# Statistical Quality Control (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 5 of 5

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## Question number: 1

» Statistical Quality Control » Sequential Sampling Plans

Appeared in Year: 2015

### Describe in Detail

Distinguish between the single sampling plan and double sampling plan. Discuss how the O. C curves can be used for comparing two sampling plans.

### Explanation

A single sampling plan in which a decision about the acceptance or rejection of a lot is based on one sample that has been inspected where double sampling plan when a decision about the acceptance or rejection of a lot has not been reached after single sample inspection from a submitted lot, a decision will always be reached when the second sampl

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## Question number: 2

» Statistical Quality Control » Control Charts » Attributes

Appeared in Year: 2014

### Describe in Detail

Find 3-sigma control limits for a

(i) C-chart with process average equal to 4 non-conformities

(ii) U chart with process average c = 4, and n = 4.

### Explanation

the 3-sigma control limits is

(i) Given that

Control limits for the C chart with a known non-conformities is

(ii) Given that c = 4 and n = 4

Control limits for the U chart is

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## Question number: 3

» Statistical Quality Control » Concepts of ATI

Appeared in Year: 2015

### Describe in Detail

For a sequential probability ratio test of strength (α, β) and stopping bounds are A and B (B < A), show that A ≤ 1-β/α and B ≥ β/1-α

### Explanation

Let X= (X _{1}, …, X _{k}) and also let E _{k} be the set of all points in k dimensional Euclidean space R _{k}, for which we reject H _{0} using the sequential probability ratio test. Also, let F _{k } be the set of all points in R _{k} for which we accept H _{0}. Notice that (E _{k}, k = 1,2, …) are mutually disjoint and (F _{k}, k = 1,2, …) are also mutually disjoint. Assu

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## Question number: 4

» Statistical Quality Control » Sequential Sampling Plans

Appeared in Year: 2015

### Describe in Detail

To test the hypothesis against for the distribution

Develop the sequential probability ratio test.

### Explanation

Let x _{1}, x _{2}, …, x _{n} are independently and identically distributed with distribution is

Let type I and type II errors are defined as

P (rejecting the lot when θ=θ _{0}) =α

P (accpeting the lot when θ=θ _{1}) =β

Under H _{0} and H _{1} the pmf is

Thus the likelihood ra

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## Question number: 5

» Statistical Quality Control » Control Charts » Variable

Appeared in Year: 2015

### Describe in Detail

Sample of sizes n = 5 are taken from a manufacturing process every hour. A quality characteristic is measured, and and R are computed for each sample. After 25 samples have been analyzed, we have and . Assume that the quality characteristic is normally distributed.

(i) Find the control limit for the and R charts.

(ii) Assume that both chart exhibit control, if specifications are 26.40±0.50, estimate the fraction nonconforming. Express your answers in terms of CDF of N (0,1) random variable.

[For n = 5, A _{2} =0.577, A = 1.342, A _{3} =1.427, D _{1} =0, D _{2} =4.918, D _{3} =0, D _{4} =2.115 and d _{2} =2.326]

### Explanation

Given that and

(i) For chart, the control limits are

For R chart, the control limits are

(ii) UCL = 26.40 + 0.50 = 26.90

LCL = 26.40 - 0.50 = 25.90

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