Chapter 22: Statistical Process Control Flashcards
Prevention approach
Instead of inspecting the product, inspecting the process to determine when the process starts producing units that do not conform to specifications.
Uses hypothesis testing concepts
Allows for earlier correction
Sources of variation
Chance
Assignable variation
Chance
Aka common variation
Caused by a number of randomly occuring events that are part of the production process and generally cannot be eliminated without changing the process
Assignable variation
Aka special variation
Variation causes by specific events/factors that are frequently temporary and can usually be identified and eliminated (malfunctions)
When production process is under control
Only sources of variation in the random variable are due to chance.
Each distribution has the same shape, mean, standard deviation
Products all fall within designated specification limits
When production process is out of control
When product falls outside of designated specification limits
When the process distribution changes and varies between individual instabces
Common ways for processes being out of control
- level shift
- instability
- trend
- cycle
Out of control process: Level shift
A change in the mean of the process distribution
Potential causes: machine breakdown, new machine or operator, environmental change
Out of control process: instability
When process standard deviation increases (wider variation)
Potential causes: problem with machinery, materials, tools, operators
Out of control process: trend
When there is a slow, steady shift in the process distribution mean in either direction.
Potential causes: irregular maintenance (residue/dirt buildup, loss of lubricant), operator fatigue
Our of control process: cycle
Repeated series of small observations followed by large observations
Potential causes: environmental changes, worn parts, operator fatigue
Control chart
Statistical method used to detect problems in processes, a plot of statistics over time
Elements of a control chart
Centerline
Upper and lower control limits
- if all points are randomly distributed between control limits then process is under control
Standard error of sample mean of x
Standard deviation / square root of b
Difference between statistical process control and hypothesis testint
Hypothesis testing - determination about a single fixed parameter
SPC - determination about a variable process distribution (dynamic process distribution with parameters subject to possible shifts)
Factors determining the sample size and frequency for a control chart
- costs or type I and Type II errors
- length of production run
- typical change in the process distribution when process goes out of control
Use Operating Characteristic (OC) curve
Operating Characteristics curve
OC curve
Plotted probabilities of one characteristic given another characteristic
Probability of a type II error
Probability the control chart will be unable to detect a shift of k # of standard deviations in the process mean on the first sample after the shift has occured
Average run length
ARL
The expected number of samples that must be taken before the chart indicates that the process has gone out of control (erroneously)
ARL=1/P
P= probability that a sample mean falls outside the control limits (probability of type II error)
Control charts for variables
Control charts for interval data
Control charts for attributes
For categorical data (defective vs non- defective
Ways to judge if a change in process distribution has occured (interval data)
- xbar chart: determine whether the distribution means have changed
- S (standard deviation) or R (range) chart: to determine if profess standard deviation has changed
SPC often uses range calcuations instead of standard deviations (sample range to estimate standard deviation)
Estimator of the mean of the distribution
Denoted by x with two bars
The mean of the sample mean so:
Sum of all values of the means for each sample / k number of samples
Used to estimate the mean of the process distribution
Standard deviation for process distribution
Denoted as S
Calculate sample variance (s^2) for each sample
To compute pooled standard deviation take the square root of (the sum of all variances divided by the number of samples)
Used to estimate the standard deviation of the profess distribution
Centerline and control limits for xbar chart
Centerline= mean of the sample means (x with two bars)
Control limit = mean of the sample mean +/- 3* (standard deviation of process distribution divided by the square root of n (number of observations in each sample))
zones of the xbar chart
Divisions of area between the centerline and control limits
C zones: areas within one standard deviation of the center line
B zones: areas between one and two standard errors of the center line
A zones: areas between two and three standard errors of the center line
Width of zones = one standard error
finding the standard error of xbar
the difference between the upper and lower control limits divided by 6
Pattern tests indicating a process is out of control
Patterns that are rare events and unlikely to occur if the process is under control
1- one point beyond zone A
2- nine points in a row in zone C or beyond on one side of the centerline
3- six increasing or decreasing points in a row
4- fourteen points in a row alternating up and down
5- two out of three points in a row in zone A on the same side of the centerline
6- four out of five points in zone B or A on the same side of the centerline
7- fifteen points in a row in zone C on both sides of the centerline
8- eight points in a row beyond zone C on both sides of the centerline
Mintab’s rules
Eight pattern tests for xbar charts
No pattern tests for S and R charts
Four pattern tests for p charts
S chart
Graphs sample standard deviations to determine if the process distribution standard deviation has changed
Similar format to xbar chart with centerline and control limits
If no points outside the control limits no evidence to believe the standard deviation has changed over the period (however points below lower control limit may be desirable : standard deviation decreasing)
Using xbar and S charts
In practice used together
Xbar chart uses S to calculate control limits and zone boundaries, so if S is our of control then the control limits in xbar will be skewed
S drawn first
Original structure made while process known to be in control and then further data points potted as time continues to monitor process
Process capability index
Measures the capability of the process to produce units whose dimensions fall within specifications
Cp= (USL-LSL)/(6sd)
Theoretical process capacity = (upper minus lower specification limit)/ (6 * standard deviation)
Issue- parameter of standard deviation generally unknown
Actual process capability
Use xbarbar and S from control chart
CPL (lower) = (xbarbar - LSL)/ 3S
CPU (upper) = (USL - xbarbar)/3S
Process capability index is the smaller of the two
Reducing process variation
Experimenting with the “four Ms” and examining the results using a control chart
- machines
- materials
- methods
- manpower
