In many industrial production processes, measurements are made periodically on critical characteristics to ensure that the process
Question:
a. Walter Shewhart invented this method in 1924 at Bell Labs. He suggested using 3 standard deviations in setting the UCL and LCL to achieve a balance between having the chart fail to diagnose a problem and having it indicate a problem when none actually existed. If the process is working properly (in statistical control) and if n is large enough that x has approximately a normal distribution, what is the probability that it indicates a problem when none exists? (That is, whats the probability a sample mean will be at least 3 standard deviations from the target, when that target is the true mean?)
b. What would the probability of falsely indicating a problem be if we used 2 standard deviations instead for the UCL and LCL?
c. When about nine sample means in a row fall on the same side of the target for the mean in a control chart, this is an indication of a potential problem, such as a shift up or a shift down in the true mean relative to the target value. If the process is actually in control and has a normal distribution around that mean, what is the probability that the next nine sample means in a row would (i) all fall above the mean and (ii) all fall above or all fall below the mean? (Use the binomial distribution, treating the successive observations as independent.)
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
Step by Step Answer:
Statistics The Art And Science Of Learning From Data
ISBN: 9780321755940
3rd Edition
Authors: Alan Agresti, Christine A. Franklin