Control charts
The purpose of control chart is to detect these changes in quality. Control Charts are based on statistical sampling theory, according to which an adequately sized sample drawn, at random, from a lot represents the lot. All processes whether semi-automatic or automatic are susceptible to variations which in turn result in changes in the quality of the products. These variations occur due to either chance causes or due to certain factors to which we can assign the causes for such variations.
A control chart primarily is a diagnostic technique. Control chart is a graphical presentation of the collected information. The information pertains to the measured or otherwise judged quality characteristics of the items or the samples. A control chart detects variations in the processing and warns if there is any departure from the specified tolerance limits.
Successively revised and plotted control chart immediately tells the undesired variations and it helps a lot in exploring the cause and eliminating manufacturing troubles.
The upper and lower limits can be 1σ, 2σ, or 3σ, depending upon whether the confidence level is 68.27%, 95.45%, or 99.73%. Normally 3σ limits are taken for plotting control charts, and (3σ +3σ) spread is known as the basic spread. Besides 3σ control limits certain control charts also show warning limits spaced at 4σ spread.
Warning limits inform the manufacturer—when the items or samples are approaching the danger level so that he can take an action before the process goes out of control. Control charts are also based on Variables.
Purpose and Advantages:
- A Control Chart indicates whether the process is in control or out of control.
- It determines process variability and detects unusual variations taking place in a process.
- It ensures product quality level.
- It warns in time, and if the process is rectified at that time, rejection can be reduced.
- It provides information about the selection of process and setting of tolerance limits.
- Control charts build up the reputation of the organization (customer’s satisfaction)
X̅ Chart:
- It shows changes in process average and is affected by changes in process variability.
- It is a chart for the measure of central tendency.
- It shows erratic or cyclic shifts in the process.
- It detects steady progress changes, like tool wear.
- It is the most commonly used variables chart.
R-Chart:
- It controls general variability of the process and is affected by changes in process variability.
- It is a chart for measure of spread.
- It is generally used along with an x-chart.
X̅ and R charts when used together form a powerful instrument for diagnosing quality problems.
- It tells when to leave the process alone and when to chase and go for the causes leading to variation.
- It secures information in establishing or modifying processes, specifications or inspection procedure.
- It controls the quality of incoming material.
p-Chart:
- It can be a fraction defective chart or % defective chart (100 p).
- Each item is classified as non-defective or defective.
- This chart is used to control the general quality and it checks if the fluctuations in product quality are due to chance cause alone.
- It can be used even if sample size is variable (i.e., different for all samples), but calculating control limits for each sample is rather Cumbersome.
- P-chart is plotted by calculating, first, the fraction defective and then the control limits. The process is said to be in control if fraction defective values fall within the control limits. In case the process is out of control an investigation to hunt for the cause becomes necessary.
C-Chart:
- It is the control chart in which numbers of defects in a piece or a sample are plotted.
- It controls number of defects observed per unit or per sample.
- Sample size is constant.
- The chart is used where average numbers of defects are much less than the number of defects which would occur otherwise if everything possible goes wrong.
- Whereas, p-chart considers the number of defective pieces in a given sample, C-chart takes into account the number of defects in each defective piece or in a given sample. A defective piece may contain more than one defect.
- C-chart is plotted in the same manner as p-chart except that the control limits are based on Poisson distribution which describes more appropriately the distribution of defects.
Plotting of Charts with UCL and LCL:
UCL = Upper control limit
LCL = Lower control limit
Table for constants as per sample size
Calculate the UCL and LCL
For X̅ Chart:
For R Chart:
For p chart:
For C-chart:
