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ETM 319 /Assignment 3 /SPC - Statistical Process Control

1- What are chance and assignable causes of variability? What part do they play in the operation and interpretation of a Shewhart control chart

2- Consider the control chart shown here. Does the pattern appear random?

3- Is the average run length performance of a control chart a more meaningful measure of performance than the type I and type II error probabilities? What information does ARL convey that the statistical error probabilities do not?

4- A manufacturer of component for automobile transmissions wants to use control charts to monitor a process producing a shaft. The resulting data from 20 samples of 4 shaft diameters that have been measured are:

(a) Find the control limits that should be used on the control charts. and x R

(b) Assume that the 20 preliminary samples plot in control on both charts. Estimate the process mean and standard deviation.

5- The data shown in Table 6E.2 are x and R values for 24 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345).

(a) Set up x and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits.

(b) If specifications on this diameter are 0.5030+/- 0.0010, find the percentage of nonconforming bearing produced by this process. Assume that diameter is normally distributed.

6- The data shown in Table 6E.4 are the deviations from nominal diameter for holes drilled din a carbon-fiber composite material used in aerospace manufacturing. The values reported are deviations from nominal in ten-thousandths of an inch.

(a) Set up x and R charts on the process. Is the process in statistical control?

(b) Estimate the process standard deviation using the range method.

(c) If specifications are at nominal  100, what can you say about the capability of this process? Calculate the PCR Cp.

7- Samples of n = 4 items are taken from a process at regular intervals. A normally distributed quality characteristic is measured Xbar and s values are calculated for each sample. After 50 subgroups have been analyzed, we have 

(a) Compute the control limit for the xbar and s control charts

(b) Assume that all points on both charts plot within the control limits. What are the natural tolerance limits of the process?

(c) If the specification limits are 19  4.0, what are your conclusions regarding the ability of the process to produce items conforming to specifications?

(d) Assuming that if an item exceeds the upper specification limit it can be reworked, and if it is below the lower specification limit it must be scrapped, what percent scrap and rework is the process producing?