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Question:Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows:

Sample number	Readings
1	1010	991	985	986
2	995	996	1009	994
3	990	1003	1015	1008
4	1015	1020	1009	998
5	1013	1019	1005	993
6	994	1001	994	1005
7	989	992	982	1020
8	1001	986	996	996
9	1006	989	1005	1007
10	992	1007	1006	979
11	996	1006	997	989
12	1019	996	991	1011
13	981	991	989	1003
14	999	993	988	984
15	1013	1002	1005	992

Develop an x-chart and an R-chart and plot the values. From the charts, what comments can you make about the process? (Use three-sigma control limits as in Exhibit 13.7.)

Step by step solution

01

Definition of X- -chart and R-chart

$\stackrel{-}{x}$ and R- (range) charts are widely utilized in statistical process control. In statistical process monitoring (SPM), $\stackrel{-}{x}$- chartand R-chart could be a style of the scheme, popularly called control chart, used to monitor the mean and range of normally distributed variables simultaneously, when samples are collected at regular intervals from a business or process. It's often used to monitor the variables data but the performance of the$\stackrel{-}{x}$- chartand R chart may suffer when the normality assumption is not valid. This can be connected to traditional statistical quality control (SQC) and statistical process control (SPC).

02

Explanation

Calculations for X- Bar and R- Bar chart:

X- Bar chart

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