ISS (Statistical Services) Statistics Paper IV: Questions 16 - 19 of 92

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Question 16

Describe in Detail

Essay▾

a) What are control charts for Attributes?

b) A quality control inspector at the Pepsi soft drink company has taken twenty-five samples with four observations each of the volume of bottles filled. If the average range for the twenty-five samples is . 29 ounces and the average mean of the observations is 15.95 ounces, obtain 3- σ control limits for ?

Explanation

a) To measure the quality characteristics, Control charts for attributes are used, that are counted rather than measured. P-charts and C-charts are common types of control charts used to measure the attributes.

P-charts measure the proportion of items in a sample that are defective. For example, proportion of broken eggs and the proportion of cars p…

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Question 17

Describe in Detail

Essay▾

Following data gives the diameter of the rings manufactured by a company. Obtain the control limits for R Chart?

Sample is Given with Observations
Sample No.Observations
15.025.014.944.994.96
25.015.035.074.954.96
34.995.004.934.924.99
45.034.915.014.984.89
54.954.925.035.055.01
64.975.065.064.965.03
75.055.015.104.964.99
85.095.105.004.995.08
95.145.104.995.085.09
105.014.985.085.074.99

Explanation

From the tables, for n = 10, we have ,

Control limits for R chart :

= (0.223) (0.115) = 0.0256

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Question 18

Appeared in Year: 2015

Describe in Detail

Essay▾

Prove that the number of basic variables is a balanced transportation problem is at most , where m is the number of origins and n is the number of destinations.

Explanation

First note that there are in all m + n constraints. We shall show that one of these is redundant so that there are in effect equation in mn variables and hence at most basic variable are there. We note

Summing the m constraints of eq (1) , we get

Summing n-1 constraints of eq (2) , we get

Subtracting eq (4) from eq (3) , we get

Which is the last con…

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Question 19

Describe in Detail

Essay▾

What are control charts for variables? Find 3- σ control limits on the chart. If we are given that μ = 15.95 σ = 0.14 and n = 4 construct control limits for ?

Explanation

Control chart for variables are used to monitor characteristics that can be measured, e. g. length, weight, diameter, time etc. When a record is made of an actual measured quality characteristic like dimension expressed as hundredths of a millimeter, the quality is expressed by variables. For quality control of such data, two types of control chart…

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