A Company Operates Four Machines During Three Shifts Each Da

A company operates four machines during three shifts each day

A company operates four machines during three shifts each day. From production records, data on machine breakdowns across these shifts were collected. To determine if there is a relationship between the number of breakdowns and the shift, a hypothesis test at the 0.05 significance level is performed to examine the independence between the number of breakdowns and the shift. The test statistic value obtained is 11.649, and the critical value at this significance level is 12.592. Based on this information, the appropriate conclusion is that the evidence indicates the number of breakdowns is independent of the shift because the test value is less than the critical value.

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The analysis of machine breakdowns in manufacturing facilities is essential for optimizing productivity, scheduling maintenance, and reducing downtime. A critical question in industrial engineering and operations management is whether the occurrence of machine breakdowns is independent of operational shifts. If breakdowns are dependent on shifts, targeted interventions might be necessary to address shift-specific issues. Conversely, if breakdowns are independent, a uniform maintenance strategy across all shifts may suffice.

In this context, a statistical hypothesis test was conducted to evaluate the independence between the number of machine breakdowns and the shift during which they occur. The null hypothesis (H0) states that breakdowns are independent of shifts, whereas the alternative hypothesis (Ha) suggests dependence. The test statistic, based on a chi-square test for independence, was calculated to be 11.649. The chi-square distribution's critical value at a 0.05 significance level with the appropriate degrees of freedom is 12.592 (Chi-square table). Since the computed test statistic is less than the critical value, it implies that there is not enough evidence to reject the null hypothesis.

This outcome indicates that the variations in breakdowns across different shifts could be due to random chance rather than any systematic shift-related factors. Therefore, the management may decide that shift-based changes or additional investigations might not be necessary solely based on this data. They can therefore proceed with current maintenance schedules, knowing that there is no statistically significant dependence between shift and breakdown frequency.

Implementing such statistical tests ensures that management decisions are data-driven. Recognizing whether breakdowns depend on shifts helps allocate resources effectively and plan maintenance activities more accurately. If further data or more detailed analysis suggest dependence, targeted interventions can then be designed to improve the overall efficiency of operations. This process exemplifies the importance of hypothesis testing in industrial settings, establishing empirical evidence for operational strategies.

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