• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Statistical Process Control.

Extracts from this document...

Introduction

Management25/10/01

Statistical Process Control

A common complaint among production personnel is that engineers responsible for specifications do not understand production problems. Inspection personnel often complain not only about the poor quality of manufactured product but also about the unreasonableness of specified tolerances. In fact, very frequently inspection practices develop that substitute the inspectors views regarding proper tolerances for those actually specified by engineers. In many organizations, there is evident need for basic on which designers, production personnel, and inspectors can understand each other’s problems. The development of Quality Circles in Japan was an approach to solving this problem.

In the past many arguments among these three groups have been carried on with more heat than light because of the absence of fact in a form that would provide a basic for agreement. In many case these facts can be provided by use of statistical quality control techniques. In fact, statistical quality control

...read more.

Middle

image01.png

X and ‘R’ (average and range) and Chart for X and ‘s’ (average and standard deviation).

  • The Shewhart control charts for fraction rejected, or ‘p’ chart.
  • The Shewhart control charts for number of nomconformities, or ‘c’ chart.
  • The portion of sampling theory that deals with the quality protection given by any specified sampling acceptance procedure.

They are used for cost reduction and quality improvement that are the most widely applied.

Two tools of the Shewhart controls charts are extremely useful in statistical quality control are the range ‘R’ and the standard deviation ‘s’. The range tool measure spread or dispersion, but it is almost never used for large subgroups, that is, for subgroups of more than 20 or 25 items.

Expressed algebraically

R= X max –X min

Where X max is largest number and X min   is the smallest number in the set.

The standard deviation of the set of numbers from their arithmetic mean is designated by ‘s’.

Expressed algebraically

image02.png

...read more.

Conclusion

The calculation of Shewhart control-chart limits for variables data is the normal or gaussian distribution. The expressed algebraically for this distribution is :

image03.png

image04.pngimage05.png

The normal distribution is probably the most important distribution in both the theory and application of statistics. If ‘x’ is a normal random variable, then the probability distribution of ‘x’ is defined as follows. The normal distribution is used so much that frequently employ a special notation. ‘x’≅ N*( μ, σ2 ), to imply that ‘x’ is normally distributed with mean (μ) and variance (σ2). This visual appearance of the normal distribution is a symmetric, unimodal or bell-shaped curve, and is shown in this figure:

image06.jpg

A plot of this function over its full range -∝ to +∝ produces the familiar symmetrical bell-shaped curve. It is a continuous curve over its fully range and has a mean value of zero and a standard deviation of one.

Although control charts and statistical types of acceptance sampling procedures were originally developed for use in mass production manufacturing, these techniques are applicable to most other types of activities in all sectors of the economy including service business, government, education, and health care.

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. The mathematical genii apply their Statistical Wizardry to Basketball

    * The shots being taken from the same free-throw position which is fifteen feet away from the base of the net and perpendicular to the back line. * The same type of shot being used - using one hand to steady the ball and one to project the ball through the air.

  2. "The lengths of lines are easier to guess than angles. Also, that year 11's ...

    For the year 11 estimates of line two, the mean percentage error was 4.08%. This is a lower percentage of error than the year 9's meaning that overall, the year 11's made less error in estimating the length of the line.

  1. Identifying Relationships -Introduction to Statistical Inference.

    In some cases this is all that will be required. A graphical presentation can help with this. ( see Week 5 lecture for the SPSS commands to produce this type of graph ) The Research Question Investigate whether the acceptance of package customers is associated with the type of hotel?

  2. An Investigation Into An Aspect Of Human Variation.

    a greater frequency of hand spans at the middle of the range of measurements. Appendix 8-Graph 7 'A frequency distribution graph to show the variation of hand span of males' shows a clear pattern of distribution. The range of data is much narrower for the hand spans of males rather than females but shows a clear 'bell shaped curve'.

  1. Development of Quantitative and Qualitative measures of Human Impact on Wimbledon Common.

    From the varied procedures mentioned in the literature given for completeness in appendix 2. Three have been chosen and suitably modified to suit the present project. By recording a minimum set of data it is possible to use any of the three methods.

  2. The average pupil.

    Open "Microsoft Excel XP edition" and open the Jordan Hill 2 file, located in the maths GCSE file within the resources folder. 2. Every name should already be assigned a number; I will use these numbers when picking my stratified sample.

  1. Analyse a set of results and investigate the provided hypothesise.

    We do this to prevent any bias. For example, if our pooled set of results contained 40 males and 90 females and we then selected 20 males and 20 females' results to analyse, our data would be bias, as the ratio of women to men or men to women would

  2. Statistics - My aim is to investigate whether it is possible to gain information ...

    So in order to get more accurate results and for the data I collect to be representative of the whole population, I am going to take 50 samples in total for both the books. > The sample should be taken at random.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work