CH 6s - Statistical Process Control

variance definition

(n.) - a difference between what is expected and what actually occurs

assignable causes of variation (special causes)

-Causes can be traced to a specific reason -e.g. poor employee training, worn tool, machine needing repair process output NOT stable over time; variations are NOT predictable

When inspections take place, quality characteristics may be measured as either attributes or variables.

Attribute inspection classifies items as being either good or defective. It does not address the degree of failure. ie the lightbulb burns or it does not. Variable inspection measures such dimensions as weight, speed, size, or strength to see if an item falls within an acceptable range. If a piece of electrical wire is supposed to be 0.01 inch in diameter, a micrometer can be used to see if the product is close enough to pass inspection.

R bar

Average of sample ranges Used to calculate the UCL and LCL ie r bar = 8 , D4 is the upper range, D3 is the lower range. UCL = D4* r bar LCL = D3* r bar

Individual​ measurements, not averages of small​ samples, are generally used in statistical process control. T/F

False

Control charts

Graphic presentations of data over time that show upper and lower limits for the process we want to control

Sampling

The process of selecting representative units from a total population

population standard deviation

The square ROOT of the population variance; a measure of the standard distance from the mean.

double x bar (target)

mean of the sample means aka overal mean of all the samples aka average of all the sample means

+-3 σ (sigma)

the control limits are +3 or -3 units from the sample mean the stdev is +3 or -3 units from the central line

> R-chart > x-bar chart

the two types of charts go hand in hand when monitoring variables because they measure the two critical parameters: central tendency and dispersion.

target value

the value given by the manufacturer of a quality control sample as the expected quality control result.

Control Charts for Variables

use hx data to distinquish between natural variations and variations due to assignable causes. ie target value (UC limit and LC limit)

population (process) standard deviation symbol

σ sigma

The overall average on a process you are attempting to monitor is 50.0 units. The process population standard deviation is 1.78. Sample size is given to be 4.

​a) Determine the ​3-sigma x bar chart control limits. USE: pop stdev/ square root of sample size = .89 units 1.78/square root of 4 1.78/2= .89 units The ​3-sigma x overbar chart control limits​ are: Upper Control Limit is x double bar (the overall avg on process, in this case 50) 50 + 3 * .89 = 52.67 units Lower Control Limit ​ 50 - 3 * .89 = 47.33 units ​b) Now determine the ​2-sigma x overbar chart control limits. The ​3-sigma x overbar chart control limits​ are: UCL = 50 + 2 * 1.78 = 51.78 units LCL = 50 - 2 * 1.78 = 48.22 units Does the standard deviation of the sampling distribution ​change? No, because the process stdev and the sample size remain the same. Note that the control limits for ​2-sigma x overbar chart are tighter than the control limits for ​3-sigma x overbar chart. How has the confidence level​ changed? The confidence level has dropped. * note the control limits of 2 sigma are tighter than the control limits of 3 sigma because you are closer to the mean (target value aka central line)

Control Chart

A graphic display of process data over time and against established control limits, which has a centerline that assists in detecting a trend of plotted values toward either control limit.

Upper Control Limit (UCL)

A line in a control chart that provides the largest value that is still acceptable without being labeled an abnormal variation. Upper control limit (UCL)=x¯¯+zσx¯ where x¯¯zσx¯σn=====mean of the sample means or a target value set for the processnumber of normal standard deviations (2 for 95.45% confidence, 3 for 99.73%)standard deviation of the sample means=σ/n√population (process) standard deviationsample size

how to construct a control chart

Target value (central line) + upper control Limit (upper line) + Lower Control LImit (lower line) (x bar mean - average these)

Variance

The SQUARE ^2 of the standard deviation, it is a description of how much each score varies from the mean.

Mistakes stemming from​ workers' inadequate training represent an assignable cause of variation. T/F

True

Some degree of variability is present in almost all processes. T/F

True

The purpose of process control is to detect when assignable causes of variation are present. T/F

True

The ​x-bar chart indicates that a gain or loss of uniformity has occurred in the central tendency of a production process. T/F

True

Lower Control Limit (LCL)

a line in a control chart that provides the smallest value that is still acceptable without being labeled an abnormal variation Lower control Lower (LCL)=x¯¯−zσx¯ where x¯¯zσx¯σn=====mean of the sample means or a target value set for the processnumber of normal standard deviations (2 for 95.45% confidence, 3 for 99.73%)standard deviation of the sample means=σ/n√population (process) standard deviationsample size

x-bar chart

a quality control chart for variables that indicates when changes occur in the central tendency of a production process

The usual purpose of an​ R-chart is to signal whether there has been​ a: Gain or Loss in Dispersion b: Change in the Consumer's Risk c: Change in the Central Tendancy of the Process Output d: Change in the % defective in a sample e: Change of the number of defects in a sample

a. Gain or Loss in Dispersion Dispersion is how spread out things are (distance from the mean either Positive or Negative)

natural cause (common causes)

affect all production processes variations are stable over time; variations are predictable forms a pattern --> described by a probability distribution for any distribution there is a measure of central tendency and dispersion If the distribution of outputs falls within acceptable limits, the process is said to be "in control"

R-chart (range chart)

indicates a gain or loss of dispersion (the range of) The R-chart values indicate that a gain or loss in dispersion has occurred. Such a change may be due to worn bearings, a loose tool, an erratic flow of lubricants to a machine, or to sloppiness on the part of a machine operator. The range (Ri) is defined as the difference between the largest and smallest items in one sample. For example, the heaviest box of Oat Flakes in Hour 1 of Example S1 was 18 ounces and the lightest was 13 ounces, so the range for that hour is 5 ounces.

SPC (statistical process control)

monitor standards by taking measurements and corrective action as a product or service is being produced ie find whan assignable causes of variation are present and helps take appropriate actions to eliminate assignable causes Samples of process outputs are examined; if they are within acceptable limits, the process is permitted to continue. If they fall outside certain specific ranges, the process is stopped and, typically, the assignable cause located and removed.

x -chart (x-bar chart)

monitors a process to see if it is "in control" or "out of control" m/b used with r chart Tracks changes of central tendency The x¯-chart tells us whether changes have occurred in the central tendency (the mean, in this case) of a process. These changes might be due to such factors as tool wear, a gradual increase in temperature, a different method used on the second shift, or new and stronger materials.

x bar

sample mean symbol

sigma/square root of n

standard deviation of the sample means