Control Charts for Variables Variables due to Variation • Concept of variation – No 2 things are alike • Variation exists – Even if variation small and appears same, precision instruments show differences • Ability to measure variation is necessary before can control
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Control Charts for Variables
Variables due to Variation
• Concept of variation– No 2 things are alike
• Variation exists– Even if variation small and appears same, precision
instruments show differences• Ability to measure variation is necessary before can control
Control Charts for Variables
Variation Area
Basically 3 categories of variation in piece part production (e.g. Light bulbs, washer, nuts, etc.) Within piece - surface roughness Piece to piece - dimensions Time to time - different outcomes e.g. morning and
afternoon, tool wear, workers’ tiredness
Control Charts for VariablesSources of Variation• Equipment
- tool wear, electrical fluctuations for welding• Material
- tensile strength, moisture content (e.g. raw material) • Environment
In this chart the sample means are plotted in order to control the mean value of a variable (e.g., size of piston rings, strength of materials, etc.).
R chart In this chart, the sample ranges are plotted in order to control the variability of a variable.
S chart In this chart, the sample standard deviations are plotted in order to control the variability of a variable.
S2 chart In this chart, the sample variances are plotted in order to control the variability of a variable.
Control Charts for Variables
Regardless of the distribution of population, the distribution of sample means drawn from the population will tend to follow a normal curve
1. The mean of the sampling distribution (x-double bar) will be the same as the population mean m
x = m
s nsx =
2. The standard deviation of the sampling distribution (sx) will equal the population standard deviation (s) divided by the square root of the sample size, n
Central Limit Theorem
Control Charts for VariablesStatistical Basis• Usually µ and are unknown, so they are estimated from
preliminary samples and subgroups.• 20-25 samples are taken usually each of which contains 4-6
observations• If m samples are taken and n observations are made in each
sample then the best estimator of process mean µ is the grand average.
• Where are the average of each sample
Control Charts for VariablesStatistical Basis (contd.)
• If x1, x2, . . . , xn is the observations for sample size n, then the range of the sample is the difference between the largest and smallest observations; that is,
• Let R1, R2, . . . , Rm be the ranges of the m samples. The average range is
Control Charts for Variables
In case of 3-sigma R chart, the control limits can be written as follows
Where is the standard deviation of range values of m samples
In case of 3-sigma x chart, the control limits can be written as follows
Where is the standard deviation of range values of m samples