please i need a complete step by step answer this is related

please i need a complete step by step answer

this is related to quality control engineering

Q :-1

A control chart is used to control a process by counting the number of defects discovered per engine assembly.each engine essembly has the same number of opportunities for defects.and the control chart is designed to control the defects per essemblyat an average of nine.caluclate the 2.5 sigma control limites of this chart.

Solution

Basic Information

The control chart is a graph used to study how a process changes over time/Space/location/sample, etc. The scope of chart is not limited to quality engineering. It is widely used in social science to Medical Science. The obvious question is what it controls or how it checks a process. Take an example of any process, e.g. blood sugar level. Doctors have specified a lower limit and upper limit for a healthy person. Because it varies from person to person and it depends upon several factors. But if it crosses the lower limit or upper limit , we suspect for any severe metabolic change in the factors that impact blood sugar.

Similarly, in a manufacturing process, the production depends upon several factors like raw material, operator, machine(s) and many more things. So there is a chance for production of a defective item caused by any one of the factors responsible for production. In a control chart for defective items we find three parameters:

Central Line (CL)

The average no. of defectives can be can be produced, if all the factors are to be in normal condition

UCL (Upper control Limit)

The Max. No. of defective products can be produced. The UCL is calculated by adding multiple times of standard deviation with the average (CL)

LCL (Lower Control Limit)

The minimum no. of defective products can be produced.. The LCL is calculated by Subtracting multiple times of standard deviation from the average (CL). (Generally it becomes negative , hence assumed to be ‘0’ )

Step -1

The control charts are of many types. Your question is problem of c- chart. C- chart is used when we can only classify the product as a defective or not, i.e. in a sample of manufactured products we can find the no. of defective products and non-defective products.

Step – 2:

In c chart, no. of defective products follows Poisson distribution. Poisson distribution is a statistical rule to calculate the chance of producing ‘x’ no. of defective products. In Poisson distribution the Mean = c (Average no. of defective products) and standard deviation = Sqrt (C)

Step 3 :

In c chart:

CL (Central Line) = c = 9 (Average no. of defective products)

2.5 sigma UCL (Upper Control Limit) = c + 2.5 * Square root(c). = 9+ 2.5*3 = 16.5

2.5 sigma LCL (Lower Control Limit) = c - 2.5 * Square root(c) = 9 - 2.5*3 = 1.5

Step – 4 :

If the no. of defectives does not lie within the limits then a shift in the process is to be suspected. By checking the pattern of changes in the no. of defectives due care has to be taken in correcting the process.