Statistical Quality Control – 1 – Control Charts – Mean Chart

Statistical Quality Control – 1 – Control Charts – Mean Chart


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Statistical Quality Control - 1 - Control Charts - Mean Chart
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Statistical Quality Control – SQC – Control Charts for Variables and Control Charts for Attributes – Mean Chart and Range Chart

Quality means confirming with certain prescribed standards. These standards may be in terms of size, weight, strength, color, etc. Some of these standards are easy to define in numerical terms.
The makers of the product normally set the quality standards. The quality consciousness among producers is always more when there is competition from rival producer.
Governments are also keen on quality standards. For making good abroad there is compulsory inspection for quality.
Statisticians’ role is there because that analysis is probabilistic. There is use of sampling and rules of statistical inference.
Definition
“Statistical Quality Control is a simple statistical method for determining the extent to which quality goals are being met without necessarily checking every item produced and for indicating whether or not variations which occur are exceeding normal expectation. Statistical Quality Control enables us to decide whether to reject or accept a particular product.” – Grant
Control Charts
Control charts is a statistical device i.e., used in controlling the manufacturing process and is a kind of a graphical chart used to decide presence of any unusual variation occurring in the process of production that put the process out of control.
A control chart has three horizontal lines starting from the right hand side of the vertical line (y-axis) and parallel to the base line (x-axis) of the chart. The vertical line is meant for showing the quality statistic of each sample and is known as quality scale. The base line is used for marking sample numbers and is termed as subgroup scale. The three horizontal lines –
i. Central Line
ii. Upper Control Limit
iii. Lower Control Limit – Are known as control lines.
If all the quality statistics of the given samples are spread between the upper control limit and lower control limit, then it can be concluded that manufacturing process is under control. If any of the quality statistics is outside the upper control limit or lower control limit, then it can be concluded that manufacturing process is not under control.
Types of Process Charts
Control charts may be grouped under two main heads:
A. Control chart for variable
i. Mean chart (x chart)
ii. Range chart R chart)
B. Control chart for attributes
i. Control chart for fraction defectives (‘P’ Chart)
ii. Control chart for number of defectives (‘np’ chart)
iii. Control chart for number of defects per unit (‘c’ chart)

Mean Chart:
Steps
i. Calculation of mean of each sample.
ii. Calculation of mean of the sample means.
iii. Computation of control limits
Control limits for X-bar chart: Control limits for R-chart:
UCLx-bar = X- double bar + A2R-bar
CLx-bar = X-double bar
LCLx-bar = X-double bar – A2R-bar

The value of A2 can be easily found from the table on the basis of the sample size
Range Chart:
Steps
i. Calculation of the range of each sample (R).
R = Highest value of the sample – Lowest value of the sample =H-L
ii. Calculation of the mean of the sample ranges (R).
iii. Computation of control limits.
UCLR = D4R-bar
CLR = R-bar
LCLR = D3R-bar
The values of D4 and D3 can be easily found from the table on the basis of the sample size

#Statistics #Math #SQC #StatisticalQualityControl #ControlChart #Variable #Mean #Range #FreeStudy #Problem #Solution

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