The x-bar and R values for 20 samples of size five are shown in the following table

August 30, 2017

Question
The x-bar and R values for 20 samples of size five are shown in the following table. Specifications on this product have been established as 0.550 ± 0.02.

Sample Number

Xbar

R

1

0.549

0.0025

2

0.548

0.0021

3

0.548

0.0023

4

0.551

0.0029

5

0.553

0.0018

6

0.552

0.0017

7

0.55

0.002

8

0.551

0.0024

9

0.553

0.0022

10

0.556

0.0028

11

0.547

0.002

12

0.545

0.003

13

0.549

0.0031

14

0.552

0.0022

15

0.55

0.0023

16

0.548

0.0021

17

0.556

0.0019

18

0.546

0.0018

19

0.55

0.0021

20

0.551

0.0022

Construct a modified control chart with three sigma limits, assuming that if the true process fraction non conforming is as large as 1%, the process is unacceptable.

Suppose that if the true process fraction nonconforming is as large as 1%, we would like an acceptance control chart to detect this out of control condition with probability 0.90. Construct this acceptance control chart and compare it to the chart obtained in part (a).

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