Question

1. Discuss the purposes and differences between the C- charts, p-charts and X-bar and R charts.

2. Define Cp and Cpk

3. The capability index allows for some drifting of the process mean. Discuss what this means in terms of product quality output.

Answer 1

(1) The P-charts and C- charts can be used to monitor proportions of a process as such the proportion of defect product in production..

P Charts can be used to display the fraction of outcomes of a process which may or may not obay some rules. The lower and upper control limits set in a way that the probability of a fraction falling out side this limit is quite low that is less than one percent.

The lower control limit may fall below zero making no sense in connection with fractions in such cases lower control limit is set to zero.

LCL= P bar - 3

P bar being the mean of n proportions considered

the band of tolerence +/ -3 (standard deviations of the disribution of proportins)

C chart is similar to the p chart , except in case of specil outcomes like (defects) of a process counted

a band of +/ -3 standard deviations of poission distribution.

X bar R charts are control charts utilized at process that have sub group sizes of two or more . These standardized charts for variables data help to determine if particular process is pridictable and stable. these are used when sub group size lies between two and ten

X - bar chart

Indicates average or mean changes over a time and used to monitor the process mean when calculating sub groups with regular intervals from a process. X - bar chart is combined with R chart to minitor process varibles.If the variable is not under the control , then the control limits might be too general. means the cause of variation that are affecting the process mean can not be pin pointed .

Y - bar chart

Indicates how the range of the sub groups changes over a time. this is used to mointor process variability .like the range when measuring sub groups less than tenat regular intervals in a process. The point on chart represents the sub group range value

The range statistic value is the center line for each sub group. The ceter line differs when sub group lines are not equal.

(2) Cp and Cpk commonly referred as process capability indicesand they are used to define the ability of a process that produce a product that meets requirements.These are recent addition to the statistical process mangement and simplfy the management of statasticlly controlled process.

Cp

The Cp index is caculated using specification limits and the standard deviation only, indicates in general whether the process is capable of producing products to specifictions.No information on the ability of process add here to the target value included in the index.

CpK index is calculated using specification limits , standerd diviation , and the mean . The index indicates whether the process is capble of producing with in specification ,and also an indicator of the ability of the process to addhere to the target specification.