### Calculate the median for the group of results tabulated and

Statistical Process Control - Introduction And Statistics

'SPC' stands for Statistical Process Control throughout this TMA.

Question 1. SPC is one of a number of tools which can be used to improve manufacturing quality standards.

(a) Outline two techniques which can be used to decide where to put SPC effort most effectively.

(b) State 3 ways in which the application of SPC can improve quality standards.

(c) State the three basic elements of SPC.

Question 2. From the data given on the next page, produce:

• a tally chart

• a frequency chart

• a ranked frequency chart with cumulative frequencies (work to whole numbers only)

• a Pareto diagram of percentage frequencies and percentage cumulative frequencies (work to whole numbers only).

Data: Record of reasons for rejection of 80 components by 10 types of defects, A to K.

CEECEEKBEC CCEBKKFKCC CCEEEEJKJH EEEECEFCCC CBBGHFEEBE AEDEBEBAHC CKEGHFEEEC HKEHEECACC.

Question 3. (a) Give examples from your own experience of discrete and continuous variables, and distinguish between the two types.

(b) State the five types of central tendency in general use. Which of these are most frequently used in SPC work?

(c) Calculate the median for the group of results tabulated below:

1, 3, 4, 6, 7, 9, 11, 14, 16, 17, 18.

Question 4. (a) What is the mathematical relationship between variance and standard deviation?

(b) Calculate the range and the arithmetic mean for the following set of data.

4, 8, 16, 20, 28, 32, 38, 44, 48, 54, 60.

(c) Supply the missing words in the following statement.

'In very many practical SPC cases approximately ................... of the results recorded will lie within a range defined by the mean plus and minus one standard deviation.'

Question 5. (a) Sketch the Standard Normal Distribution curve.

(b) State the area under this curve from -∞ to +∞.

(c) With reference to the Standard Normal Distribution curve, what percentage of results lie within the following ranges?

(i) Mean ±1 standard deviation
(ii) Mean ±2 standard deviation
(iii) Mean ±3 standard deviations.

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