Sample mean chart - control charts for variables, Operation Management

Assignment Help:

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


Related Discussions:- Sample mean chart - control charts for variables

What is an e-r diagram, Conceptual Modeling looks at how the data is struct...

Conceptual Modeling looks at how the data is structured and what the characteristics of the data are. What characteristics of data are represented in an E-R diagram?

Describe the topic of joint versus separate preference, Explain the topic o...

Explain the topic of joint versus separate preference reversal.

What is meant by direct cost, What is meant by Direct Cost? Ans: Dir...

What is meant by Direct Cost? Ans: Direct Cost is Direct Material cost and Labour cost.

Production planning and control (ppc), Production Planning and Control (PPC...

Production Planning and Control (PPC) Production in manufacturing comprise  a series  of steps by  which  material is given  a new  form to  satisfy a predetermined objective,

Compute the value of cash flow based on discount rate, Calculate the presen...

Calculate the present value of a stream of cash flows based on a discount rate of 8%. Annual cash flow is as follows 1. Year 1 = $100,000 2. Year 2 = $150,000 3. Year 3 = $200,0

Explain what is the probability that you will make money, The owner of Fire...

The owner of Firewood-2-Go is considering buying a hydraulic wood splitter which sells for $50000. He figures it will cost an additional $80 per cord to purchase and split wood wit

Generate the from-to matrix and the interaction matrix, A manufacturing fac...

A manufacturing facility consists of five departments, 1, 2, 3, 4, and 5.  It produces four components having manufacturing product routings and production volumes indicated below.

Explain opportunity costs of capital at tep, How would the EBQ change if th...

How would the EBQ change if the set-up costs were reduced by 50 percent, and the holding costs were reassessed by 40 percent, taking account of the opportunity costs of capital at

Explain statistical differences between men and women, What rule of thumb o...

What rule of thumb or guidelines would you recommend for deciding whether statistical differences between men and women, or non-minorities and minorities, reflect discrimination oc

Explain risks to a broad generic business strategy, What are some drawbacks...

What are some drawbacks and risks to a broad generic business strategy? To a focused strategy?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd