Product Study Using Control Charts Assessment Answer

Introduction

A lathe is used to create a component that is a part of a power transmission unit. The inspector gathered information from twenty samples, each with five components, that were taken every half-hour. The course of the day is punctuated by a variety of (non-)technical mishaps. Among these include eating a meal and tweaking or restarting the machine.

It is determined that the process mean is 3.5 cm, and the mean sample range is 0.0007 cm.

Solution 1

Setting the process's control boundaries is the inspector's goal. As the process mean and mean range are provided in this case, the R Chart and X Bar chart are the optimal methods for creating control charts.

To verify the spread of the process over time, a R chart is first made. If the size of the subgroup is less than 10 or more, a S chart is next created. The next step is to generate the X Bar chart to check or monitor the mean if it appears that the variability in the R chart is under control.

It is given that the process mean follows normal distribution.

The formulas for the R Chart and X Bar chart are given as follows:

R Chart:

Upper Control Chart = D4 X R

Center line = R

Lower Control Limit = D3 X R           

X Bar Chart:

Upper Control Chart = X + A2 X R

Center line = X

Lower Control Limit = X - A2 X R

The inspector is currently gathering information from five components. Five subgroups are utilised as a result. The control chart table is used to determine the values for A2, D4, and D3.

The value corresponding to n = 5 the values are given as follows:

A2 = 0.577

D3 = 0

D4 = 2.114

Hence, the control limits are calculated as follows:

The calculations for R Chart are given as follows:

Upper control limits, UCL = 2.114 * 0.0007 = 0.0015

Center limit, = 0.0007

Lower Control Limit, LCL = 0

The calculations for X Bar Chart are given as follows:

Upper control limits, UCL = 3.5 + 0.577 * 0.0007 = 3.5004

Center limit, = 3.5

Lower Control Limit, LCL = 3.5 – 0.577 * 0.0007 = 3.4996

The control charts are constructed as follows:

Solution 2

Following are the specified tolerance limits:

3.498 Lower Specification Limit;

3.502 Higher Specification Limit

The term "voice of the customer" also applies to the specification restrictions. The buyer establishes his own parameters and does not let any product to exceed them. There must be changes made to the process if any limit exists that is outside the bounds of the requirements. To check the capability of the process that how well the process is going. Let’s find the capability process as follows:

CP = USL-LSL/6σ

Where is calculated from the data given.

Hence, from the data set the calculated sigma is 0.2341.

CP = 3.502-3.498/6*2341

Here, the process is not performing well as the Cp < 1.

Solution 3

The inspector now gathered the information for five shifts. To determine if the process is under control or not, we shall plot the numbers on the control chart.

The following are the calculations for the X Bar Chart:

For R chart:

For X Bar chart,

The points are plotted on the X Bar chart as follows:

The machine operates optimally throughout all sessions, including those in the morning, following tool clamp adjustment, lunch, and tool resent by 0.15 c, however it struggles to operate optimally following tool resent.

The data gathered for the entire day are completely unrelated to the observations made.

Also, because to the wide range of values in the data set, such information is not taken into account when creating the control chart.

Conclusion

According to the charts, the average points fall between the top and lower bounds. By selecting values parallel to the x-axis, these points are plotted. The average range and average values for both control charts are displayed on the blue line. When a series of five or more consecutive data points fall into the same pattern, for example, we might conclude that a pattern has been observed. Hence, the existence of a pattern is a sign of volatility.

The data values show no discernible trend, and the values for both charts fall within the bottom and higher control ranges. Hence, there is no evidence that the process is operating outside of or below the specified bounds. Thus, we may conclude that the procedure is effective when carrying out various machine tasks.

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