Question

1. Set up three-sigma control limits with the given data. Determine the following:

a. The center line of the chart
b. Lower and upper control limits
c. Develop a p chart

2. Is the process in control? If the observations are within control limits, does that guarantee that the process variation contains only randomness?

3. Based on your analysis what is the problem?

4. What advice would you give to Larraine based on the information that you now have?

5. Larraine’s last remark was “we can’t be Motorola with Six Sigma quality, but let’s try for three sigma”. Based on this argument, describe the concept of Six Sigma quality and how does it differ from continuous improvement’s PDSA?. Why is such a high quality level important?

Note: please attach to your deliverable your calculations on an MS Excel file

Bills Incorrect Number of Day نرا نو ذرا ذرا نا نا نا نا Bills Incorrect Number of Day UT UT Ui a UI UT A w w Bills Incorrect Number of

Answer 1

1.

Central line	2.833333
3-sigma value	1.601793
UCL	4.435126
LCL	1.23154

2.

Day	Number of incorrect bills	Fraction defective
1	2	0.066666667
2	2	0.066666667
3	1	0.033333333
4	2	0.066666667
5	2	0.066666667
6	3	0.1
7	2	0.066666667
8	2	0.066666667
9	1	0.033333333
10	2	0.066666667
11	1	0.033333333
12	2	0.066666667
13	3	0.1
14	3	0.1
15	2	0.066666667
16	3	0.1
17	2	0.066666667
18	2	0.066666667
19	1	0.033333333
20	3	0.1
21	3	0.1
22	3	0.1
23	3	0.1
24	4	0.133333333
25	5	0.166666667
26	5	0.166666667
27	6	0.2
28	5	0.166666667
29	5	0.166666667
30	5	0.166666667

p-chart
Central line	0.094444
3 sigma limits	0.160179
UCL	0.254624
LCL	0

P Chart of Number of incorrect bills UCL 0.2546 0.25 0.20 0.15 0.10 P= 0.0944 W 0.05 LCL=0 0.00 7 13 16 19 25 28 Sample 22 10 Proportion

No there is a gathering at the proximity of the central line, indicating presence of assignable causes.

3.

P Chart Diagnostic for Number of incorrect bills Binomial Probability Plot Ratio of observed variation to expected variation 75.8% 95% Upper Limit for ratio if process P is constant = 159.8 % Using a P chart should not result in an elevated false alarm rate. The upper limit depends on the number of subgroups, the average subgroup size, and the overall process P.

Hence Larraine's information may not be required.

5.

Six Sigma is a statistical term used to measure the number of defects that processes create. The term implies high-quality performance because a process performing at a Six Sigma level allows only 3.4 defects per one million opportunities.

The higher the sigma level the better the quality of the product or service and the fewer the defects. Organizations with a Six Sigma quality have an advantage over others who perform at three, four or even five sigma levels.

Let’s make Six Sigma performance non-theoretical, and consider a real-life example.

Suppose that a bank’s new accounts department processes 360,200 applications per year (about 1,000 every day), and that there were nine different ways for each application to be processed incorrectly. Different sigma levels of quality would lead to the following number of defects.

Three Sigma quality – This level of performance produces a defect-free product 93.32% of the time. 770 applications would be processed incorrectly and would require rework every day.

High quality level is important for the betterment of the process