97
2	23
6	12
8	9
10	7
4	6
9	5
7	4
1	2
Total	267

Step 2: The cumulative frequency is obtained by adding the current and immediate previous frequency.

Step 3: Select No. of defects, and Cumm. Freq (%) columns then goto INSERT > Recommended Charts > Combo > Clustered Column - Line on Secondary Axis. The screenshot is shown below,

The chart is obtained. The screenshot is shown below,

Conclusion:

From the Pareto Chart, we can see that approximately 80% of the defects are due to the cause 5 and 3 which means 80% of the poor quality arises from cause 5 and cause 3.