Statistical Quality Control-Control Charts (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 2 of 2

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Question number: 1

» Statistical Quality Control » Control Charts » Attributes

Appeared in Year: 2014

Essay Question▾

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 Equation

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

Equation

Equation

Equation

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

Control limits for the U chart is

Equation

Equation

Equation

Question number: 2

» Statistical Quality Control » Control Charts » Variable

Appeared in Year: 2015

Essay Question▾

Describe in Detail

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

(i) Find the control limit for the Equation 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 Equation and Equation

(i) For Equation chart, the control limits are

Equation

Equation

Equation

Equation

Equation

Equation

Equation

For R chart, the control limits are

Equation

Equation

Equation

Equation

Equation

Equation

Equation

(ii) UCL = 26.40 + 0.50 = 26.90

LCL = 26.40 - 0.50 = 25.90

Equation

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