Flashcards in Maths & Stats Deck (25):

1

## What are the description of population?

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Norm distribution: mean + SD

Skew Data: 5 point summary (median + lower quartile + upper quartile + min + max value)

2

## What is standard error?

### Std Error = SD divided by square root of the sample size

3

## What is Std deviation

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The Standard Deviation is a measure of how spread out numbers are.

Its symbol is σ (the greek letter sigma)

The formula is easy: it is the square root of the Variance.

4

## What is variance

### The average of the squared differences from the Mean.

5

## What is a box plot?

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A boxplot is a way of summarizing a set of data measured on an interval scale. It is often used in exploratory data analysis. It is a type of graph which is used to show the shape of the distribution, its central value, and variability. The picture produced consists of the most extreme values in the data set (maximum and minimum values), the lower and upper quartiles, and the median.

Box = Q3 and Q1

Whiskers = min and max

Line in box = median

5-point summary plot

6

## What are confidence intervals?

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CI: used as a means of conveying info about the estimated population parameters

Put error boudns on the estimates - good practice

95% CI = mean +/- (1.96SD / square root of n)

99% CI = mean +/- (2.57SD / square root of n)

7

## What are the applications of control charts?

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Basis of monitoring perfomance of many ongoing processes

Based on very simple statistical preincples and desgined for easy implementation

Monitoring of continous data: viscosity of a solution + weight of a tablet

Monitoring of attribute data: labelled correctly + tablet packs contains a chipped tablet + dye-bath test detects leakage

Suitable for mateirals not necessarily produced in discrete units

Identify special cause variations - id prob and correct before going out of spec

8

## What are the two fundamental types of variations?

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Common cause (Random) variation:

always inherent in a process and likley to create variation in the future

Always present

Lots of them

Small cumulative effect

Hard to remove/reduce

Special cause variation:

occasionally exists in a process and less likely to happen again

Irregular occurences

Relatively rare

Large impact

Mostly easy to correct

9

## What is a normal probability model?

###
Assume normal distribution

Probability reduces away from mean - both direction

68.26% - 1 SD

95.46% - 2 SD

99.73% - 3 SD

10

## How is a control chart constructed?

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levels: Mean + 2 SD + 3 SD

2 SD = warnling line

3 SD = Upper control line

outisde 3 SD = not in control

11

## What are rules for special cause?

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1. Points beyond control limits

2. Rules of 7: Seven in a row below or upper mean

3. Unsual patterns: cyclical patterns or bunchign of mean values

4. Middle third rule:number of points within 1sd much greater or less than 2/3 of the total number

12

## CUSUM chart?

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Intended for continuous data only

Cumulative sum is plotted

process intended to be in control around a reference level

13

## what are v masks

###
Norm drawn on a clear film

Common V Mask (5, 10, 10)

i.e. 10 sd - 10 intervals - 5 sd

14

## What is process capability?

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A measure of whether a process is capable of meeting the designer's specficiaton of the customer's tolerances

15

## What are the measures of process capability?

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Cp and Cpk

Cp: Tolerance spread vs process spread

Cp compares the tolerance spread 2T (upper tolerance level and lower tolerance level) to the process spread - 6sd

If index 1.5 process is capable

CpK - a means of detecting "Straddling"

CpK = Min of (upper range - mean / 3 sd) or (lower range - mean / 3sd)

If index 1.5 process is capable

16

## What can you tell me about ISO2859-1/BS6001?

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Application

Provides sampling plans acceptable to the producer and the consumer - batch by batch inspection

Designed for the insepction fo units delviered in isolated batches i.e. RM and containers

The unit will be assessed as defective or non defective

Types of defects

Crticial:Likely to result in hazardous or unsafe usage or likely to contribute to the overall failure of a system

Major: Likely to result in failure of the unit or reduce its usability

Minor: Not likely to reduce usability or is unlikely to have any bearing on the effective use of the unit

Measurement:

Percent defective or defects per hundred units

defects per hundred most commonly used: can accommodate inspection size >100

Acceptable Quality Level (AQL)

Maximum percent defective or the maximum nubmer of defects per hundred considered satisfactory as a process average

Sampling plan do not guarantee that individual batches will not exceed the AQL

On average over a large number of batches - AQL will apply

Sampling

Random sampling: each unit has an equal chance of being sampled

Single sampling

Given AQL - specific sample size n

c = number of defect allowed

Accept or reject based on a single sample

Reduced and tightened modes

Adjust sampling plan based on history

Start at normal level

Normal to reduced: more than 10 consecutive batches not been rejected

Normal to tightened: 2 out of 5 consecutive batches rejected

Reduced to normal: single batch rejected

Tightened to normal: 5 consecutive batches accepted

Inspection levels:

Three levels: 1 , 2 and 3

Normally starts at level 2

Level 1: inspection process not need to be precise

Level 3: need to be precise

17

## What is the disadvantages of using square root of N as the sampling plan?

###
Does not take into account of any changes of AQL

no statistical basis

18

## What are the applications of statistical significance testing?

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Important method for comapring samples and sets of data

i.e. compare quality of RM from different suppliers or if product spec diff between processes

Dixon tests - test for outlier

t - test comparing 2 groups

ANOVA comparing 3 groups or more

Dixon tests - test for outlier

19

## Test procedure for comparison of two groups of data.

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1. State characteristics to be compared i.e. mean

2. Our question: are they equal - null hypothesis

3. Alternative hypothesis - null is false

4. Hypothesis testing: Compute the probability of obtaining samples as different as the observed data if Null is true

5. Computed probability = p-value

6. Small p value = null hypothesis is untrue

Assume random sampling and representative data

20

## what is ANOVA

### Analysis of variance: ANOVA is a general technique that can be used to test the hypothesis that the means among two or more groups are equal, under the assumption that the sampled populations are normally distributed.

21

## Test procedure for ANOVA.

###
Test for comparing means of difference amongst groups - comparing sources of variation

Calculate total variation in the data set: subtract the mean of all the data from each datum and summing thesuares of the values obatined

Split total variation into possible sources: method variation and experimental error

22

## What is a least square plot in regression?

###
Plot a straight line: Y = A + BX

Sum of the quare of the distance of each point from the line is made as small as possible

Need to know how to draw regression line + CI in stability testing

Log transformed for first order changes

23

## What is PAT?

### A system for designing, analysing and controlling manufacturing through timely measurements (during processing) of critical quality and performance attributes of raw and in-process materials and processes with the goal of ensuring final product quality

24

## How dose PAT increase process understanding?

###
Measurement: data collection

Data integration: clean up the collected data

Data analysis

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