This article throws light upon the two main types of control charts. The types are: 1. Control Charts for Variables 2. Control Charts for Attributes.
Type # 1. Control Charts for Variables:
These charts are used to achieve and maintain an acceptable quality level for a process, whose output product can be subjected to quantitative measurement or dimensional check such as size of a hole i.e. diameter or depth, length of a screw/bolt, wall thickness of a pipe etc.
These are used for measureable, quality characteristics. Let the quality characteristics of all the products be measured in subgroups. The subgroups are the samples having fixed number of items/products/ component taken at random over a period of time.
The mean and the standard deviations of the quality characteristics are calculated for each sample and the following situations regarding the process may be encountered during practice:
Advantages of Control Charts:
Various advantages of control charts for variables are as follows:
(1) Control charts warn in time, if required rectification is done, well in time the scrap and percentage rejection can be reduced.
(2) Thus ensures product quality level.
(3) A control chart indicates whether the process is in control or out of control thus information about the selection of process and tolerance limits are provided.
(4) The inspection work is reduced.
(5) The control charts separate out the chance and assignable causes of variations in the observation thus substantial quality improvement is possible.
(6) Determines process variability that and detects unusual variations taking place. So reputation of the concern/firm can be built by application of these charts.
Objectives or Purpose of Control Charts for Variables:
Various objectives of control charts for variables are as follows:
(1) To establish whether the process is in statistical control and in which case the variability is attributable to chance. The variability that is inherent in the process cannot be removed, unless there is a change in the basic conditions under which the production system/process is operating.
(2) It guides the production engineer in determining whether the process capability is compatible with the design specifications.
(3) To detect the trend of the observations for further planning, adjustment and resetting tools.
(4) To get prior information regarding the process, if that is likely to go out to control.
These charts are drawn as follows:
A number of samples of components coming out of the process are taken over a period of time, each sample consisting of a number units n (n is usually 4 or 5 units or some times more). The quality measurements x1, x2, x3 ………..xn are taken.
For each sample the average value x of all the measurements and the range R (i.e., the difference between the highest and the lowest readings) are calculated.
After calculating x and R the control limits of the X and R charts are calculated as follows with UCL and LCL as abbreviation for upper control limit and lower control limits.
where the factors A1, D2 and D3 depend on the number of items per sample and the larger this number, the closer the limits. Table 9.1 gives values for these factors for various sample sizes. As long as the X and R values for each sample are within the control limits the process is said to be in statistical control.
Type # 2. Control Charts for Attributes:
These charts are used to achieve and maintain an acceptable quality level for a process whose output products are not subjected to dimensional or quantitative measurement but can be classified as good or bad or acceptable and non-acceptable, for example surface finish of a product brightness of an item is either acceptable or not acceptable.
In inspection by variables as is done in x and R charts, actual measurement of the dimensions is required that is sometimes difficult as well as uneconomical.
There is another way of inspection also i.e., inspection by attributes. In this method actual measurements are not done, instead the number of faults or defectives are counted. The size of the defect and its location are not so important.
We can also say that the products are inspected the same way as by ‘Go’ and ‘Not Go’ gauges? The products are either accepted or rejected and their actual dimensions are not measured for example 100 fan blades are inspected out of which 12 are found to be defective so those 12 pieces are rejected.
The four most commonly used control charts for attributes are:
(1) Control charts from fraction defectives (p-charts)
(2) Control charts for number Defectives (n p charts)
(3) Control charts for percent defectives chart or 100 p-charts.
(4) Control charts for number of defects per unit or C-chart.
(1) Control Charts for Fraction Defective (p-chart):
Let samples of size n be taken randomly from the production process or output at different time intervals. If d is the number of defectives in a sample, then the fraction defective in the sample.
P = d/n = Number of defective unit in a sample/Total number of unit or items in a sample
Or Actual number of defectives
d = n.p
If p̅ is the proportion of defectives produced by the entire processing or the average fraction defective and it is given by
p̅ = Total number of defective items in all the samples inspected/Total number of items in all samples.
The p-chart is based on binomial distribution. The binomial distribution has the standard deviation σp which is given by the relation.
Since the number of defective products cannot be negative if LCL sometimes comes out to be negative, it is taken as zero, p-chart is used to plot and control fraction defectives when the sample size remains uniform or it varies.
(2) Control Charts for Number of Defectives (np-chart):
Using the same notations as in p-chart the standard deviation and control limits of np-chart are as follows:
(3) Control Charts for Percent Defective (100 p-chart):
Using the same notation as in p, np charts, the standard deviation and control limits are as follows:
Applicability of P-Charts:
(i) np or Number of defective chart is used where group size or sample size i.e. n is constant.
(ii) p-chart of fraction defective chart and 100 p or percent defective charts can be used where sample size is variable or constant.
Comparison of x̅ -R-charts and P-charts:
x̅ – R-Charts:
1. These are Control Charts for variables.
2. Cost of data collection is more due to actual dimensional measurements.
3. Sample sizes are small.
4. The control limits are affected by sample size.
5. For different measurable quality characteristics different charts are to be drawn.
6. The method is much superior in diagnosing of causes of variability.
1. These are Control Charts for attributes.
2. Data collection is comparatively cheaper.
3. Larger size samples are to be taken.
4. There is less effect of the sample size over control limits.
5. Same P-chart may be applied to any number of quality characteristics on one item under inspection.
6. The method is comparatively inferior regarding diagnosing the causes of trouble or rejections.
(4) Control Charts for Number of Defects per Unit (C-chart):
This is another method of plotting attribute characteristics. In number of cases, it is more convenient to work with number of defects per unit rather than with fraction defective. The r-chart is used for the control of the number of defects observed per unit.
The difference between p-chart and the r-chart is that the former takes into account the number of items found defective in a given sample size (each defective item may have one or more defects in it) while the latter records the number of defects found in a given sample size.
Although the application of c-chart is somewhat limited, compared with p-chart, there are instances in industry where it is very useful e.g. in the control of number of defects in a bus body, an aircraft a T.V. set, a computer, welding defect in a truss etc.
The construction of the control chart is similar to that of the p-chart except that here the control limits are based on the Poisson distribution which has often been found fit to describe distribution of defects.
The standard deviation in this case is given by