CONTROL CHART
Control chart is a time ordered plot of representative sample statistics obtained from an ongoing process.
It has upper and lower limits called control limits, that define the range of acceptable.
Conversely if the data point that falls outside of either limit will would be taken as evidence that the process output is non random. Not in control.
Purpose of a control chart is to monitor process output to see if it is random.
SPC uses control charts to determine if a process is within the controlled parameters:
1)if it is determined that the process is out of control
2)SPC provides the opportunity to investigate and determine the cause of this condition.
3)when the root cause of the problem s determined the strategy can be identified to correct it.
Control chart is a time ordered plot of sample statistics used to distinguish between random and non random variability.
Basis for the control chart is the sampling distribution.
Control limits : the dividing lines between random and non random deviations from the mean of the distribution.
Control charts have two limits that separate random variation and non random variation.
Larger value is upper control limit and lower value is the lower control limit.
Characteristics of control charts
A nominal value or centre line .
Two control limits used to judge whether the action is required ,an UCL and LCL.
Advantages
Simple and effective
After the process is in statistical control its performance can be further improved to reduce variation.
There are four commonly used control charts .
Two are used for variable(mean and range charts)
Two are used for attributes.
Attributes :generates data that are counted .( no.of defectives,no of calls per day)
Variable : generated data that are measured .(amount of tie needed to complete a task , length or width of the part.
Control charts for variables
Two types of control charts for variables are:
Control charts for means :monitor the central tendency
Control charts for range : monitors the dispersion of a process.
Mean charts: it can be constructed in one of two ways
The choice depends on what information is available.
Range control charts: are used to monitor process dispersion.
CONTROL CHARTS FOR ATTRIBUTES
Control charts for attributes are used when the process characteristic is counted rather than measured.
Two types of attributes control
Where the nature of product is such that the characteristic cannot be measured quantitavely , the items are classified only defectives and non defectives at the time of the final inspection.
The defects can be measured in any of the following two ways:
1)number of defective items are taken in different samples.
Here p chart or np chart is used.
2)number of defects in one item.in this case C chart is used.
pChart (fraction defective)
When observations can be placed into one of two categories.
These charts are constructed by recording at least 20successive inspections.
Observations can be classified as
Good or bad
Pass or fail
cCharts
cChart –used to monitor the number of defects per unit.
Goal is to control the number of occurrences per unit.
Ex: scratches ,chips,dents or errors per item
cracks or faults per unit of distance
breaks or distances per unit area
calls,complaints,failures, equipment breakdowns.
Acceptance Sampling
Acceptance sampling is a process of inferring the quality of a large number of items ( a batch or lot) before or after a process to judge conformance with the predetermined standards.
It might be used by the customer to evaluate the quality of incoming materials or by a producer to evaluate the quality of outgoing product.
If number of defective items in the sample is greater than some specified level it means that the batch probably has an unacceptable number of defective items and we reject it.
If the number of defective items in the sample is less than or equal to the specified number the batch is deemed to be of acceptable quality.
Average outgoing quality: when a sampling plan rejects a lot .The lot may be subjected to 100% inspection. Any defectives found in the lot replaced by good items so that the lot contains all the good items.
AOQ= average number of defectives * 100
_____________________________
no of items in lot
Accepted quality level: it represents maximum proportion of defectives which the consumer finds acceptable.
It is the maximum percent defectives that for the purpose of sampling inspection can be considered satisfactory.
Lot tolerance percent defective: the upper limit on the percentage of defects that a customer is willing to accept.
Consumer’s risk (beta): the probability that a lot containing defects exceeding LTPD will be accepted.
Producer’s risk (alpha): the probability that a lot containing accepted quality level will be rejected.
Operating Characteristics Curve
The probability curve that shows the probabilities of accepting lots with various fraction defectives.
OC curves describes an important feature of acceptable sample plans.
The following can happen when we go for acceptance sampling plans.
We accept good lots
We reject bad lots
We may accept bad lots
We may reject good lots
When good lot is rejected the error is known as type 1 error
Risk of rejecting a good lot based on the evidence is known as producer’s risk.
When a bad lot is accepted as a good lot based on the sample evidence the error is known a s type 11 error and the risk of accepting the bad lot as good in known as consumer’s risk (beta).
OC curve is used for :
Design and development of sampling plans
Evaluation of sampling plans
Comparison between sampling plans
Types of acceptance sampling
Single sampling: In single plan one random sample is drawn from each lot and every item in the sample is examined and classifies as either good or defective.
Double sampling plan: allows for the opportunity to take a second sample if the results in the initial sample are inconclusive.
Multisampling plan : is similar to double sampling plan except more than two samples may be required .
