# Purdue University Quality Control and PM Excel Worksheet

6-1. ABC, Inc., is a manufacturer of hydraulic machine tools. It has had a history leakage trouble resulting from a certain critical fitting. Twenty five samples of machined parts were selected, one per shift, and the diameters of the fitting was measured. Ignore the last set of data.

See attachments to access the data:

Required:

(a). Construct x-bar- and R-charts for the data. What do you observe?

(b). If the regular machine operator was absent when samples 4, 8, 14, 22 were taken, how will the results in part (a) be affected? Hint: Remove those samples and Reconstruct the charts.

6-2. Using the data provided for for a sample of 100 items, prepare a p-chart and explain whether the process is in statistical control.

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7-1. Consider the following problem:

For computations, use Excel. For drawing, you can utilize Excel or Word. Refer to the Solved Problem example for some hints. Feel free to utilize Excel QM or QM for Windows to verify your answers.

Tom Marcus, a director of personnel at Management Resources, Inc., is in the process of designing a program that its customers can use in the job-finding process. Some of the activities include preparing resumes, writing letters, making appointments to see prospective employers, researching companies, and industries, and so on. Necessary information on the activities is shown in the following table:

 DAYS ACTIVITY o (otimistic) p (pessimistic) m (most likely) IMMEDIATE PREDECESSORS A 4 6 5 – B 2 8 5 – C 5 9 7 A D 4 6 5 A E 2 6 4 B F 3 9 6 B G 10 12 11 C, E H 7 9 8 D, F

Required:
(a). Construct a network for this problem.
(b). Compute the expected time for each activity, also the variance. Note: Expected time = (optimistic time + pessimistic time + 4 * most likely)/6. Variance = (pessimistic – optimistic)^2/36.
(c). Determine ES, EF, LS, LF, and slack for each activity.
(d). Determine the critical path and project completion time. Also the standard deviation for the completion time. Note: To compute the standard deviation of the project completion time, you need to sum the variances of the the critical path activities, and then take the square root of that sum.
(e). Determine the probability that the project will be finished in 23 days or less.
(f). Determine the probability the the project will NOT be finished in 26 days or less.
(g). Determine the probability that the project will be finished in 25 days or less.
(h). If a manager considers crashing any of the tasks to reduce the duration of the project completion time, which tasks should he/she focus on? Why?

7-2.

A. A new shopping mall is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed.

(i). Find the probability that the employee is idle.

(ii). Find the proportion of the time that the employee is busy.

(iii). Find the average number of people receiving and waiting to receive information.

(iv). Find the average number of people waiting in line to get information.

(v). Find the average time a person seeking information spends at the desk.

(vi). Find the expected time a person spends just waiting in line to have a question answered

B. Suppose that the desk employee earns \$10/hour. The cost of waiting time, in terms of customer unhappiness with the mall, is \$12/hour of time spent waiting in line. Find the total expected costs over an 8-hour day. HINT: Total costs = cost of waiting and service charge.

C. Suppose that if an additional employee is hired, the cost of waiting time will be \$6. The cost of waiting time to receive service will be reduced by half. Should a new employee be hired? Show the new total cost and justify.

Please use Excel QM, I have shared the link below to install the excel feature and book is also in the same link