Question

Customer expectations on pizza delivery are such that most people are happy with a 20 minute delivery and very upset if it takes more than 40 minutes. You have observed the delivery time for a random sample of customers for two days as follows:

Day        1              2              3              4              5              6              7              8              9              10

1              12           23           22           28           34           10           55           20           37           41

2              32           23           27           35           12           48           40           21           35           30

Answer the following questions pertaining to this data (hint: irst calculate the mean and thee standard deviation of this data)

1. Competition is really cut-throat and in an effort to improve service delivery quality, one proposal calls for disciplining and/or reprimanding the delivery person(s) who takes more than 40 minutes for delivery. What do you think about the proposal?
2. What is the appropriate measure of process capability here: Cp or Cpk?/ Why?
3. What is the capability of the process? Is a control chart useful for this situation? Why or why not?
4. Suggest the upper and lower control limits of a control chart that would monitor the pizza delivery process?
5. How would you use this control chart?
6. Suggest at least three process/quality improvement efforts that are appropriate given the above data and observations.

Answer 1

1. Mean & Standard Deviation

Customer	Day 1	Day 2	Mean & Std. Dev.
1	12	32
2	23	23
3	22	27
4	28	35
5	34	12
6	10	48
7	55	40
8	20	21
9	37	35
10	41	30
Mean	28.20	30.30	29.25
Std. Dev.	13.82	10.22	2.55

Excel Formula Sheet:

Customer	Day 1	Day 2	Mean & Std. Dev.
1	12	32
2	23	23
3	22	27
4	28	35
5	34	12
6	10	48
7	55	40
8	20	21
9	37	35
10	41	30
Mean	=AVERAGE(B2:B11)	=AVERAGE(C2:C11)	=AVERAGE(B12:C12)
Std. Dev.	=STDEV(B2:B11)	=STDEV(C2:C11)	=STDEV(B13:C13)

2. Competition is really cut-throat and in an effort to improve service delivery quality, one proposal calls for disciplining and/or reprimanding the delivery person(s) who takes more than 40 minutes for delivery. What do you think about the proposal?

I accept, in any business delivery on time and customer satisfaction plays a key role in sales and profit. One who takes more than 40 min can never satisfy a customer, so reprimanding the delivery person(s) is advisable.

3. What is the appropriate measure of process capability here: Cp or Cpk?/ Why?

Customer	Day 1	Day 2	Mean & Std. Dev.
1	12	32
2	23	23
3	22	27
4	28	35
5	34	12
6	10	48
7	55	40
8	20	21
9	37	35
10	41	30
Mean	28.20	30.30	29.25
Std. Dev.	13.82	10.22	2.55
Upper Limit	55	48
Lower Limit	10	12
Potential Cp	0.543	0.587
Actual Cpk Index	0.439	0.597

Excel Formula sheet:

Customer	Day 1	Day 2	Mean & Std. Dev.
1	12	32
2	23	23
3	22	27
4	28	35
5	34	12
6	10	48
7	55	40
8	20	21
9	37	35
10	41	30
Mean	=AVERAGE(B2:B11)	=AVERAGE(C2:C11)	=AVERAGE(B12:C12)
Std. Dev.	=STDEV(B2:B11)	=STDEV(C2:C11)	=STDEV(B13:C13)
Upper Limit	=MAX(B2:B11)	=MAX(C2:C11)
Lower Limit	=MIN(B2:B11)	=MIN(C2:C11)
Potential Cp	=(B14-B15)/(6*B13)	=(C14-C15)/(6*C13)
Actual Cpk Index	=ABS(MIN((B14-B12)/(3*B13), (B15-B12)/(3*B13)))	=ABS(MIN((C14-C12)/(3*C13), (C15-C12)/(3*C13)))

4. What is the capability of the process? Is a control chart useful for this situation? Why or why not?

The capability of the process is less than its actual potential: Cp < Cpk

5. Suggest the upper and lower control limits of a control chart that would monitor the pizza delivery process?

	LCL	Delivery Time	UCL
Day 1-1	20	12	40
Day 1-2	20	23	40
Day 1-3	20	22	40
Day 1-4	20	28	40
Day 1-5	20	34	40
Day 1-6	20	10	40
Day 1-7	20	55	40
Day 1-8	20	20	40
Day 1-9	20	37	40
Day 1-10	20	41	40
Day 2-1	20	32	40
Day 2-2	20	23	40
Day 2-3	20	27	40
Day 2-4	20	35	40
Day 2-5	20	12	40
Day 2-6	20	48	40
Day 2-7	20	40	40
Day 2-8	20	21	40
Day 2-9	20	35	40
Day 2-10	20	30	40

6. How would you use this control chart?

I would enumerate how many delivery took more than 40 min, how many delivery took less than 20 min and how many delivery took time between 20-40 min.

7. Suggest at least three process/quality improvement efforts that are appropriate given the above data and observations.

• Process standardization.
• Pre-prepared pizzas for faster processing and delivery.
• FIFO technique.