Math Problem Solver

SECTION B (Solve the quality questions below and draw the necessary graphs as well)

The customers of a pizza delivery shop expect their pizzas to be delivered within 25 to 35 minutes. In order to improve its customer service levels, the shop collected past data on delivery times and found that the average delivery time was 27 minutes with a standard deviation of 3 minutes. What is the Six Sigma quality level of this pizza delivery process and the percentage of late deliveries?

X and R Charts

The time to make beds at a motel should fall into an agreed-on range of times. A sample of four maids was selected, and the time needed to make a bed was observed on three different occasions:

Service Time, Sec.

Maid Sample 1 Sample 2 Sample 3

Ann 120 190 150

Linda 130 110 140

Marie 200 180 175

Michael 165 155 140

a. Determine the upper and lower control limits for an X-chart and an R-chart with a sample size of four.

b. Is this process stable or not?

P-charts

Several complaints recently have been sent to the Gotham City police department regarding the increasing incidence of congestion on the city’s streets. The complaints attribute the cause of these traffic tie-ups to a lack of synchronization of the traffic lights. The lights are controlled by a main computer system, and adjusting this program is costly. Therefore, the controllers are reluctant to change the situation unless a clear need is shown.

During the past year, the police department has collected data at 1,000 intersections. The data were compiled on a monthly basis as shown below:

Month Congestion Incidence

January 14

February 18

March 14

April 12

May 16

June 18

July 19

August 12

September 14

October 17

November 10

December 18

a. Construct a p-chart based on the above data.

b. Should the system be modified if, during the next 3 months, reports of congestion at these 1,000 intersections are 15 , 9 and 11.

C-chart

• King’s Court Hotel, in its ongoing efforts to improve its service to its guests, is planning to develop a c-chart to monitor the number of customer complaints it receives each day. The data collected is large enough to assume it is normally distributed.

• Data on customer complaints for 20 days were collected and are given in the next slide.

Days 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Number of complaints 4 3 4 5 2 3 7 2 4 5 3 5 6 3 2 1 5 2 3 5

1. Use the data to construct a c-chart to determine if the customer service guest improvement program is stable or not

2. What target value (in terms of six-sigma) is accepted or can be considered as acceptable if King’s hotel averages about 120 customers per day. Use a z-value of 3.