A manufacturer of components for automobile transmissions wants to use control c

ID: 3121824 • Letter: A

Question

A manufacturer of components for automobile transmissions wants to use control charts to monitor a process producing a shaft. The resulting data from 20 samples of 7 shaft diameters that have been measured are: sigma^2_i=1 0x_i = 10.375, sigma^2_i=1 0Ri = 1.012 a) Find the control limits that should be used on the control charts. b) Estimate the process mean and standard deviation. A company manufacturing oil seals wants to establish x- R control charts on the process. There are 25 preliminary samples of size 5 on the internal diameter of the seal. The summary data (in mm) are as follows sigma^2_i = 1 5x_i = 1253.75, sigma^2_i = 1 0 R_i = 14.08 a) Find the control limits that should be used on the control charts. b) Estimate the process mean and standard deviation.

Explanation / Answer

Back-up Theory

1.Grand Average, xdouble bar = (sum of xi bar over i)/k

2.Average Range, R bar = (sum of Ri over i)/k

3.LCL (Lower Control Limit) for x bar chart: x double bar - (A2).(R bar)

4.UCL (Upper Control Limit) for x bar chart: x double bar + (A2).(R bar)

5.LCL (Lower Control Limit for R chart): (D3).(R bar)

6.UCL (Upper Control Limit) for R chart: (D4).(R bar)

7.Estimate of Standard Deviation, = R bar/d2

8.Values of A2, D3, D4 and d2 are available in Table of Control Chart Constants

Now, to work out solution,

Given k = 20; n = 7; sum(Xibar) = 10.375; sum(Ri) = 1.012.

From Control Chart Constants Table, for n =7,

A2 = 0.419; D3 = 0.076; D4 = 1.924; d2 = 2.704

Part 1(a)

Xdouble bar = 10.375/20 = 0.51875 Rbar = 1.012/20 = 0.0506

LCL (Lower Control Limit) for x bar chart: x double bar - (A2).(R bar) = 0.49745

UCL (Upper Control Limit) for x bar chart: x double bar + (A2).(R bar) 0.53995

LCL (Lower Control Limit for R chart): (D3).(R bar) = 0.00385

UCL (Upper Control Limit) for R chart: (D4).(R bar) = 0.09735

ANSWER

Part 1(b)

Estimate of process mean = Xdouyble bar = 0.51875

Estimate of process standard deviation = Rbar/d2 = 0.01869