P chart, Other Management

P Chart

As against the   668_p chart.png   and R charts which deal with quantitative aspects, these charts deal with the attributes which are qualitative factors possessed by the data. An example would be a person being a major or a minor or the marital status of the person. In these examples, we note that a person is either a major or not, similarly a person is either married or not. That is we are looking at whether the given data set is in confirmation with the given qualitatitive factor or not. The answer would be an emphatic yes or no and either a success or a failure. There is no neutral state of acceptance. In statistical process control, the data set which can take on only two values is called an attribute. From this point of view, it can  be said that the quality of the product conforms to the specified standards or it does not. Since we take into account the attributes of the given data set, the measure we will employ is the proportion of the data points satisfying the given criteria and the proportion of the data points that does not satisfy the criteria. With respect to this, let us recollect that the probability of success in the binomial distribution is denoted by "p" and the proportion of units that have a particular characteristic in a given population is symbolized by "p" and the same in a sample is denoted as   1038_p chart1.png  . Remember that using the binomial distribution to form interval estimates of a population proportion would be tedious and as the sample size increases the binomial distribution can be approximated by a normal distribution and therefore the number of successes are converted to the proportion of success by dividing np by n. Since np gives us the mean of the binomial distribution, the mean of the sampling distribution is given by np/n = p. q is used to denote the probability of failure and the proportion of units that do not show the characteristic under consideration. The standard deviation is also obtained on similar lines. That is, the mean and the standard deviation of the sampling distribution of the proportion are given by

2366_p chart2.png

With the fractional values of p and the center line at   1424_p chart3.png  , we plot the p chart. The control limits are given by

1647_p chart4.png

In case we do not know the p value, we estimate it by using the overall sample fractions. The mathematical expression for the same is shown below.

                    2183_p chart5.png   

where

          1502_p chart6.png       is the sample fraction in the j th interval of time

         k        is the sum of all the samples considered. 

Therefore in the equations given above to calculate lower and upper control limits, p should be replaced by   2438_p chart7.png  .

An important point to note is that if the value of LCL is below zero, we take the value of LCL as zero and if the value of UCL exceeds 1, it is considered as 1. Do you find any similarity between this concept and the concept of probability? Yes. If you recollect, the classical probability defines probability as the ratio of number of the outcomes where that particular event occurs to the number of all the possible outcomes. From this definition we can see the relationship between probability and the proportion of the units satisfying a particular characteristic out of all the units manufactured.

Then from the plot we identify the pattern and if required the corrective action is taken.

Posted Date: 9/17/2012 12:51:23 AM | Location : United States







Related Discussions:- P chart, Assignment Help, Ask Question on P chart, Get Answer, Expert's Help, P chart Discussions

Write discussion on P chart
Your posts are moderated
Related Questions
QUESTION 1 Policy implementation is the most critical stage of the policy process. Critically analyse some of the main constraints that hinder the implementation of public poli

Let us review some questions that as a negotiator you can face while conducting a negotiation and the considerations to find answers to these questions:  Framing the opening

Make yourself aware of the range of issues involved in the "Greening of Hotels" phenomenon by reading widely on the topic. Become conversant with the full range of current and e

#question. I want detailed information about entrepreneurship.

QUESTION 1 "Values drive behaviour". Discuss with reference to- (1) virtuous values and behaviour (2) how an ethical culture can be developed at the workplace? QUESTI

Developing a Project Management Culture Moving the organisation to embrace a "project management culture" takes time and patience. The initial step an organisation can take is

Question 1: Show the importance of facilities planning and design with regards to: (i) Land (ii) Esthetics (iii) Space (iv) Buildings (v) Innovation (vi) Acces

Library service is, in essence, the retrieval and dissemination of embodied knowledge to individual members and groups in a community. Hence, the two essential parameters which aff

The most important test of a new organization comes when it is hit by a major catastrophe. It is required to manage such emergencies intelligently and forthrightly with the news me

Bibliographic data formats Bibliographic data formats adopted for exchange of data consist of three basic components:  A defined physical structure: Rules for the arra