Sample mean chart - control charts for variables, Operation Management

Sample Mean Chart - Control Charts for Variables

This figure depicts a typical means chart, on which sample means would be progressively plotted, left to right. Two sets of control limits have been drawn symmetrically about the process population mean (estimated as the grand mean of several samples). The inner pair, the upper and lower warning limits, are positioned ±1.96 standard errors (s) above and below the population mean. For a stable process, there is a 1 in 40 chance that a sample mean will exceed the upper warning limit, and likewise for the lower warning limit. The outer pair, the upper and lower action limits, are positioned ±3.09s above and below the population mean. Again, for a stable process, there is only a 1 in 1000 chance of a sample mean breaching the upper limit, and likewise for the lower limit. If we determine the ranges of several samples, we can compute the average sample range (¯R). Remembering that the standard error s = σ / √n, we can take advantage of the findings of a statistician, Hartley, who quantified the relationship: σ = ¯R/dn where dn is a coefficient which varies with sample size. Hartley's constants (dn), for sample sizes 2 to 6, are presented in this table.

2077_Sample Mean Chart - Control Charts for Variables.png

For convenience, the coefficients 1.96/dn √n and 3.09/dn √n have been calculated for a series of sample sizes. These values are presented as A' 0.025 and A' 0.001 in this table.

Sample size             A'0.025                A'0.001 

2                                  1.23                 1.94 

3                                  0.67                 1.05 

4                                  0.48                 0.75 

5                                  0.38                 0.59 

6                                   0.32                0.50

The final expressions are, therefore:

Warning limits = μ+A'0.025 ¯R

Action limits = μ+A'0.001 ¯R

Posted Date: 3/15/2013 5:58:34 AM | Location : United States







Related Discussions:- Sample mean chart - control charts for variables, Assignment Help, Ask Question on Sample mean chart - control charts for variables, Get Answer, Expert's Help, Sample mean chart - control charts for variables Discussions

Write discussion on Sample mean chart - control charts for variables
Your posts are moderated
Related Questions
In estimating the difference between two population means, if a 95 percent confidence interval includes zero, then we can conclude that there is a 95 percent chance that the differ

To develop what you believe is a terrific idea for a video game, you lease 50,000 square feet in an office building from Commercial Property, LLC, under a written five-year lease.

Why do you think the capstone course for the MBA program has a heavy emphasis on ethical decision making?

Aman work at the Bank, to help customers, including retired people, to plan for the future.  Often the value of pensions does not keep up with inflation.  Hence retired people requ

Time (in Days) Activity Immediate Predecessor Optimistic Most Likely Pessimistic A - 3 6 8 B - 2 4 4 C - 1 2 3 D C 6 7 8

How is the search industry changing? What forces seem most likely to bring about major change to the industry within the next three to five years?

Consider a layout decision which has been made in your own organisation. How was the layout devised? What were the key issues?

• What is an ethics audit and why is it important to an organization? Explain the benefits and challenges of conducting one. • Why is it important to link the ethics audit bac

As a library or internet assignment, find the U.S. productivity rate (increase) last year for (a) national economy, (b) manufacturing sector, and (c) service sector.

Explain various numbers of goods as output from similar amount of resources (input) in improving productivity. Management can raise productivity that is management can get vari