Flashcards in Maths & Stats Deck (25):
What are the description of population?
Norm distribution: mean + SD
Skew Data: 5 point summary (median + lower quartile + upper quartile + min + max value)
What is standard error?
Std Error = SD divided by square root of the sample size
What is Std deviation
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.
What is variance
The average of the squared differences from the Mean.
What is a box plot?
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
What are confidence intervals?
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)
What are the applications of control charts?
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
What are the two fundamental types of variations?
Common cause (Random) variation:
always inherent in a process and likley to create variation in the future
Lots of them
Small cumulative effect
Hard to remove/reduce
Special cause variation:
occasionally exists in a process and less likely to happen again
Mostly easy to correct
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
How is a control chart constructed?
levels: Mean + 2 SD + 3 SD
2 SD = warnling line
3 SD = Upper control line
outisde 3 SD = not in control
What are rules for special cause?
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
Intended for continuous data only
Cumulative sum is plotted
process intended to be in control around a reference level
what are v masks
Norm drawn on a clear film
Common V Mask (5, 10, 10)
i.e. 10 sd - 10 intervals - 5 sd
What is process capability?
A measure of whether a process is capable of meeting the designer's specficiaton of the customer's tolerances
What are the measures of process capability?
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
What can you tell me about ISO2859-1/BS6001?
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
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
Random sampling: each unit has an equal chance of being sampled
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
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
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
What are the applications of statistical significance testing?
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
Test procedure for comparison of two groups of data.
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
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.
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
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
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
How dose PAT increase process understanding?
Measurement: data collection
Data integration: clean up the collected data