STAT702 Industrial and Business Analytics

Assignment Two

Attempt ALL questions. Total 80 marks (30% overall)

Produce your answers as a single word document with imported charts from R where appropriate.

Due: Monday May 25th

Question One (24 marks)

(a) Calculate the parameters of the mean and range chart (including warning lines) for filling cans

of pineapple pieces by ensuring the following:

(i) The specification limits are 400 and 415 grams.

(ii) Assume fills follow a Normal distribution.

(iii) Samples of six filled cans of pineapple pieces are to be selected every 15 minutes and the

mean and range calculated for each.

(iv) The process capability index Cp is to be set at 1.33.

(b) How would your answers in (a) change if CP was reduced to 1.0?

(c) Using the parameters calculated in (a), construct a mean and a range chart for the cans of

pineapple pieces.

(d) Production output was compared to the charts constructed in (c) using the following data

from 20 samples of six filled cans:

Sample

Mean

Sample

Range

Sample

Mean

Sample

Range

(g) (g) (g) (g)

407 7 405 5

408 5 405 4

407 6 407 5

408 4 406 3

409 8 408 3

409 9 407 2

406 5 409 4

405 4 408 5

407 7 408 4

406 5 407 5

Plot these points on your charts. Are there any indicator(s) for action? If so, specify each one

and suggest a possible remedy for each.

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Question Two (10 marks)

We wish to compare the weights of 36 count trays of kiwifruit from three growers A, B and C. The

weight specifications for export trays, in order to gain a maximum return for the grower, are that the

weight of a 36 count tray be: 3.4 kg 0.4 kg. Statistical Process Control (S.P.C.) analyses done by the

packing house have indicated that the weights of packed kiwifruit were in statistical control when

packed from these growers. Random samples of packed trays from these growers yielded the

following:

Grower Mean kg Std Dev kg

A 3.40 0.14

B 3.55 0.04

C 3.30 0.03

Which grower’s would you recommend for export? Explain your logic and show any calculations

that you make to back up your recommendation. What assumption is required about the

weights in order to make your calculations valid? (10)

Question Three (8 marks)

The annual demand for Brand B toothpaste from a warehouse is 30,000 tubes with the demand

occurring at a constant rate throughout the year. The cost of manufacture is $1.20 per tube which is

the purchase price paid by the warehouse. The cost of the warehouse placing each order is $15

regardless of the size of the order. The cost of holding one tube in inventory for one year is 18 cents.

This cost is calculated from the stock insurance and warehouse rental costs.

(a) Find the optimum order quantity of Brand B toothpaste for the warehouse. (2)

(b) What is the time between orders using the order quantity in (a)? (1)

(c) Find the total annual warehouse inventory costs for Brand B toothpaste. (2)

(d) Assuming orders don’t arrive instantaneously; find what the reorder level should be set at

by the warehouse to allow for a lead time of 2 weeks. (1)

(e) Assume that the demand for the toothpaste doesn’t occur at a constant rate throughout

the year. If the warehouse sticks to using the order quantity calculated in (a), what

problem (s) do you envisage for the warehouse. Justify your answer. (2)

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Question Four (4 marks)

Suppose the demand for a certain brand of hair conditioner is normally distributed with mean 700

units per week and a standard deviation of 35 units per week. What should the reorder level be set at

in order to ensure that all demand during the standard lead time of three weeks can be met 95% of

the time? Assume that the demand for the hair conditioner occurs independently from one week to

the next. (4)

Question Five (12 marks)

Choose any product of interest that you haven’t seen in the notes.

Describe how you would perform a capability study by relating each of the six steps of a capability

study to your product. (12)

Question Six (6 marks)

A quality analyst is checking the process capability associated with the filling process of cheesecakes.

Twenty five samples of size 4 were taken. From these samples, the mean weight was calculated as

513.5g and the mean range calculated as 31g. The specification limits were 515g 20g. Calculate

6 , C p and C pk Interpret your values. (6)

Question Seven (16 marks)

A wholesaler decides to operate an inventory system which permits backorders for his most popular

12cm by 8cm by 10 cm plastic storage box. He estimates that the cost of these backorders in terms of

lost future sales is $0.76 per box per annum. However the cost of holding a storage box in inventory

for one year is higher than this, because of the insurance and air-conditioning charges. He estimates

that this holding cost is $1.54 per box per annum. The demand for this particular storage box is at a

constant rate which is known to produce a total annual demand of 25,000 boxes. The cost of any order

is $55.

For this inventory system having an optimum ordering policy;

Find the optimum order quantity.

Find the maximum level of stock.

Find the optimum time between orders.

What proportion of time is the wholesaler “out-of-stock” and consequently having to take

backorders?

Find the total annual inventory cost.

Sketch a graph showing the first two inventory cycles.