Question

One of New England​ Air's top competitive priorities is​ on-time arrivals. Quality VP Clair Bond decided to personally monitor New England​ Air's performance. Each week for the past 30​ weeks, Bond checked a random sample of 100 flight arrivals for​ on-time performance.

Sample ​(week)	Late Flights	Sample ​(week)	Late Flights
1	3	16	2
2	2	17	1
3	11	18	13
4	11	19	2
5	2	20	1
6	1	21	3
7	8	22	19
8	6	23	3
9	11	24	1
10	0	25	3
11	2	26	2
12	3	27	0
13	2	28	1
14	2	29	4
15	7	30	4

a)   Using a 95% confidence level, plot the overall percentage of late flights ( p ) and the upper and lower control limits on a control chart.

b)   Assume that the airline industry’s upper and lower control limits for flights that are not on time are .1000 and .0400, respectively. Draw them on your control chart.

c)   Plot the percentage of late flights in each sample. Do all samples fall within New England Air’s control limits? When one falls out-side the control limits, what should be done?

d)   What can Clair Bond report about the quality of service?

(Please Screen shot the Excel if its in excel

Answer 1

Answer:

Sample ​(week)	Late Flights		Percent of defective	Pbar
1	3	100	0.0300	0.0430
2	2	100	0.0200	0.0430
3	11	100	0.1100	0.0430
4	11	100	0.1100	0.0430
5	2	100	0.0200	0.0430
6	1	100	0.0100	0.0430
7	8	100	0.0800	0.0430
8	6	100	0.0600	0.0430
9	11	100	0.1100	0.0430
10	0	100	0.0000	0.0430
11	2	100	0.0200	0.0430
12	3	100	0.0300	0.0430
13	2	100	0.0200	0.0430
14	2	100	0.0200	0.0430
15	7	100	0.0700	0.0430
16	2	100	0.0200	0.0430
17	1	100	0.0100	0.0430
18	13	100	0.1300	0.0430
19	2	100	0.0200	0.0430
20	1	100	0.0100	0.0430
21	3	100	0.0300	0.0430
22	19	100	0.1900	0.0430
23	3	100	0.0300	0.0430
24	1	100	0.0100	0.0430
25	3	100	0.0300	0.0430
26	2	100	0.0200	0.0430
27	0	100	0.0000	0.0430
28	1	100	0.0100	0.0430
29	4	100	0.0400	0.0430
30	4	100	0.0400	0.0430

Answer:a

The given confidence interval of 95% corresponds to the 1.96 value.
Hence,
UCLp-bar= P + 1.96*σ p-bar
LCLp-bar= P - 1.96*σ p-bar

Proportion of defects=P	total defectives/total observations	0.043
Q=	1-P	0.957
N=	average sample size	100
Standard deviation, σp-bar	squareroot(P*Q/N)	0.020
UCLp-bar=	P + 1.96*σ p-bar	0.0828
LCLp-bar=	P - 1.96*σ p-bar	0.0032

Answer b


UCLp-bar= 0.1000
LCLp-bar= 0.0400

then

Answer c

Sample ​(week)	Late Flights		Percent of defective
1	3	100	3%
2	2	100	2%
3	11	100	11%
4	11	100	11%
5	2	100	2%
6	1	100	1%
7	8	100	8%
8	6	100	6%
9	11	100	11%
10	0	100	0%
11	2	100	2%
12	3	100	3%
13	2	100	2%
14	2	100	2%
15	7	100	7%
16	2	100	2%
17	1	100	1%
18	13	100	13%
19	2	100	2%
20	1	100	1%
21	3	100	3%
22	19	100	19%
23	3	100	3%
24	1	100	1%
25	3	100	3%
26	2	100	2%
27	0	100	0%
28	1	100	1%
29	4	100	4%
30	4	100	4%
Total	130	3000

As we can see in the chart above with the information provided to us, there are 5 instances where the % of late flights is above the UCL limit for the firm. and 5 instances where the % of late flights is above the UCL limit of the industry.
Hence not all % percentage of late flights fall within the firm's control limits.

In such a case, the airline should investigate and find out the best corrective action and implement it as early as possible.

Answer d:

Clair Bond needs to report that the airline is faling to meets its own quality standards (in terms of punctuality) and is also failing to meets the quality standards of the industry.