Fraction Defective P Chart - Control Charts for Attributes

This type of chart is used when it is impractical or inconvenient to maintain a constant sample size. Instead of plotting the number of defectives in each sample, the proportion (p) or fraction of defectives is calculated and then plotted. Clearly, to ensure that meaningful plots are made, the sample sizes must be large enough to ensure that a number of defectives will typically be found. This may seem to imply that some level of non-conformance is being accepted, but this is not necessarily so. For example, consider the Go/Not-go gauging example shown in the figure on page 249. Whilst the design limits of size on the component diameter might be, say, 24.98 mm and 25.02 mm; for process control purposes the gaps in the gauge might be set at, say, 24.99 and 25.01 respectively. Remembering that, for attributes, only two states are possible (defective/non defective) the relevant probability distribution is the binomial distribution, the mean of which (¯p) can be estimated by inspecting a large number of items:

¯p = total number of defectives/ total number inspected

An estimate of the standard deviation of the binomial distribution (σ_p), for samples of size n is given by:

σ_p = √(¯p (1-¯p) / n)

For small values of n the profiles of the binomial distributions are distinctly skewed, but, for large values of n and, particularly, when the product p n is greater than about 5, the distributions are sufficiently symmetrical to be well-approximated by the normal distribution. In this latter situation the control chart limits can be determined in the same manner as for variables charts.

It will be realised that the implied constant sample size (n) in these expressions presents some difficulty in a procedure when the sample size is allowed to vary. This can be surmounted by using an average value for n, and limiting variation in the size of subsequent samples to, say, ±20 per cent of this value: the results will still be sufficiently accurate for most process control purposes.

Posted Date: 3/16/2013 1:41:42 AM | Location : United States

Ask an Expert

Related Discussions:- Fraction defective p chart - control charts for attributes, Assignment Help, Ask Question on Fraction defective p chart - control charts for attributes, Get Answer, Expert's Help, Fraction defective p chart - control charts for attributes Discussions

Write discussion on Fraction defective p chart - control charts for attributes
Your posts are moderated

Write your message here..

Related Questions

Explain external sales and inter-divisional transfers, A company specialisi... A company specialising in the manufacture and sale of baths. Each bath consists of a main unit plus a set of bath fittings. The company is split into two divisions, A and B. Divisi

Aggregate planning, how to solve aggregate planning how to solve aggregate planning

Explain individual employees and improve cooperation, How can a pay for per... How can a pay for performance system increase motivation of individual employees and improve cooperation?

How global businesses subscribe to a global code of conduct, Do you think g... Do you think global businesses would be willing to subscribe to a global code of conduct?

Regression analysis, advantages of simple regression method for cost estima... advantages of simple regression method for cost estimation.

Product , Product Product is anything that can be offered to a market ... Product Product is anything that can be offered to a market that might satisfy a want or need. There are two concepts of product narrow concept and wide concept. In its narrow

Implementation of the cost of quality, Question: What are different con... Question: What are different conditions which a company has to make sure before the implementation of the Cost of Quality? Description/Definition of cost of Quality • The

Explain re-negotiate a new relationship, You are very annoyed by one of you... You are very annoyed by one of your third-party service providers (3PL) and want to confront him and re-negotiate a new relationship. How would you go about this important task?

Describe develop a system for evaluating the productivity, As the administr... As the administrative manager in a law office, you have been asked to develop a system for evaluating the productivity of the 15 lawyers in the office. What difficulties are you go

Performance cycle variance, how performance cycle variance can be controlle... how performance cycle variance can be controlled?