Fraction defective p chart - control charts for attributes, Operation Management

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 (σp), for samples of size n is given by:

σp = √(¯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.

2206_Fraction Defective P Chart - Control Charts for Attributes.png

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







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
Related Questions
What is meant when a variable, like the possible selling prices for a new item like a mouse pad, is said to be uniformly distributed?

How might incentives stimulate positive organizational behaviours? Discuss the place of rewards and punishments for organizational members. What is it important to know? What incen

First, visit a local retail store and look at the brand names, package designs, and labels for various products. Choose one product that you think is a "good" example of these prod

What kinds of information do you think recruiters can legitimately expect to learn on a social networking site? What would they have to learn elsewhere? How do you protect yourself

Solve for x: log_10?x=3 5. You've earned your degree and have been hired by an established company. You were able to negotiate a beginning salary of $2500 per month with annual 6%

Goldratt - Theory of Constraints 1 identify the systems constraints  2 exploit the systems constraints  3 subordinate everything else to the above decision  4 elevate

Some have argued the Six Sigma programs are merely repackaged versions of older quality improvement programs that originally accompanied TQM initiatives in the 1980s. Present argum

CASE STUDY; Turnaround at the Preston Plant SPC is an operational level technique of ensuring quality conformance. How many of the benefits of bringing the plant under control wou

Christopher's Cranks uses a machine that is designed to produce 100 cranks per hour. The firm operates eight hours per day, five days per week. Due to operating constraints (regu

Performance Measures - Operation Strategy It is common to find that measures are made of operational factors which do not contribute to the winning of orders, whilst key facto